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 𝑣2?

  • A4𝑅
  • B2𝑅
  • C𝑅4
  • D𝑅2
  • Eπ‘…οŠ¨

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 orange line
  • BThe green line
  • CThe red line
  • DThe blue 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 5.97Γ—10οŠͺ kg for the mass of Earth and 6.67Γ—10 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 𝑅9, at what speed, in terms of 𝑣, would it have to move in order to maintain its orbit?

  • A𝑣
  • B𝑣9
  • C𝑣3
  • D3𝑣
  • E9𝑣

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 2.18Γ—10 kg. What is the radius of the planet’s orbit in astronomical units? Use a value of 6.67Γ—10 m3/kgβ‹…s2 for the universal gravitational constant and 1.50Γ—10 m for the length of 1 AU. Give your answer to 3 significant figures.

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 5.97Γ—10οŠͺ kg for the mass of Earth and 6.67Γ—10 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 6.67Γ—10 m3β‹…kgβˆ’1β‹…sβˆ’2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A1.02Γ—10 kg
  • B3.91Γ—10 kg
  • C1.13Γ—10 kg
  • D1.24Γ—10 kg
  • E5.67Γ—10 kg

Q8:

The formula 𝑀=4πœ‹π‘ŸπΊπ‘‡οŠ¨οŠ©οŠ¨ 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 6.67Γ—10 m3/kgβ‹…s2 for the universal gravitational constant and 1.50Γ—10 m for the length of 1 AU. Give your answer to 3 significant figures.

  • A9.66Γ—10 kg
  • B8.54Γ—10 kg
  • C2.43Γ—10 kg
  • D2.68Γ—10 kg
  • E2.44Γ—10 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 6.67Γ—10 m3/kgβ‹…s2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A3.23Γ—10 kg
  • B1.10Γ—10 kg
  • C6.58Γ—10οŠͺ kg
  • D5.48Γ—10 kg
  • E1.90Γ—10 kg

Q10:

Phobos is the largest moon of Mars. It orbits Mars at a speed of 2.14 km/s. Assuming that the moon follows a circular orbit, what is the radius of its orbit? Use a value of 6.42Γ—10 kg for the mass of Mars and a value of 6.67Γ—10 m3/kgβ‹…s2 for the universal gravitational constant. Give your answer in km to 3 significant figures.

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