the precession of mercury’s perihelion - daniel · pdf filethe precession of...
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![Page 1: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/1.jpg)
The Precession of Mercury’s PerihelionWhere Newton failed and Einstein succeeded.
Dan Wysocki
SUNY Oswego
QUEST 2014
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 1 / 24
![Page 2: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/2.jpg)
Introduction
throughout human history, many explanations have been put forth to explainthe motions of the stars and planets, with varying degrees of success
many models were accurate during the lifespan of the people who createdthem, but over long periods of time began to lose accuracy
eventually a new model comes along which takes its place, until yet anothermodel replaces that one
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 2 / 24
![Page 3: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/3.jpg)
Introduction
throughout human history, many explanations have been put forth to explainthe motions of the stars and planets, with varying degrees of success
many models were accurate during the lifespan of the people who createdthem, but over long periods of time began to lose accuracy
eventually a new model comes along which takes its place, until yet anothermodel replaces that one
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 2 / 24
![Page 4: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/4.jpg)
Introduction
throughout human history, many explanations have been put forth to explainthe motions of the stars and planets, with varying degrees of success
many models were accurate during the lifespan of the people who createdthem, but over long periods of time began to lose accuracy
eventually a new model comes along which takes its place, until yet anothermodel replaces that one
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 2 / 24
![Page 5: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/5.jpg)
Geocentric Model of the Universe
most ancient view of the Universe
Earth is located at the center of the Universe
all stars and planets move about the Earth
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 3 / 24
![Page 6: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/6.jpg)
Geocentric Model of the Universe
most ancient view of the Universe
Earth is located at the center of the Universe
all stars and planets move about the Earth
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 3 / 24
![Page 7: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/7.jpg)
Geocentric Model of the Universe
most ancient view of the Universe
Earth is located at the center of the Universe
all stars and planets move about the Earth
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 3 / 24
![Page 8: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/8.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon, Mercury, Venus, Mars,Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 9: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/9.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon, Mercury, Venus, Mars,Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 10: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/10.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun,
the Moon, Mercury, Venus, Mars,Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 11: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/11.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon,
Mercury, Venus, Mars,Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 12: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/12.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon, Mercury,
Venus, Mars,Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 13: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/13.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon, Mercury, Venus,
Mars,Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 14: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/14.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon, Mercury, Venus, Mars,
Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 15: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/15.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon, Mercury, Venus, Mars,Jupiter,
and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 16: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/16.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon, Mercury, Venus, Mars,Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 17: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/17.jpg)
Celestial Sphere and Planets
stars lie on a great sphere which encirclesthe Earth, and rotates once per day
the obvious exceptions to this rule are the 7classical “planets”, or “wanderers”
the Sun, the Moon, Mercury, Venus, Mars,Jupiter, and Saturn
these planets were thought to circle theEarth in their own paths, presumably closerto Earth than the sphere
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 4 / 24
![Page 18: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/18.jpg)
Retrograde Motion of the Planets
the planets’ orbital paths appear to makesmall loops in their otherwise circular orbits
difficult to explain this in a geocentric model
most explanations involved “epicycles”
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 5 / 24
![Page 19: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/19.jpg)
Retrograde Motion of the Planets
the planets’ orbital paths appear to makesmall loops in their otherwise circular orbits
difficult to explain this in a geocentric model
most explanations involved “epicycles”
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 5 / 24
![Page 20: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/20.jpg)
Retrograde Motion of the Planets
the planets’ orbital paths appear to makesmall loops in their otherwise circular orbits
difficult to explain this in a geocentric model
most explanations involved “epicycles”
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 5 / 24
![Page 21: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/21.jpg)
Epicycles
planets were thought to have a secondaryorbit about their main orbit
if tuned just right, these could predict themotions of the planets for years
slowly they would go out of sync withobservations
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 6 / 24
![Page 22: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/22.jpg)
Epicycles
planets were thought to have a secondaryorbit about their main orbit
if tuned just right, these could predict themotions of the planets for years
slowly they would go out of sync withobservations
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 6 / 24
![Page 23: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/23.jpg)
Epicycles
planets were thought to have a secondaryorbit about their main orbit
if tuned just right, these could predict themotions of the planets for years
slowly they would go out of sync withobservations
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 6 / 24
![Page 24: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/24.jpg)
Geocentric Complexity
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 7 / 24
![Page 25: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/25.jpg)
Geocentric Complexity
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 7 / 24
![Page 26: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/26.jpg)
Proper Motion
Edmund Halley discovered in 1717 whencomparing his star maps to those ofTimocharis and Aristyllus (300 B.C.E.) andHipparchus (150 B.C.E.), and noticed thatthe stars’ positions had changed since then
all of the stars as a whole had advanced 25◦
in longitude
apart from that, the stars had all drifted inseemingly random directions and speeds
some of the brighter stars had drifted byalmost an entire degree
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 8 / 24
![Page 27: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/27.jpg)
Proper Motion
Edmund Halley discovered in 1717 whencomparing his star maps to those ofTimocharis and Aristyllus (300 B.C.E.) andHipparchus (150 B.C.E.), and noticed thatthe stars’ positions had changed since then
all of the stars as a whole had advanced 25◦
in longitude
apart from that, the stars had all drifted inseemingly random directions and speeds
some of the brighter stars had drifted byalmost an entire degree
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 8 / 24
![Page 28: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/28.jpg)
Proper Motion
Edmund Halley discovered in 1717 whencomparing his star maps to those ofTimocharis and Aristyllus (300 B.C.E.) andHipparchus (150 B.C.E.), and noticed thatthe stars’ positions had changed since then
all of the stars as a whole had advanced 25◦
in longitude
apart from that, the stars had all drifted inseemingly random directions and speeds
some of the brighter stars had drifted byalmost an entire degree
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 8 / 24
![Page 29: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/29.jpg)
Proper Motion
Edmund Halley discovered in 1717 whencomparing his star maps to those ofTimocharis and Aristyllus (300 B.C.E.) andHipparchus (150 B.C.E.), and noticed thatthe stars’ positions had changed since then
all of the stars as a whole had advanced 25◦
in longitude
apart from that, the stars had all drifted inseemingly random directions and speeds
some of the brighter stars had drifted byalmost an entire degree
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 8 / 24
![Page 30: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/30.jpg)
Copernican Revolution
in 1543, Nicolaus Copernicus published thefirst model of the Solar system whichaccurately put the Sun at the center, withthe planets (including Earth) orbiting it
not a perfect model, but was able tosimplify the motions of the planets
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 9 / 24
![Page 31: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/31.jpg)
Copernican Revolution
in 1543, Nicolaus Copernicus published thefirst model of the Solar system whichaccurately put the Sun at the center, withthe planets (including Earth) orbiting it
not a perfect model, but was able tosimplify the motions of the planets
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 9 / 24
![Page 32: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/32.jpg)
Copernican Retrograde Motion
explains the retrograde motion without anyepicycles
the motion is only apparent
same effect as passing a car on the highway
both cars are moving forward, but theslower car appears to be moving backwards
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 10 / 24
![Page 33: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/33.jpg)
Copernican Retrograde Motion
explains the retrograde motion without anyepicycles
the motion is only apparent
same effect as passing a car on the highway
both cars are moving forward, but theslower car appears to be moving backwards
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 10 / 24
![Page 34: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/34.jpg)
Copernican Retrograde Motion
explains the retrograde motion without anyepicycles
the motion is only apparent
same effect as passing a car on the highway
both cars are moving forward, but theslower car appears to be moving backwards
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 10 / 24
![Page 35: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/35.jpg)
Copernican Retrograde Motion
explains the retrograde motion without anyepicycles
the motion is only apparent
same effect as passing a car on the highway
both cars are moving forward, but theslower car appears to be moving backwards
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 10 / 24
![Page 36: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/36.jpg)
Kepler’s Laws
first elegant, mathematical, and highlyaccurate model of the Solar system
corrects Copernicus’ false assumption thatorbits are circular, when they are in factelliptical
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 11 / 24
![Page 37: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/37.jpg)
Kepler’s Laws
first elegant, mathematical, and highlyaccurate model of the Solar system
corrects Copernicus’ false assumption thatorbits are circular, when they are in factelliptical
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 11 / 24
![Page 38: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/38.jpg)
Kepler’s First Law
orbits are elliptical
r – a planet’s distance from the Sun
r0 – distance of closest approach to the Sun, or “perihelion”
φ – angle travelled from perihelion (φ = 0 at the perihelion)
ε – eccentricity of the orbit
r = r01 + ε
1 + ε cosφ(1)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 12 / 24
![Page 39: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/39.jpg)
Kepler’s First Law
orbits are elliptical
r – a planet’s distance from the Sun
r0 – distance of closest approach to the Sun, or “perihelion”
φ – angle travelled from perihelion (φ = 0 at the perihelion)
ε – eccentricity of the orbit
r = r01 + ε
1 + ε cosφ(1)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 12 / 24
![Page 40: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/40.jpg)
Kepler’s First Law
orbits are elliptical
r – a planet’s distance from the Sun
r0 – distance of closest approach to the Sun, or “perihelion”
φ – angle travelled from perihelion (φ = 0 at the perihelion)
ε – eccentricity of the orbit
r = r01 + ε
1 + ε cosφ(1)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 12 / 24
![Page 41: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/41.jpg)
Kepler’s First Law
orbits are elliptical
r – a planet’s distance from the Sun
r0 – distance of closest approach to the Sun, or “perihelion”
φ – angle travelled from perihelion (φ = 0 at the perihelion)
ε – eccentricity of the orbit
r = r01 + ε
1 + ε cosφ(1)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 12 / 24
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Kepler’s First Law
orbits are elliptical
r – a planet’s distance from the Sun
r0 – distance of closest approach to the Sun, or “perihelion”
φ – angle travelled from perihelion (φ = 0 at the perihelion)
ε – eccentricity of the orbit
r = r01 + ε
1 + ε cosφ(1)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 12 / 24
![Page 43: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/43.jpg)
Kepler’s First Law
orbits are elliptical
r – a planet’s distance from the Sun
r0 – distance of closest approach to the Sun, or “perihelion”
φ – angle travelled from perihelion (φ = 0 at the perihelion)
ε – eccentricity of the orbit
r = r01 + ε
1 + ε cosφ(1)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 12 / 24
![Page 44: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/44.jpg)
Kepler’s Second and Third Laws
Kepler’s second law
orbit sweeps out equal areas in equal times
A – rate at which area is swept out
dA
d t= c (2)
Kepler’s third law
P – orbital perioda – semi-major axis
P 2
a3= c (3)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 13 / 24
![Page 45: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/45.jpg)
Kepler’s Second and Third Laws
Kepler’s second law
orbit sweeps out equal areas in equal timesA – rate at which area is swept out
dA
d t= c (2)
Kepler’s third law
P – orbital perioda – semi-major axis
P 2
a3= c (3)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 13 / 24
![Page 46: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/46.jpg)
Kepler’s Second and Third Laws
Kepler’s second law
orbit sweeps out equal areas in equal timesA – rate at which area is swept out
dA
d t= c (2)
Kepler’s third law
P – orbital perioda – semi-major axis
P 2
a3= c (3)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 13 / 24
![Page 47: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/47.jpg)
Kepler’s Second and Third Laws
Kepler’s second law
orbit sweeps out equal areas in equal timesA – rate at which area is swept out
dA
d t= c (2)
Kepler’s third law
P – orbital period
a – semi-major axis
P 2
a3= c (3)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 13 / 24
![Page 48: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/48.jpg)
Kepler’s Second and Third Laws
Kepler’s second law
orbit sweeps out equal areas in equal timesA – rate at which area is swept out
dA
d t= c (2)
Kepler’s third law
P – orbital perioda – semi-major axis
P 2
a3= c (3)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 13 / 24
![Page 49: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/49.jpg)
Kepler’s Second and Third Laws
Kepler’s second law
orbit sweeps out equal areas in equal timesA – rate at which area is swept out
dA
d t= c (2)
Kepler’s third law
P – orbital perioda – semi-major axis
P 2
a3= c (3)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 13 / 24
![Page 50: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/50.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 51: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/51.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 52: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/52.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 53: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/53.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 54: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/54.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 55: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/55.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 56: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/56.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 57: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/57.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 58: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/58.jpg)
Newtonian Gravity
Sir Isaac Newton (1642 – 1727)
for the first time in history, a physical explanation of the planets’ motions wasfound
F – force of gravity
m – mass of the orbiting object
M – mass of the object being orbited
r – distance between the two objects
r̂ – vector pointing from the first object to the second
G – universal gravitational constant
F = GmM
r2r̂ (4)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 14 / 24
![Page 59: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/59.jpg)
Deriving Kepler’s Laws
Newton was able to derive all of Kepler’s laws of planetary orbits, using hislaw of gravity along with his three laws of motion
orbits should be elliptical
solved for the constant in Kepler’s second law
h – ratio of planet’s angular momentum to its mass
dA
d t=h
2(5)
solved for the constant in Kepler’s third law
P 2
a3=
4π2
GM(6)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 15 / 24
![Page 60: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/60.jpg)
Deriving Kepler’s Laws
Newton was able to derive all of Kepler’s laws of planetary orbits, using hislaw of gravity along with his three laws of motion
orbits should be elliptical
solved for the constant in Kepler’s second law
h – ratio of planet’s angular momentum to its mass
dA
d t=h
2(5)
solved for the constant in Kepler’s third law
P 2
a3=
4π2
GM(6)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 15 / 24
![Page 61: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/61.jpg)
Deriving Kepler’s Laws
Newton was able to derive all of Kepler’s laws of planetary orbits, using hislaw of gravity along with his three laws of motion
orbits should be elliptical
solved for the constant in Kepler’s second law
h – ratio of planet’s angular momentum to its mass
dA
d t=h
2(5)
solved for the constant in Kepler’s third law
P 2
a3=
4π2
GM(6)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 15 / 24
![Page 62: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/62.jpg)
Deriving Kepler’s Laws
Newton was able to derive all of Kepler’s laws of planetary orbits, using hislaw of gravity along with his three laws of motion
orbits should be elliptical
solved for the constant in Kepler’s second law
h – ratio of planet’s angular momentum to its mass
dA
d t=h
2(5)
solved for the constant in Kepler’s third law
P 2
a3=
4π2
GM(6)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 15 / 24
![Page 63: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/63.jpg)
Deriving Kepler’s Laws
Newton was able to derive all of Kepler’s laws of planetary orbits, using hislaw of gravity along with his three laws of motion
orbits should be elliptical
solved for the constant in Kepler’s second law
h – ratio of planet’s angular momentum to its mass
dA
d t=h
2(5)
solved for the constant in Kepler’s third law
P 2
a3=
4π2
GM(6)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 15 / 24
![Page 64: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/64.jpg)
Deriving Kepler’s Laws
Newton was able to derive all of Kepler’s laws of planetary orbits, using hislaw of gravity along with his three laws of motion
orbits should be elliptical
solved for the constant in Kepler’s second law
h – ratio of planet’s angular momentum to its mass
dA
d t=h
2(5)
solved for the constant in Kepler’s third law
P 2
a3=
4π2
GM(6)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 15 / 24
![Page 65: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/65.jpg)
Deriving Kepler’s Laws
Newton was able to derive all of Kepler’s laws of planetary orbits, using hislaw of gravity along with his three laws of motion
orbits should be elliptical
solved for the constant in Kepler’s second law
h – ratio of planet’s angular momentum to its mass
dA
d t=h
2(5)
solved for the constant in Kepler’s third law
P 2
a3=
4π2
GM(6)
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 15 / 24
![Page 66: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/66.jpg)
Orbital Precession
in a two-body system, a planet’s orbitrepeats the same way forever
in the presence of other planets, a planet’sorbit rotates slowly over time
this is due to the gravitational force thatthey all exert on each othern
Newton’s law of gravity predicts this, whileKepler’s laws do not
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 16 / 24
![Page 67: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/67.jpg)
Orbital Precession
in a two-body system, a planet’s orbitrepeats the same way forever
in the presence of other planets, a planet’sorbit rotates slowly over time
this is due to the gravitational force thatthey all exert on each othern
Newton’s law of gravity predicts this, whileKepler’s laws do not
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 16 / 24
![Page 68: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/68.jpg)
Orbital Precession
in a two-body system, a planet’s orbitrepeats the same way forever
in the presence of other planets, a planet’sorbit rotates slowly over time
this is due to the gravitational force thatthey all exert on each othern
Newton’s law of gravity predicts this, whileKepler’s laws do not
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 16 / 24
![Page 69: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/69.jpg)
Orbital Precession
in a two-body system, a planet’s orbitrepeats the same way forever
in the presence of other planets, a planet’sorbit rotates slowly over time
this is due to the gravitational force thatthey all exert on each othern
Newton’s law of gravity predicts this, whileKepler’s laws do not
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 16 / 24
![Page 70: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/70.jpg)
Newtonian Precession Predictions
Planet (δψ̇)obs (δψ̇)thMercury 575.19′′ 532.08′′
Venus 21.6′′ 13.2′′
Earth 1170′′ 1165′′
Table: Precession rates in arc-seconds percentury
Newton’s laws do a good jobapproximating the rate of precessionfor all the planets except Mercury
error for the other planets can beexplained by imprecision ofmeasurements, but Mercury’s is toolarge
mystery puzzled physicists for manyyears
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 17 / 24
![Page 71: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/71.jpg)
Newtonian Precession Predictions
Planet (δψ̇)obs (δψ̇)thMercury 575.19′′ 532.08′′
Venus 21.6′′ 13.2′′
Earth 1170′′ 1165′′
Table: Precession rates in arc-seconds percentury
Newton’s laws do a good jobapproximating the rate of precessionfor all the planets except Mercury
error for the other planets can beexplained by imprecision ofmeasurements, but Mercury’s is toolarge
mystery puzzled physicists for manyyears
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 17 / 24
![Page 72: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/72.jpg)
Newtonian Precession Predictions
Planet (δψ̇)obs (δψ̇)thMercury 575.19′′ 532.08′′
Venus 21.6′′ 13.2′′
Earth 1170′′ 1165′′
Table: Precession rates in arc-seconds percentury
Newton’s laws do a good jobapproximating the rate of precessionfor all the planets except Mercury
error for the other planets can beexplained by imprecision ofmeasurements, but Mercury’s is toolarge
mystery puzzled physicists for manyyears
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 17 / 24
![Page 73: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/73.jpg)
Corrections to Newtonian Gravity
attempts were made to modify Newton’s gravity to make it match the data
these modifications could not be justified physically
much like the epicycles added to the geocentric model, these complicated apreviously simple model, without justification
Urbain Le Verrier (1811 – 1877) predicted the existance of Neptune by theprecession of Uranus, so he hypothesized another planet, named Vulcan,existed between the Sun and Mercury
no such planet has ever been found
a new explanation was in order
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 18 / 24
![Page 74: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/74.jpg)
Corrections to Newtonian Gravity
attempts were made to modify Newton’s gravity to make it match the data
these modifications could not be justified physically
much like the epicycles added to the geocentric model, these complicated apreviously simple model, without justification
Urbain Le Verrier (1811 – 1877) predicted the existance of Neptune by theprecession of Uranus, so he hypothesized another planet, named Vulcan,existed between the Sun and Mercury
no such planet has ever been found
a new explanation was in order
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 18 / 24
![Page 75: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/75.jpg)
Corrections to Newtonian Gravity
attempts were made to modify Newton’s gravity to make it match the data
these modifications could not be justified physically
much like the epicycles added to the geocentric model, these complicated apreviously simple model, without justification
Urbain Le Verrier (1811 – 1877) predicted the existance of Neptune by theprecession of Uranus, so he hypothesized another planet, named Vulcan,existed between the Sun and Mercury
no such planet has ever been found
a new explanation was in order
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 18 / 24
![Page 76: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/76.jpg)
Corrections to Newtonian Gravity
attempts were made to modify Newton’s gravity to make it match the data
these modifications could not be justified physically
much like the epicycles added to the geocentric model, these complicated apreviously simple model, without justification
Urbain Le Verrier (1811 – 1877) predicted the existance of Neptune by theprecession of Uranus, so he hypothesized another planet, named Vulcan,existed between the Sun and Mercury
no such planet has ever been found
a new explanation was in order
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 18 / 24
![Page 77: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/77.jpg)
Corrections to Newtonian Gravity
attempts were made to modify Newton’s gravity to make it match the data
these modifications could not be justified physically
much like the epicycles added to the geocentric model, these complicated apreviously simple model, without justification
Urbain Le Verrier (1811 – 1877) predicted the existance of Neptune by theprecession of Uranus, so he hypothesized another planet, named Vulcan,existed between the Sun and Mercury
no such planet has ever been found
a new explanation was in order
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 18 / 24
![Page 78: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/78.jpg)
Corrections to Newtonian Gravity
attempts were made to modify Newton’s gravity to make it match the data
these modifications could not be justified physically
much like the epicycles added to the geocentric model, these complicated apreviously simple model, without justification
Urbain Le Verrier (1811 – 1877) predicted the existance of Neptune by theprecession of Uranus, so he hypothesized another planet, named Vulcan,existed between the Sun and Mercury
no such planet has ever been found
a new explanation was in order
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 18 / 24
![Page 79: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/79.jpg)
General Relativity
Einstein formulated his general theory ofrelativity in 1916
rejected the notion that gravity was a force
spacetime itself is bent in the presence ofmass
the planets aren’t travelling in a curved patharound the Sun, the space around the Sun isitself curved
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 19 / 24
![Page 80: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/80.jpg)
General Relativity
Einstein formulated his general theory ofrelativity in 1916
rejected the notion that gravity was a force
spacetime itself is bent in the presence ofmass
the planets aren’t travelling in a curved patharound the Sun, the space around the Sun isitself curved
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 19 / 24
![Page 81: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/81.jpg)
General Relativity
Einstein formulated his general theory ofrelativity in 1916
rejected the notion that gravity was a force
spacetime itself is bent in the presence ofmass
the planets aren’t travelling in a curved patharound the Sun, the space around the Sun isitself curved
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 19 / 24
![Page 82: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/82.jpg)
General Relativity
Einstein formulated his general theory ofrelativity in 1916
rejected the notion that gravity was a force
spacetime itself is bent in the presence ofmass
the planets aren’t travelling in a curved patharound the Sun, the space around the Sun isitself curved
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 19 / 24
![Page 83: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/83.jpg)
General Relativity Precession Calculations
using general relativity, we can adapt Newton’s law of gravity to be moreprecise
F =
[G
Mm
r2+ 3G
Mmh2
c2 r4
]r̂ (7)
using this modified equation adds an extra 41′′ of precession per century toMercury’s orbit
this is exactly the amount that was missing from Newtonian predictions
this was one of the first things that Einstein calculated to test his theory out
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 20 / 24
![Page 84: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/84.jpg)
General Relativity Precession Calculations
using general relativity, we can adapt Newton’s law of gravity to be moreprecise
F =
[G
Mm
r2+ 3G
Mmh2
c2 r4
]r̂ (7)
using this modified equation adds an extra 41′′ of precession per century toMercury’s orbit
this is exactly the amount that was missing from Newtonian predictions
this was one of the first things that Einstein calculated to test his theory out
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 20 / 24
![Page 85: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/85.jpg)
General Relativity Precession Calculations
using general relativity, we can adapt Newton’s law of gravity to be moreprecise
F =
[G
Mm
r2+ 3G
Mmh2
c2 r4
]r̂ (7)
using this modified equation adds an extra 41′′ of precession per century toMercury’s orbit
this is exactly the amount that was missing from Newtonian predictions
this was one of the first things that Einstein calculated to test his theory out
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 20 / 24
![Page 86: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/86.jpg)
General Relativity Precession Calculations
using general relativity, we can adapt Newton’s law of gravity to be moreprecise
F =
[G
Mm
r2+ 3G
Mmh2
c2 r4
]r̂ (7)
using this modified equation adds an extra 41′′ of precession per century toMercury’s orbit
this is exactly the amount that was missing from Newtonian predictions
this was one of the first things that Einstein calculated to test his theory out
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 20 / 24
![Page 87: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/87.jpg)
General Relativity Precession Calculations
using general relativity, we can adapt Newton’s law of gravity to be moreprecise
F =
[G
Mm
r2+ 3G
Mmh2
c2 r4
]r̂ (7)
using this modified equation adds an extra 41′′ of precession per century toMercury’s orbit
this is exactly the amount that was missing from Newtonian predictions
this was one of the first things that Einstein calculated to test his theory out
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 20 / 24
![Page 88: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/88.jpg)
Conclusions
every model of the Universe (so far) has its flaws
given enough time, those flaws will become apparent
attempts to adapt the model to account for its flaws can have some success,but ultimately are a sign that a new model is needed
sometimes a completely new approach is needed to be successful
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 21 / 24
![Page 89: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/89.jpg)
Conclusions
every model of the Universe (so far) has its flaws
given enough time, those flaws will become apparent
attempts to adapt the model to account for its flaws can have some success,but ultimately are a sign that a new model is needed
sometimes a completely new approach is needed to be successful
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 21 / 24
![Page 90: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/90.jpg)
Conclusions
every model of the Universe (so far) has its flaws
given enough time, those flaws will become apparent
attempts to adapt the model to account for its flaws can have some success,but ultimately are a sign that a new model is needed
sometimes a completely new approach is needed to be successful
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 21 / 24
![Page 91: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/91.jpg)
Conclusions
every model of the Universe (so far) has its flaws
given enough time, those flaws will become apparent
attempts to adapt the model to account for its flaws can have some success,but ultimately are a sign that a new model is needed
sometimes a completely new approach is needed to be successful
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 21 / 24
![Page 92: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/92.jpg)
References I
url: http://www.spaceanswers.com/wp-content/uploads/2013/01/Celestial-sphere-illus.jpg.url: http://www.astronomy.ohio-state.edu/~pogge/Ast162/Movies/uma.gif.url: https://lh3.ggpht.com/-
cgMuSQK8oEg/TqnJBliUhxI/AAAAAAAAANk/yRe1t5WUbzo/s1600/old+geocentric+model.jpg.url: http://www.lasalle.edu/~smithsc/Astronomy/images/marsmovie.gif.url: http://faculty.fullerton.edu/cmcconnell/Models/ptolemy.gif.url: https://upload.wikimedia.org/wikipedia/commons/0/0e/Cassini_apparent.jpg.url: https://upload.wikimedia.org/wikipedia/commons/2/28/Copernican_heliocentrism_diagram-
2.jpg.url: http://faculty.fullerton.edu/cmcconnell/Models/Copernicus_Mars.gif.url: https://upload.wikimedia.org/wikipedia/commons/f/f7/An_image_describing_the_semi-
major_and_semi-minor_axis_of_eclipse.png.url: https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Kepler-first-law.svg/500px-
Kepler-first-law.svg.png.url: https://upload.wikimedia.org/wikipedia/commons/6/69/Kepler-second-law.gif.url: https://upload.wikimedia.org/wikipedia/commons/8/89/Precessing_Kepler_orbit_280frames_
e0.6_smaller.gif.url: http://www.science4all.org/wp-content/uploads/2013/05/Gravity.jpg.Carroll, Bradley W. and Dale A. Ostlie. An Introduction to Modern Astrophysics. 2nd ed. Pearson Education,
Inc., 2007.
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 22 / 24
![Page 93: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/93.jpg)
References II
Fitzpatrick, Richard. Classical Mechanics: an introductory course. 2006. url: http://web.archive.bibalex.org/web/20060523200517/farside.ph.utexas.edu/teaching/301/lectures/node155.html.
— .Newtonian Dynamics. 2011. url: http://farside.ph.utexas.edu/teaching/336k/lectures/.Gerber’s Gravity. url: http://www.mathpages.com/home/kmath527/kmath527.htm.Halley, Edmund. “Considerations on the Change of the Latitudes of Some of the Principal Fixt Stars”. In:
Philosophical Transactions of the Royal Society 30 (1717).Roseveare, N. T. “Mercury’s Perihelion from Le Verrier to Einstein”. In: The British Journal for the
Philosophy of Science 35 (2), pp. 188–191.The Precession of the Perihelion of Mercury. url:
http://www.relativity.li/en/epstein2/read/i0_en/i1_en/.
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 23 / 24
![Page 94: The Precession of Mercury’s Perihelion - Daniel · PDF fileThe Precession of Mercury’s Perihelion ... Retrograde Motion of the Planets ... small loops in their otherwise circular](https://reader030.vdocuments.us/reader030/viewer/2022021504/5aa2aa6c7f8b9a436d8d40b6/html5/thumbnails/94.jpg)
Questions?
Dan Wysocki (SUNY Oswego) Mercury Precession QUEST 2014 24 / 24