By Consumer Dummies

Using physics, you can calculate the orbital speed and radius of an object as it revolves around another one. For example, given the orbital speed of a satellite around Earth, you can calculate the satellite’s orbital radius.

Here are some practice questions that you can try.

Practice questions

  1. A satellite orbits Earth at an altitude of 400 kilometers above the planet’s surface. What is its speed in meters per second?

    Round your answer to three significant digits.

  2. The GMVX satellite is “pulled” along by the force of Earth’s gravity at a speed of 1,200 meters per second. How many kilometers from Earth’s center is the GMVX located?

    Round your answer to two significant digits.

Answers

The following are the answers to the practice questions:

  1. image0.png

    Use the orbital velocity equation:

    image1.png

    where G is the gravitational constant, m is the mass of the central body — in this case, Earth — and r is the distance from the satellite to Earth’s center (in meters). First, convert 400 kilometers to the correct units:

    image2.png

    If the radius of Earth is

    image3.png

    then the distance r from the center of Earth to the satellite is:

    image4.png

    Here, h is the altitude of the satellite above the Earth’s surface.

    Therefore, substituting that value along with the mass of Earth into the orbital velocity equation yields:

    image5.png

  2. image6.png

    Use the orbital velocity equation,

    image7.png

    where m is the mass of the orbited body (here, Earth) and r is the distance the orbiting object (the satellite) is separated from the center of the body it’s orbiting.

    image8.png

    Now convert to kilometers:

    image9.png