Johannes Kepler
(Creepy looking guy to the right)
Danish astronomer Tycho Brahe
(1546-1601) spent years
cataloguing the stars and planets
with great accuracy. His assistant
Johannes Kepler (1571-1630) put
his observations to good use. He
developed three important laws of
astronomy. His first law describes
the shapes of planetary orbits. His
second law describes the speed at
which the planets travel along
their orbits. His third law relates
the different planetary orbits to
one another. FYI: Newton, born in
1642, came after Kepler.
Kepler’s Laws
Kepler's three laws of planetary motion can be described as follows:
1. The path of the planets about
the sun are elliptical in shape, with the
center of the sun being located at one
focus. (The Law of Ellipses)
2. An imaginary line drawn from
the center of the sun to the center of
the planet will sweep out equal areas in
equal intervals of time. (The Law of
Equal Areas)
3. The ratio of the squares of the
periods of any two planets is equal to
the ratio of the cubes of their
average distances from the sun. (The
Law of Harmonies)
The Orbit Lab
Objective: The student will draw an ellipse to simulate the orbit of a planet and then
analyze how the gravitational force varies with position in the orbit.
Important terms:
Perihelion
Aphelion
Materials:
2 thumbtacks, 21 cm x 28 cm piece of cardboard,
Sheet of unlined paper, 30 cm of string or thread
Procedure:
1. Push the thumbtacks into the paper and cardboard so that they are between 6
and 10 cm apart.
2. Make a loop with the string. Place the loop over the two thumbtacks. Keep the
loop tight as you draw the ellipse.
3. Remove the tacks and string. Draw a small star centered as one of the tack
holes.
Observation and Data:
1. Draw the position of the planet in the orbit where it is farthest from the star.
2. Draw the position of the planet when it is nearest the star.
3. Determine the distance from these positions to the star’s center (below).
Analysis:
1. Choose one of the planets in the solar system.
2. Calculate the gravitational force when the planet is at perihelion and aphelion.
You will need to use the enclosed charts to find the distances and masses
required. Draw your planet at the perihelion and aphelion distances and label
the force vectors accordingly.
3. Draw your planet at two additional phases. Draw the tangential velocity vector
at each phase (all four phases).
NAME
MASS (kg)
Sun
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
1.991 x 1030
3.2 x 1023
4.88 x 1024
5.979 x 1024
6.42 x 1023
1.901 x 1027
5.68 x 1028
8.68 x 1026
1.03 x 1026
1.2 x 1022
PLANETARY DATA
PERIHELION
APHELION DIST.
DIST. (megamiles) (megamiles)
PERIHELION
Date
APHELION
Date
28.6
66.8
91.4
128.4
460.3
837.6
1699.0
2771.0
2756.0
10/16/95
8/11/95
12/21/95
2/19/96
5/5/99
5/26/03
3/1/2050
3/2030
8/1989
11/29/95
12/1/95
6/21/96
1/28/97
3/29/2005
2/8/2018
4/17/2008
2/2112
8/2113
43.4
67.7
94.5
154.9
507.2
936.2
1868.0
2819.0
4555.0
AP Physics 1
Mr. Kuffer
Orbit Lab – Your Ellipse
NAME:_________________
Period: ________
*Show all work below. This should include several conversion for aphelion and
perihelion from Megamiles to meters and the gravitational force of attraction at those two
points. Every number should have a unit attached to it. If it does not… IT IS WRONG!
Recall:
1 megamile = _______ x 106 miles
1 mile = 1609 m
Planet Chosen: _______________________
Distance at Aphelion:
Distance at Perihelion:
Difference in Distance:
Fg at Aphelion:
Fg at Perihelion:
Difference in Fg:
*Now visit https://www.youtube.com/watch?v=zNeFI_JCXlY&app=desktop.
Using concept over computation, add components necessary to exemplify, explain and
defend Kepler’s Laws. This will require you to add key elements to the diagram on the
previous page.
Determining Planetary Gravitational Forces
Instructions: Using the data in your packet, complete the following chart.
Make sure you change miles to meters and do not forget to square the
distance in the denominator.
Fg = Gm1m2/ d2
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Fg @ Perihelion (N)
Fg @ Aphelion (N)
Application of Kepler’s 3rd and Universal Gravitation
1. Jupiter is 5.2 times farther than Earth is from the sun. Find Jupiter’s
period in Earth years.
2. Uranus requires 84 years to circle the sun. Find Uranus’ orbital radius
as a multiple of Earth’s orbital radius.
3. A satellite is placed in an orbit with a radius that is half the radius of
the moon’s orbit. Find its period in units of the period of the moon.
4. An apparatus like the one Cavendish used to find G has a large lead
ball that is 5.9 kg in mass and a small one that is 0.047 kg. Their
centers are separated by 0.055 m. Find the force of attraction
between them.