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Kepler’s Laws Questions
1. Use the data from your astronomical data handout to confirm Kepler’s
third law, comparing Mars and Venus.
2. Galileo discovered four moons of Jupiter. Io, which he measured to be
4.2 units from the center of Jupiter, has a period of 1.8 days. He
measured the radius of Ganymede’s orbit as 10.7 units. Use Kepler’s
third law to find the period of Ganymede.
3. The fourth moon of Jupiter, Callisto, has a period of 16.7 days. Find
its distance to Jupiter using the data from the previous problem.
4. Kepler’s laws apply not only to the planets, but to any object in orbit,
such as an asteroid. Predict the period of the asteroid (in years) if its
mean orbital radius is twice that of Earth’s.
5. The moon has a period of 27.3 days and has a mean distance of 3.9 x
105 km from the center of the Earth. Find the period of an artificial
satellite that is 6.7 x 103 km from the center of the Earth.
6. Geosynchronous satellites are positioned so that their period is one
day, i.e. they remain above the same spot on the Earth’s surface.
These are very important for weather observations, communications,
etc. From the data on the period and radius of revolution of the moon
in the previous problem, find the average distance from Earth’s center
to an artificial satellite that has a period of 1 day.
7. Kepler’s first law states that the orbits of planets are ellipses with one
focus at the sun. Why do the planets travel in ellipses and not circles?
8. Kepler’s second law states that a radius of a planet sweeps out equal
areas in equal amounts of time. Explain how this might be a
consequence of conservation of angular momentum.
9. Take a guess as to where the location of the other focus of the ellipse
is in Kepler’s first law. Justify your answer.