Worksheet: Kepler's Third Law of Planetary Motion

In this worksheet, we will practice using Kepler's third law of planetary motion to find the orbital characteristics of planets and satellites.

Q1:

Epsilon Eridani b is an exoplanet that orbits the star Epsilon Eridani. The host star has a mass of 0.83 times that of the Sun, and the exoplanet orbits at a radius of 3.39 AU. What is the orbital period of Epsilon Eridani b? Use a value of 1 . 9 9 × 1 0 kg for the mass of the Sun, 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant, and 1 . 5 0 × 1 0 m for the length of 1 AU. Give your answer in days to 3 significant figures.

Q2:

Two moons, moon 𝐴 and moon 𝐵 , orbit the same gas giant. Both moons have circular orbits. If moon 𝐵 has an orbital radius that is 9 times that of moon 𝐴 , how many times greater is the orbital period of moon 𝐵 than moon 𝐴 ?

Q3:

Kepler-17b is an exoplanet orbiting the star Kepler-17. It was discovered in 2011. The mass of Kepler-17 is 2 . 3 1 × 1 0 kg, and Kepler-17b orbits its host star with a period of just 1.49 days. What is the orbital radius of the exoplanet? Assume that the exoplanet has a circular orbit. Give your answer in astronomical units to 3 significant figures. Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the value of the universal gravitational constant and a value of 1 . 5 0 × 1 0 m for the length of 1 AU.

Q4:

The Moon completes one full orbit of Earth every 27.3 days. The semimajor axis of the Moon’s orbit is 384,000 kilometers. Use these values to calculate 𝑇 𝑟 for the Moon’s orbit around Earth. Give your answer to 3 significant figures.

  • A 1 . 7 1 × 1 0 s2/m3
  • B 2 . 7 3 × 1 0 s2/m3
  • C 7 . 1 1 × 1 0 s2/m3
  • D 8 . 8 4 × 1 0 s2/m3
  • E 9 . 8 3 × 1 0 s2/m3

Q5:

Neptune has an average orbital radius of 30.1 AU. Use the orbital period and orbital radius of Earth to find the orbital period of Neptune in years. Give your answer to 3 significant figures.

  • A 165 years
  • B 27.3 years
  • C 248 years
  • D 9.68 years
  • E 330 years

Q6:

Uranus takes 84.0 years to orbit the Sun. Use the orbital period and orbital radius of Earth to find the average orbital radius of Uranus in astronomical units. Give your answer to 3 significant figures.

  • A 4.38 AU
  • B 9.17 AU
  • C 28.8 AU
  • D 38.4 AU
  • E 19.2 AU

Q7:

Earth has a mass of 5 . 9 7 × 1 0 kg. What orbital radius must satellites have in order to maintain geostationary orbit? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the value of the universal gravitational constant. Give your answer to 3 significant figures.

Q8:

Two planets, planet A and planet B, orbit the same star. Both planets have circular orbits. If planet B has an orbital period that is 8 times that of planet A, how many times greater is the orbital radius of planet B than planet A? Give your answer to 2 significant figures.

Q9:

Two stars, star A and star B, have different masses. Star A has a mass 1.5 times that of star B. If a planet were located 1 AU away from each star, around which star would the planet have a shorter orbital period?

  • AStar B
  • BThe orbital period of star A equals the orbital period of star B.
  • CStar A

Q10:

A number of exoplanets have been discovered orbiting the star Kepler-90. The orbital characteristics of three exoplanets in the Kepler-90 system are shown in the table.

Name Orbital Period (Days) Orbital Radius (AU)
Kepler-90f 125 0.480
Kepler-90g 211 0.710
Kepler-90h 332 1.01

For each exoplanet listed, use Kepler’s third law to find the mass of the star, and then find the average of these values. Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant and 1 . 5 0 × 1 0 m for the length of 1 AU. Give your answer to 3 significant figures.

  • A 2 . 1 8 × 1 0 kg
  • B 4 . 3 6 × 1 0 kg
  • C 6 . 9 5 × 1 0 kg
  • D 1 . 8 9 × 1 0 kg
  • E 5 . 4 6 × 1 0 kg

Q11:

The Sun has a mass of 1 . 9 9 × 1 0 kg. Use this value to calculate an approximate value for 𝑇 𝑟 for the planets of the solar system. Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the value of the universal gravitational constant. Give your answer to 3 significant figures.

  • A 1 . 4 9 × 1 0 s2/m3
  • B 9 . 4 7 × 1 0 s2/m3
  • C 7 . 4 4 × 1 0 s2/m3
  • D 2 . 9 7 × 1 0 s2/m3
  • E 7 . 5 3 × 1 0 s2/m3

Q12:

Omega Serpentis b is an exoplanet that orbits the star Omega Serpentis. The exoplanet has an orbital period of 277 days and an orbital radius of 1.10 AU. What is the mass of the host star? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant and a value of 1 . 5 0 × 1 0 m for the length of 1 AU. Give your answer to 3 significant figures.

  • A 3 . 4 9 × 1 0 kg
  • B 1 . 1 6 × 1 0 kg
  • C 1 . 4 8 × 1 0 kg
  • D 2 . 3 2 × 1 0 kg
  • E 4 . 6 4 × 1 0 kg

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