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Planet Ellipse Project
Objectives:
1. Students will apply Kepler's Three Laws to the motion and orbit of an undiscovered planet.
2. Students will use Newton's Law of Universal Gravitation to calculate the force of gravity in
different locations of a planet's orbit.
3. Students will use centripetal motion calculations to predict the velocity of the orbit at different
locations.
Procedure:
1. Choose your planet information for the project and write down the information in the table.
Planet Info
Eccentricity
Semi Major Axis- a (AU)
Radius of Planet (kilometers)
Your Planet
2 AU, 2.9920 x 1011 m
30,000 km, 3.0 x 107 m
Earth
1 AU, 1.49598 x 1011 m
6371 km, 6.371 x 106 m
2.
Choose a name for your planet and give a brief description of your planet (feel free to be creative).
Explain whether your planet is terrestrial or a gas giant. In the description give the reason for
naming the planet. Choose a traditional historical name from any astronomically inclined culture
such as the Greek, Roman, Chinese, Muslim, Latin, etc. cultures and provide the history behind
your name.
3. On a piece of poster board draw the elliptical orbit of your planet and the Earth's orbit (as a
reference orbit). Make sure to label the semi-major axis (a), the semi-minor axis (b), c value, the
vertex, the two foci (F1, F2), periods (T), masses, locations of the sun, each planet, and an
appropriate scale in the bottom left corner. Use tacks as your foci and string to draw the orbits.
4. Include Kepler's Three Laws each color-coded to the appropriate features labeled on your drawing.
For the 1st law draw the elliptical orbits of both Earth and your planet and use the same color for
the orbital paths of each. Use the same color to write out Kepler's 1st Law on your poster board.
5. For Kepler's 2nd law show equal areas in equal time periods by drawing two triangles of equal area
across the major axis of your planet's orbit. Color-code the triangles to the written 2nd Law on your
posterboard. (Hint: use smaller triangles for more accuracy)
6. For Kepler's 3rd Law, solve for the period of your planet using Kepler's 3rd Law. Label the
periods of Earth and your planet near their orbits on your poster board. Color-code your periods
and semi major axis to the written 3rd Law on your poster board.
Use Newton's corrected version of Kepler's 3rd Law to solve for the mass of your planet.
Calculate the force of gravity using Newton's law of Universal Gravitation at the perihelion,
aphelion,and both ends of the minor axis. Color-code these calculations in the same color as the
written Law of Gravitation on your poster board.
9. Using a force arrow of appropriate scale length (ex: 1cm = 1N) draw the force vector arrows at
each of the four points mentioned in step #8. Use the same color code as step #8.
10. Calculate the velocity at each of the four points mentioned in step #8 using centripetal motion
formula.
11. Using a velocity arrow of appropriate scale length (ex: 1cm = 100m/s) draw the velocity vector
7.
8.
arrows at each of the four points mentioned in step #8. Use the same color code as step #8.
12. Find the acceleration of gravity (g) on your planet and label it on your poster board.
Formulas:
Eccentricity
e=
Semi Major / Semi Minor Axis
c
a
b = a2 - c 2
Newton’s Law of Universal Gravitation
m m
Fg = G A 2 B
d
Velocity in orbit
Gmcenter
v=
r
Kepler’s 3rd
æ TA ö æ aA ö 3
2
3
ç ÷ = ç ÷ or T = a
è TB ø è aB ø
2
Newton’s Correction to Kepler’s 3rd
a3
T = 2p
G( M + m p )
Newton’s 2nd Law
F = ma
Planet Info
Eccentricity - e
Semi Major Axis – a (AU)
Semi Minor Axis – b (AU)
½ Foci Distance - c (AU)
Orbital Period – T (years)
Mass – m (kg)
Force Gravity – Fg (N) @ p1
Force Gravity – Fg (N) @ p2
Force Gravity – Fg (N) @ p3
Force Gravity – Fg (N) @ p4
Tangential Velocity – v (m/s)
@ p1
Tangential Velocity – v (m/s)
@ p2
Tangential Velocity – v (m/s)
@ p3
Tangential Velocity – v (m/s)
@ p4
Acceleration of Gravity – g
(m/s2)
or
Fg = mg
Your Planet
Earth
Calculations:
1.
Find the (c) value and (b) value using the eccentricity formula, show
your work for both your planet and Earth.
Your Planet
Earth
2.
Find the Period (years and seconds) for both planets.
Your Planet
Earth
3.
Find the mass (kg) of each planet using Newton’s correction to
Kepler’s 3rd.
Your Planet
Earth
4.
Find the force of gravity in four positions at the end of each major and
minor axis for both planets using Newton’s Law of Universal Gravitation.
Your Planet
Earth
5.
Find the tangential velocities at each of the four positions for both
planets using the orbital velocity formula.
Your Planet
Earth
6.
Find the acceleration of gravity (g) on your planet using Newton’s 2nd
law.
Your Planet
Earth