galileo, brahe, and kepler · 2018-09-27 · • died before invention of telescope 9. tycho’s...
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Galileo Galilei (1564-1642)
• Supported Copernican
model.
• Used telescope to observe
sky (1610).
– Mountains on the moon
– Rings of Saturn
– Sunspots
– Milky Way is made of
stars
2
Observations of Venus
• Venus has phases similar to the moon.
• The apparent size of Venus changes with
the phase.
4
Phases of Venus
• If Venus was orbiting the Earth, its distance
would not change and its size would stay
the same.
5
Basic Geocentric View
• Order of planets somewhat arbitrary.
• Mercury and Venus always orbit at velocity to
keep them near the Sun.
E
Sun
Moon
Mercury
SaturnCelestial Sphere
Jupiter
Mars
Venus
6
Galileo’s observations of Jupiter
• Observed the 4 largest
moons of Jupiter
(Galilean Moons).
• The fact that bodies
could orbit other
planets supported
heliocentric view.
7
What would you expect to see if Venus orbited the
Earth in the manner Ptolemy described?
A. You would not observe all of the
phases, but the size would change.
B. You would observe all of the
phases and the size would change.
C. You would observe all of the
phases but the size would not
change.
D. You would not observe all of the
phases and the size would not
change.
8
Tycho Brahe
(1546-1601)
• Born 18 years before
Galileo
• Supported geocentric
model
• Died before invention of
telescope
9
Tycho’s Observations
• Designed state of the art instruments to observe
sky (all naked eye observations).
• Made detailed observations of planetary and
stellar positions.
– Positions accurate up to 1 arcminute (1/60 of a
degree)
11
Tycho’s observations
• Used many
instruments to confirm
results.
• Same method used by
modern astronomers.
12
Tycho’s Supernova (1592)
• Believed stars unchanging
– “New” star must be near Earth
• Tried to measure distance to
object using parallax.
• No parallax observed
– Object much more distant that
originally thought.
– Heavens are not unchanging
13
A key contribution that Tycho Brahe made to
astronomy is
A. his theoretical predictions of
planetary positions
B. his observation that a
supernova was very distant.
C. his observations of the
phases of Venus.
D. his invention of the
telescope.
14
Johannes Kepler (1571-1630)
• Assistant to Brahe (1600-01)
• Believed in heliocentric
model (Copernicus).
• Wanted mathematical model
of orbits
• Used observations by Brahe
• Used trial and error to test
models
15
Kepler’s First Law17
• The orbit of a planet about the Sun is an
ellipse with the Sun at one focus.
• Animation
of how to draw
18
Focus
Focus
Semi-major axis
There is nothing physically at the
second focus of the ellipse.
For the Sun and the planets the orbits are are almost circular.
Perihelion: closest
distance to the Sun
Aphelion: furthest
distance from the Sun
Elliptical Orbit
Animation
appleta
b
19
Eccentricity = Shape of Orbit
• Values range from 0 to 1
▪ ε = 0 = circle
▪ ε = 0.5 = ellipse
▪ ε = 1 = straight line
2
2for the curious: 1
b
a = −
20
Kepler’s Second Law
• “The Law of Equal Areas” -- A line joining
a planet and the Sun always sweeps out
equal areas in equal intervals of time.
Animation
applet
What does Kepler’s Second Law imply
about the speed of the planet?
A. It moves fastest when it is
midway between the nearest and
farthest points from the Sun.
B. It moves faster when it is far
from the Sun.
C. It moves faster when it is near
the Sun.
D. Its speed is constant.
21
Planet moves
fastest at
perihelion
Planet moves
slowest at aphelion
Speed of planets in elliptical
orbits
Animation
22
Kepler’s Third Law
• P2 = a3
– P = sidereal period in years
– a = semi-major axis in AU
– The closer a planet is to the Sun, the less time it takes to
go around the Sun.
( )22 3
3
Example: If 8.0 years then
8.0 y 64
64 4.0 AU
P
P a
a
=
= = =
= =
23
What is the semi-major axis of an asteroid
that orbits the Sun with a period of 11 years?
A. 3 AU
B. 5 AU
C. 7 AU
D. 11 AU
24
What is the semi-major axis of an asteroid
that orbits the Sun with a period of 11 years?
A. 3 AU
B. 5 AU
C. 7 AU
D. 11 AU
3 2
3 2 311 121
4.95 AU 5 AU
a P
a
=
= =
=
25
If this asteroid has a perihelion distance
of 1.5 AU, what is its aphelion distance?
26
A. 1.5 AU
B. 3.5 AU
C. 5.0 AU
D. 8.5 AU
If this asteroid has a perihelion distance
of 1.5 AU, what is its aphelion distance?
A. 1.5 AU
B. 3.5 AU
C. 5.0 AU
D. 8.5 AU
( )
2
2
2 5 AU 1.5 AU
8.5 AU
PD AD a
AD a PD
AD
+ =
= −
= −
=
27
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