Gravitation

History of the Heavens

What’s the oldest science? Why?

Common measures of time are astronomical in origin.

What can be seen in the sky without a telescope?

How was time measured?Year

  Month  Week  Day

Astrology

Astronomy is NOT Astrology

“The fault, dear Brutus, is not in the stars…”

Astrology is BEST described as a complex web of SUPERSTITIOUS beliefs. It has no basis in fact.

Planetary Models

GeocentricThe theory which stated that the Earth was the center of the solar system, believed to be an accurate description of the solar system until the 17th century.

Heliocentric The true model of the solar system in which the Sun is the center around which the planets orbit.

Geocentric Theorist

Greeks - 340 BCRecognized the sky is 3-dimensional.

Understood that the earth was a sphere.• Shadow of Earth on Moon during a lunar eclipse. • The North Star Polaris is higher in the sky as one goes north. • A ship’s sail comes over the horizon first and only later its hull.

Four earthly and one heavenly element.• Earth, Air, Fire, Water, Quintessence

Universe composed of concentric celestial spheres

Geocentric Theorist

AssumptionsEarth is immovable.

Earth at the center of the celestial sphere.

All other celestial bodies:• move with uniform

speed.• in pure circular

motion.• are perfect and

unchangeable

Geocentric Theorist

ProblemsRetrograde Motion The apparent backward motion of a planet when it appears, as observed from Earth, to reverse its natural direction of travel and move backwards across the sky.

Transient Phenomena • Comets• Meteors• Supernova

Geocentric Theorist

Ptolemy of Alexandria 150 C.E. Wrote “Almagest”, the first authoritative compilation of Western astronomy.Introduced a sophisticated geocentric model to account for retrograde motion of the planets.Epicycles and Deferents

Geocentric Theorist

Problems An approximation, errors accumulate over time.

Arguments for Ptolemaic System • Can you feel the Earth’s motion?• Stellar parallax not observed.• Church supports a geocentric model.• Worked for 1500 years (not overly cumbersome).

Heliocentric Theorist

Nicolaus Copernicus – 1543 C.E. Wrote “De Revolutionibus Orbium Coelestium”, the first heliocentric model in 2000 years (Aristarchus 310 – 230 BC).

Died just as theory was published.

Less accurate than Ptolemaic system. (conceptually simpler but more complicated)

Work was not condemned by the Church. Why?The book’s introduction present the author’s writing as an amusing work not to be taken seriously.

Heliocentric Theorist

Assumptions • Kept circular orbits, uniform motion• Sun is the center of the solar system.• The planets and earth move around the sun.• Earth spins on its axis.

Predictions• Planetary distances were fixed and easily calculated.• Understood variations in planetary speed, brightness, direction of motion (retrograde motion).

Heliocentric Theorist

Problems• What keep the planets and earth moving?• Why should things still fall to the earth?• Why don’t objects fly off rotating earth?• Why no parallax of stars?

Heliocentric Theorist (Geo-Helio)

Tycho Brahe – 1546 –1601 • Collect astronomical

data without the use of a telescope.

• Proposed a Compromise Model.

• Hired Johannes Kepler to analysis data.

Astrolabe Sextant Quadrant

Heliocentric Theorist

Galileo Galilei – 1564-1642 • Based knowledge of nature on observation and

experiment.• Expressed laws mathematically.• Observational evidence for a heliocentric model:

• Phases of Venus.• Satellites of Jupiter.• Sun Spots• Moon’s Craters

• Catholic church’s opposition to a heliocentric model (pardoned in 1992).

Io, Europa, Ganymede, Callisto

2004

Heliocentric Theorist

Johannes Kepler – 1571 - 1630 • A strong believer in the Copernican theory.• Work simultaneously on the orbit of Earth and

Mars using Brahe’s data.• Show first part of Kepler’s Law video.

Kepler’s Laws Pre Lab

• Plot the first of each month on earth’s orbit.• The earth orbits counterclockwise about the

sun.• Let all months equal 30 days; therefore, each

month equals 30 degrees. • Triangulate the position of Mars using paired

readings A-B, C-D, E-F, G-H, I-J, K-L, M-N, O-P.

Kepler’s Laws Pre Lab

• Place a protractor on each letter’s date and project the line of sight at the recorded angle.

• Mars is located at the point where paired lines of sight intersect.

• The orientation of the protractor must always be such that zero degrees points to the right.

Example TriangulationsApril 23 – 162 degrees March 8 – 210 degrees

September 1st – 25 degreesOctober 15th – 320 degrees

Kepler’s Laws Post Lab

Questions1. During which month(s) is the distance between

Mars and the orbit of the Earth the greatest?2. During which month(s) is the distance between

Mars and the orbit of the Earth the least? 3. What is the shape of Mars’ orbit?4. Define Kepler’s First Law of Planetary Motion.5. Compare the areas of the wedges. 6. Define Kepler’s Second Law of Planetary

Motion.  

Kepler’s Laws Post Lab

Questions 7. Indicate when Mars is moving the slowest in

its orbit. 8. Indicate when Mars is moving the fastest in its

orbit.9. Define Kepler’s Third Law of Planetary Motion. 10.Using Kepler’s Third Law of Planetary Motion

calculate the period of Mars.11.If a picture of Mars were taken today (when

would the next picture need to be taken in order to locate Mars’ position?

Example #1

Venus has a period of revolution of 225 days about the sun. What’s its orbital radius as a multiple of the Earth’s.

Example #2

The moon is 3.9 X 105 km from Earth’s center, r = 6.4 X 106 m. What’s the orbital period of the international space station if it’s 250 km above the surface of the Earth?

Newton’s Law of Universal Gravitation

Isaac Newton•Formulated Law of Mechanics•Formulated a Theory of Gravity•Invented Calculus.  NLUG Equation

221

r

mGmFg

Newton’s Law of Universal Gravitation

Qualitative UnderstandingComplete the chart. Let a mass of m and a distance of r equal one unit of gravitational force, Fg.

m1 m2 r Fg

Example m m r Fg

Example #3

Using NLUG, calculate the force due to gravity between a 65 kg person standing on the surface of the earth and the earth itself? The mass of the earth is 6 x 1024 kg and its radius is 6,400,000 m.

Example #3

How much would a 65 kg person weigh on Earth?

Example #3 cont.

Combining the formulas for weight:

and force due to gravity:

What does the acceleration due to gravity depend on?

221

r

mGmFg

W=mg, or Fw = mg

Example #4

From the period of a 1 meter long pendulum, determine the acceleration due to gravity in your classroom.

Example #4

Using the data from the previous page, what is the mass of Earth if the radius of Earth is 6,400 km? (Isn’t it cool that you can determine the mass of a planet with a string and a watch!)

Example #5

The mass of Venus was not known until 1961 when the Russian probe Venera 1 established a stable orbit around the planet. If the Venera probe orbited at a speed of 2 x 103 m/s at a distance of 8.2 x 107m from the center of Venus, what mass of Venus was determined from this orbit?