# 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 and with an orbital speed . At what radius, in terms of , would the satellite have to orbit in order to have an orbital speed of ?

- A
- B
- C
- D
- E

**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 kg
for the mass of Earth and m^{3}/kgβ
s^{2}
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 and with an orbital speed . If the satellite were moved closer to Earth, so that it followed a circular orbit with a radius of , at what speed, in terms of , would it have to move in order to maintain its orbit?

- A
- B
- C
- D
- E

**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 kg. What is the
radius of the planetβs orbit in astronomical units? Use a value of
m^{3}/kgβ
s^{2} for the universal gravitational
constant and 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 kg
for the mass of Earth and m^{3}β
kg^{β1}β
s^{β2} 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 m^{3}β
kg^{β1}β
s^{β2}
for the universal gravitational constant. Give your answer to 3 significant figures.

- A kg
- B kg
- C kg
- D kg
- E kg

**Q8: **

The formula
can be used to calculate the mass,
, of a planet or star given the orbital period,
, and orbital radius,
, 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
m^{3}/kgβ
s^{2}
for the universal gravitational constant and
m for the length of
1 AU.
Give your answer to 3 significant figures.

- A kg
- B kg
- C kg
- D kg
- E 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 Ioβs orbit is circular with a radius of
422,000 km,
calculate the mass of Jupiter.
Use a value of
m^{3}/kgβ
s^{2}
for the universal gravitational constant. Give your answer to 3 significant figures.

- A kg
- B kg
- C kg
- D kg
- E kg