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 1.5×10 km and at a speed of 30 km/s. Planet B orbits the star at a distance of 4.8×10 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.

Q2:

A satellite orbits Earth at an orbital radius of 10,000 km. Its orbital period is 2.8 hours. How fast is the satellite moving? Give your answer in kilometers per second and to 2 significant figures.

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)
Diameter5,150 km
Orbital Radius1,220,000 km
Orbital Speed5.57 km/s
Mass1.35×10 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? 𝑇 represents the orbital period, 𝑣 represents the orbital speed, and 𝑟 represents the orbital radius.

  • A𝑣=𝜋𝑟𝑇
  • B𝑣=𝑟𝑇
  • C𝑣=𝑇2𝜋𝑟
  • D𝑣=2𝜋𝑟𝑇
  • E𝑣=𝑇2𝜋𝑟

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.

  • A1.4×10 km
  • B2.28×10km
  • C3.4×10km
  • D1.6×10km

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.

1 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.

Q12:

An object is executing an orbital motion. If the radius of its circular orbit is increased to six times its original value, by how much is the centripetal force acting on it required to change to keep the speed constant?

  • AThe centripetal force should increase to three times its original value.
  • BThe centripetal force should decrease to one-third of its original value.
  • CThe centripetal force should increase to six times its original value.
  • DThe centripetal force should decrease to one-sixth of its original value.

Q13:

A planet is orbiting a star. If the distance between them increases, then .

  • Athe periodic time decreases and the orbital velocity increases
  • Bthe periodic time decreases and the orbital velocity decreases
  • Cthe periodic time increases and the orbital velocity decreases
  • Dthe periodic time increases and the orbital velocity increases

Q14:

The International Space Station (ISS) orbits Earth with a tangential speed of 7.67 km/s. If the distance between the ISS and the centre of Earth is 6.77×10 m, then the periodic time of the satellite is .

  • A2.27𝜋×10 s
  • B1.77𝜋×10 s
  • C1.77𝜋 s
  • D2.27𝜋 s

Q15:

A merry-go-round is rotating with tangential speed 15 m/s. If it covers a distance of 93 m during 12 of a revolution, what is the periodic time of the merry-go-round?

  • A1.4 s
  • B1.0 s
  • C2.9 s
  • D2.1 s

Q16:

Two satellites, A and B, have masses 𝑀 and 2𝑀 respectively. Both satellites orbit Earth at the same height. The ratio of the periodic time of A to the periodic time of B is .

  • A12
  • B11
  • C21
  • D12

Q17:

A moon is orbiting a planet at a speed of 7.3×10 m/s. If the moon takes 2.3 h to complete one full cycle, then the length of its circular path equals .

  • A1.01×10 km
  • B1.33×10 km
  • C6.04×10 km
  • D2.63×10 km

Q18:

In a satellite-planet system, which of the following would cause the greatest change in the periodic time of a satellite if doubled?

  • AThe mass of the satellite
  • BThe distance from the centre of the planet
  • CThe mass of the planet
  • DThe gravitational constant

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