# Worksheet: Orbital Mechanics

In this worksheet, we will practice how to use the formula T = 2πr/v to calculate the orbital characteristics of a planet, moon, or man-made satellite in a circular orbit.

**Q1: **

Two planets, A and B, orbit a star. Both planets have circular orbits. Planet A orbits the star at a distance of km and at a speed of 30 km/s. Planet B orbits the star at a distance of km and at a speed of 17 km/s.

How many times is the length of planet B’s orbit greater than planet A’s?

How many times longer does it take for planet B to orbit the star than planet A? Give your answer to 1 decimal place.

**Q3: **

Titan is the largest moon of Saturn. It has a roughly circular orbit and it orbits Saturn at a distance of 1,220,000 km with a period of 15.9 days. At what speed is Titan moving along its orbit? Give your answer in kilometers per second and to 2 significant figures.

**Q4: **

The table shows some data about Saturn’s moon, Titan. Using this data, calculate the orbital period of Titan around Saturn. Assume that Titan has a circular orbit. Give your answer in days to the nearest day.

Titan (Moon of Saturn) | |
---|---|

Diameter | 5,150 km |

Orbital Radius | 1,220,000 km |

Orbital Speed | 5.57 km/s |

Mass | kg |

**Q5: **

A satellite orbits Earth at an orbital radius of 7,720 km and moves at a speed of 7.2 km/s. The satellite has a circular orbit.

What is the circumference of the satellite’s orbit? Give your answer in kilometers to 3 significant figures.

What is the period of the satellite’s orbit? Give your answer in minutes to the nearest minute.

**Q6: **

A satellite orbits Earth at an orbital radius of 42,200 km and moves at a speed of 3.1 km/s. The satellite has a circular orbit.

What is the circumference of the orbit of the satellite? Give your answer in kilometers to 3 significant figures.

What is the period of the satellite’s orbit? Give your answer in hours to the nearest hour.

**Q7: **

Which of the following is the correct formula for the orbital speed of a satellite following a circular orbit around a planet given its orbital radius and orbital period? represents the orbital period, represents the orbital speed, and represents the orbital radius.

- A
- B
- C
- D
- E

**Q8: **

Mercury travels 364 million kilometers as it makes 1 full orbit around the Sun. Assuming that Mercury has a circular orbit, at what distance away from the Sun does Mercury orbit? Give your answer to 2 significant figures.

**Q9: **

Mars orbits the Sun at a distance of about 228,000,000 km. Assuming that Mars has a circular orbit, what is the distance traveled by the planet as it makes 1 full orbit around the Sun? Give your answer in scientific notation to 2 significant figures.

- A km
- B
- C
- D

**Q10: **

Venus takes 225 days to orbit the Sun.

How long is this period in Earth years? Use a value of 365 for the number of days in an Earth year. Give your answer to 2 decimal places.

How long does Earth take to orbit the Sun in Venus years? Give your answer to 2 decimal places.

**Q11: **

Jupiter takes 4,333 days to orbit the Sun.

How long is this period in Earth years? Use a value of 365 for the number of days in an Earth year. Give your answer to 1 decimal place.

How long does Earth take to orbit the Sun in Jupiter years? Give your answer to 2 decimal places.

One day on Jupiter is 9.925 hours long. How many Jupiter days are in 1 Earth year? Use a value of 365 for the number of days in an Earth year. Round your answer to the nearest day.