Worksheet: Kepler's Laws of Planetary Motion

In this worksheet, we will practice using Kepler's first, second, and third laws of planetary motion to determine the dynamics of elliptical orbits.

Q1:

The asteroid Eros has an elliptical orbit about the Sun, with a perihelion distance of 1.13 AU and aphelion distance of 1.78 AU. What is the period of its orbit?

Q2:

An asteroid has speed 15.5 km/s when it is located 2.00 AU from the sun. At its closest approach, it is 0.400 AU from the Sun. What is its speed at that point?

Q3:

A geosynchronous Earth satellite is one that has an orbital period of precisely one Earth day. A satellite in a geosynchronous orbit remains directly above a particular point on Earth’s surface throughout its orbit. What is the orbital radius of such a satellite if a day is considered as 8 6 4 × 1 0 3 s? Take the radius of Earth to be 6 3 7 0 km.

  • A 4 8 . 6 × 1 0 3 km
  • B 1 5 3 × 1 0 3 km
  • C 3 5 . 8 × 1 0 3 km
  • D 4 2 . 2 × 1 0 3 km
  • E 2 0 . 7 × 1 0 3 km

Q4:

If a planet with a mass that is 3.50 times that of Earth was orbiting the Sun at the same orbital radius at which Earth orbits the Sun, what would the planet’s orbital period be?

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

Q5:

A satellite in a geosynchronous circular orbit is 4 6 1 2 0 . 0 0 km from the center of Earth. A small asteroid collides with the satellite, sending it into an elliptical orbit of apogee 4 3 0 0 0 . 0 0 km. What is the speed of the satellite at apogee? Assume that the satellite’s angular momentum is conserved. Use 𝑚 = 5 . 9 7 2 1 9 × 1 0 𝐸 2 4 k g as Earth’s mass.

Q6:

A satellite orbits Jupiter with an average orbital radius of 9 6 3 7 0 0 km and an orbital period of 3.269 days. Find the mass of Jupiter, considering a day as 8 6 4 . 0 × 1 0 3 s.

  • A 6 . 6 3 6 × 1 0 2 7 km
  • B 1 . 8 7 4 × 1 0 3 3 km
  • C 6 . 8 8 6 × 1 0 2 5 km
  • D 6 . 6 4 1 × 1 0 2 7 km
  • E 1 . 3 2 5 × 1 0 3 0 km

Q7:

The perihelion of Halley’s comet is 0.622 AU and the aphelion is 16.6 AU. The speed of Halley’s comet at the perihelion is 39 km/s. Find its speed at the aphelion. Use a value of 1 . 4 9 6 × 1 0 1 1 m for one AU.

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