Practice Problems (5.4– Kepler’s Laws)
1. Use Kepler’s third law to determine the orbital period of Jupiter. Its orbital radius is 5.203 AU.
2. Pluto takes 90 553 Earth days to orbit the Sun. Use this value to determine its mean orbital radius.
(Earth orbits the sun in 365.24 days)
3. A piece of rocky debris in space has a mean orbital distance of 45.0 AU. What is its orbital period
of the Sun?
4. Mars has two moons, Deimos and Phobos (Figure 5.41). Phobos has an orbital radius of 9378 km
and an orbital period of 0.3189 Earth days. Deimos has an orbital period of 1.262 Earth days. What
is the orbital radius of Deimos.
5. The Cassini-Huygens probe began orbiting Saturn in December 2004. It takes 147 days for the
probe to orbit Saturn. Use Tethys, one of Saturn’s moons, to determine the average orbital radius
of the probe. (Tethys orbital period is 1.887 Earth days. Mean Orbital Radius is 2.947 X 108m)
6. We send a probe to orbit a nearby asteroid and take some pictures of it. The probe enters an orbit
that puts it 850m from the centre of the asteroid. If the probe moves at 12m/s, determine the mass
of the asteroid.
7. Earth’s Moon is 3.844X 105 km from Earth. Determine the orbital speed of the Moon.
8. Neptune’s average orbital radius is 4.50 X 1012 m from the Sun. The mass of the Sun is 1.99 x 1030
kg. What is Neptune’s orbital speed?
9. The moon Miranda orbits Uranus at a speed of 6.68 X 103 m/s. Use this speed and the mass of
Uranus to determine the radius of Miranda’s orbit. The mass of Uranus is 8.68 X 1025 kg.
10. LandSat is an Earth-imaging satellite that takes pictures of Earth’s ozone layer and geological
features. It orbits Earth at the height of 912 km (Figure 5.46). What are its orbital speed and its
period?
11. The International Space Station orbits Earth at a height of 359.2 km. What is its orbital speed?
12. The Chandra X-ray satellite takes X-ray pictures of high-energy objects in the universe. It is
orbiting Earth at an altitude of 114 593 km. What is its orbital period?
Solutions
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11.87 a
39.465 AU
302 a
2.346 X 104 km
5.38 X 109 m
1.8 X 1015 kg
1.02 X 103 m/s
5.43 X103 m/s
1.30 X 108 m
7.390 X 103 m/s and 6.20 X 103 s (slightly off – different values of mass of Earth)
7.69 X 103 m/s (slightly off – different values of mass of Earth)
4.19 X 105 s