Practice Orbital Motion in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Motion of an object held by gravity in a curved path — often a closed path (ellipse or circle) — around a planet, moon, star, or other mass.

An orbit is like falling around a planet instead of straight down onto it.

Showing a random 20 of 50 problems.

Example 1

easy

A satellite's orbital speed is

v = \sqrt{GM/r}

. If

r

quadruples, how does

v

change?

Example 2

medium

Use

T = 2\pi\sqrt{r^3/(GM)}

to find the period of a low Earth orbit at

r = 6.7\times10^6\text{ m}

(

GM = 4\times10^{14}

Example 3

medium

A satellite at

r = 7\times10^6\text{ m}

has mass

500\text{ kg}

. Find its gravitational potential energy (

GM = 4\times10^{14}

Example 4

easy

Find the orbital speed for a low Earth orbit where

GM = 4\times10^{14}

and

r = 6.4\times10^6 \text{ m}

Example 5

challenge

A satellite drops to a lower circular orbit (smaller

r

). Does its orbital speed increase or decrease, and what happens to its total energy?

Lower orbit → higher speed (v_lo > v_hi), yet total energy E

Example 6

medium

Escape speed at radius

r

\sqrt{2}

times the ___ at that radius.

Example 7

medium

Two satellites orbit the same planet at radii

r

and

4r

. Find the ratio of their orbital speeds (inner to outer).

At radii r and 4r, the inner satellite's speed is twice the outer: v1 : v2 = 2 : 1.

Example 8

medium

A moon orbits a planet with period

T

. If a second moon orbits at

r

that is

4

times larger, find its period ratio using

T \propto r^{3/2}

Example 9

easy

In a circular orbit, the force of gravity is directed ___ (toward / away from) the center of the planet.

Example 10

easy

True or false: a moon in a stable circular orbit does no net work on itself per cycle.

Example 11

medium

A satellite orbits at radius

r = 8 imes10^6 ext{ m}

around Earth (

GM = 4 imes10^{14}

). Find its orbital speed.

Example 12

easy

A satellite orbits at

v = 5000\text{ m/s}

at radius

r = 1.0\times10^7\text{ m}

. Find its centripetal acceleration.

Example 13

medium

Find the orbital period for a circular orbit of speed

v = 8000 \text{ m/s}

at radius

r = 7\times10^6 \text{ m}

Example 14

medium

What is the escape speed from Earth's surface (

GM = 4\times10^{14}

R = 6.4\times10^6\text{ m}

Example 15

medium

An astronaut of mass

80\text{ kg}

orbits at

r = 7\times10^6\text{ m}

(

GM = 4\times10^{14}

). Find the gravitational force on her.

Example 16

hard

A satellite drops from a circular orbit at radius

r_1 = 8\times10^6\text{ m}

r_2 = 7\times10^6\text{ m}

. Find the change in orbital speed (

GM = 4\times10^{14}

Example 17

hard

100\text{ kg}

probe in circular orbit at

r = 1.0\times10^7\text{ m}

(

GM = 4\times10^{14}

) fires its engine, adding

1\times10^9\text{ J}

. Determine whether the probe escapes the planet.

Example 18

medium

For a

500\text{ kg}

satellite at

r = 7\times10^6\text{ m}

around Earth (

GM = 4\times10^{14}

), find total mechanical energy.

Example 19

medium

A satellite orbits Earth (

GM = 4\times10^{14}

) at radius

r = 8\times10^6\text{ m}

. Find the period.

Example 20

easy

If a satellite's orbital radius is doubled, by what factor does its speed change (using

v \propto 1/\sqrt{r}

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Related Concepts

Gravity Gravitational Field Centripetal Force Escape Velocity