Calculate Orbital Period: Worksheet
Use Kepler's Third Law (T² = a³ in AU and years) to solve these problems. Refer to the solar system data table to check your answers.
Practice Problems
Problem 1: Mars has a semi-major axis of 1.524 AU. What is its orbital period in years?
Hint: T = √(a³) = √(1.524³)
Hint: T = √(a³) = √(1.524³)
Problem 2: Saturn takes 29.46 years to orbit the Sun. What is its semi-major axis in AU?
Hint: a = (T²)1/3
Hint: a = (T²)1/3
Problem 3: An asteroid has a semi-major axis of 3.0 AU. How long does it take to orbit the Sun?
Problem 4: A hypothetical planet orbits a star identical to the Sun at a distance of 10 AU. What is its orbital period?
Problem 5: Io, a moon of Jupiter, has an orbital period of 1.77 days and a semi-major axis of 421,700 km. Europa has a semi-major axis of 671,100 km. Using Kepler's Third Law, calculate Europa's orbital period.
Hint: Use the ratio form: (TE/TI)² = (aE/aI)³
Hint: Use the ratio form: (TE/TI)² = (aE/aI)³
Answers
- T = √(3.540) ≈ 1.881 years (actual: 1.881)
- a = (867.9)1/3 ≈ 9.54 AU (actual: 9.537)
- T = √(27.0) ≈ 5.20 years
- T = √(1000) ≈ 31.62 years
- (TE/1.77)² = (671100/421700)³ = (1.5916)³ = 4.035, so TE = 1.77 × √4.035 ≈ 3.55 days (actual: 3.55)