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=GM/rv = \sqrt{GM/r}. If rr quadruples, how does vv change?

Example 2

medium
Use T=2πr3/(GM)T = 2\pi\sqrt{r^3/(GM)} to find the period of a low Earth orbit at r=6.7×106 mr = 6.7\times10^6\text{ m} (GM=4×1014GM = 4\times10^{14}).

Example 3

medium
A satellite at r=7×106 mr = 7\times10^6\text{ m} has mass 500 kg500\text{ kg}. Find its gravitational potential energy (GM=4×1014GM = 4\times10^{14}).

Example 4

easy
Find the orbital speed for a low Earth orbit where GM=4×1014GM = 4\times10^{14} and r=6.4×106 mr = 6.4\times10^6 \text{ m}.

Example 5

challenge
A satellite drops to a lower circular orbit (smaller rr). Does its orbital speed increase or decrease, and what happens to its total energy?

Example 6

medium
Escape speed at radius rr is 2\sqrt{2} times the ___ at that radius.

Example 7

medium
Two satellites orbit the same planet at radii rr and 4r4r. Find the ratio of their orbital speeds (inner to outer).

Example 8

medium
A moon orbits a planet with period TT. If a second moon orbits at rr that is 44 times larger, find its period ratio using T∝r3/2T \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=8imes106extmr = 8 imes10^6 ext{ m} around Earth (GM=4imes1014GM = 4 imes10^{14}). Find its orbital speed.

Example 12

easy
A satellite orbits at v=5000 m/sv = 5000\text{ m/s} at radius r=1.0×107 mr = 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 m/sv = 8000 \text{ m/s} at radius r=7×106 mr = 7\times10^6 \text{ m}.

Example 14

medium
What is the escape speed from Earth's surface (GM=4×1014GM = 4\times10^{14}, R=6.4×106 mR = 6.4\times10^6\text{ m})?

Example 15

medium
An astronaut of mass 80 kg80\text{ kg} orbits at r=7×106 mr = 7\times10^6\text{ m} (GM=4×1014GM = 4\times10^{14}). Find the gravitational force on her.

Example 16

hard
A satellite drops from a circular orbit at radius r1=8×106 mr_1 = 8\times10^6\text{ m} to r2=7×106 mr_2 = 7\times10^6\text{ m}. Find the change in orbital speed (GM=4×1014GM = 4\times10^{14}).

Example 17

hard
A 100 kg100\text{ kg} probe in circular orbit at r=1.0×107 mr = 1.0\times10^7\text{ m} (GM=4×1014GM = 4\times10^{14}) fires its engine, adding 1×109 J1\times10^9\text{ J}. Determine whether the probe escapes the planet.

Example 18

medium
For a 500 kg500\text{ kg} satellite at r=7×106 mr = 7\times10^6\text{ m} around Earth (GM=4×1014GM = 4\times10^{14}), find total mechanical energy.

Example 19

medium
A satellite orbits Earth (GM=4×1014GM = 4\times10^{14}) at radius r=8×106 mr = 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∝1/rv \propto 1/\sqrt{r})?
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