Worksheet: Orbital Speed

In this worksheet, we will practice calculating the orbital speed of an object moving along a circular orbit given its orbital radius and the mass of the orbiting object.

Q1:

A satellite follows a circular orbit around Earth at a radial distance 𝑅 and with an orbital speed 𝑣 . At what radius, in terms of 𝑅 , would the satellite have to orbit in order to have an orbital speed of 𝑣 2 ?

  • A 4 𝑅
  • B 𝑅 4
  • C 2 𝑅
  • D 𝑅 
  • E 𝑅 2

Q2:

Which line on the graph shows the relation between orbital speed and orbital radius for objects moving along circular orbits due to gravity?

  • AThe blue line
  • BThe red line
  • CThe orange line
  • DThe green line

Q3:

Nilesat 201 is a communications satellite that orbits Earth at a radius of 35,800 km. What is the orbital speed of Nilesat 201? Assume that the satellite follows a circular orbit. Use a value of 5 . 9 7 Γ— 1 0  οŠͺ kg for the mass of Earth and 6 . 6 7 Γ— 1 0    m3/kgβ‹…s2 for the universal gravitational constant. Give your answer to 3 significant figures.

Q4:

A satellite follows a circular orbit around Earth at a radial distance 𝑅 and with an orbital speed 𝑣 . If the satellite were moved closer to Earth, so that it followed a circular orbit with a radius of 𝑅 9 , at what speed, in terms of 𝑣 , would it have to move in order to maintain its orbit?

  • A 𝑣 3
  • B 𝑣
  • C 𝑣 9
  • D 9 𝑣
  • E 3 𝑣

Q5:

A planet has a circular orbit around a star. It orbits the star at a speed of 17.9 km/s, and the star has a mass of 2 . 1 8 Γ— 1 0   kg. What is the radius of the planet’s orbit in astronomical units? Use a value of 6 . 6 7 Γ— 1 0    m3/kgβ‹…s2 for the universal gravitational constant and 1 . 5 0 Γ— 1 0   m for the length of 1 AU. Give your answer to 3 significant figures.

  • A 32.1 AU
  • B 0.331 AU
  • C 54,200 AU
  • D 1,160 AU
  • E 3.03 AU

Q6:

For a satellite to follow a circular orbit around Earth at a radius of 10,000 km, what orbital speed must it have? Use a value of 5 . 9 7 Γ— 1 0  οŠͺ kg for the mass of Earth and 6 . 6 7 Γ— 1 0    m3β‹…kgβˆ’1β‹…sβˆ’2 for the value of the universal gravitational constant. Give your answer to 3 significant figures.

Q7:

Titan is the largest moon of Saturn. Assuming that Titan follows a circular orbit, with a radius of 1,220,000 km and an orbital speed of 5.57 km/s, calculate the mass of Saturn. Use a value of 6 . 6 7 Γ— 1 0    m3β‹…kgβˆ’1β‹…sβˆ’2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A 1 . 2 4 Γ— 1 0   kg
  • B 1 . 1 3 Γ— 1 0   kg
  • C 3 . 9 1 Γ— 1 0   kg
  • D 1 . 0 2 Γ— 1 0   kg
  • E 5 . 6 7 Γ— 1 0   kg

Q8:

The formula 𝑀 = 4 πœ‹ π‘Ÿ 𝐺 𝑇    can be used to calculate the mass, 𝑀 , of a planet or star given the orbital period, 𝑇 , and orbital radius, π‘Ÿ , of an object that is moving along a circular orbit around it. A planet is discovered orbiting a distant star with a period of 105 days and a radius of 0.480 AU. What is the mass of the star? Use a value of 6 . 6 7 Γ— 1 0    m3/kgβ‹…s2 for the universal gravitational constant and 1 . 5 0 Γ— 1 0   m for the length of 1 AU. Give your answer to 3 significant figures.

  • A 8 . 5 4 Γ— 1 0   kg
  • B 2 . 4 4 Γ— 1 0   kg
  • C 9 . 6 6 Γ— 1 0   kg
  • D 2 . 4 3 Γ— 1 0   kg
  • E 2 . 6 8 Γ— 1 0   kg

Q9:

Io is one of the four Galilean moons of Jupiter. Io makes one complete orbit of Jupiter every 1.77 days. Assuming that Io’s orbit is circular with a radius of 422,000 km, calculate the mass of Jupiter. Use a value of 6 . 6 7 Γ— 1 0    m3/kgβ‹…s2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A 1 . 1 0 Γ— 1 0   kg
  • B 1 . 9 0 Γ— 1 0   kg
  • C 5 . 4 8 Γ— 1 0   kg
  • D 6 . 5 8 Γ— 1 0  οŠͺ kg
  • E 3 . 2 3 Γ— 1 0   kg

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