Education Technology

Space Trajectories

Published on 06/09/2008

Activity Overview

In this activity, students will explore different models for the motion of satellites. They work with two-and three-body problems, and consider both artificial and natural satellites.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 95 - 104 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:
    A Geosynchronous Orbit:

  • Enter the values for a satellite in geosynchronous orbit with velocity in m/s, time in seconds and radius in meters
  • Convert the second order system of two equations in two unknown functions into a first order system in four unknowns.
  • Set initial conditions
  • Change settings to view the plotting position as it moves two revolutions
  • Use equally scaled axes to make the plot resemble a circle


  • A Shuttle Orbit:
  • Use the same equation as in the first example and find the radius and the velocity needed for a low earth orbit
  • Change the initial conditions and the window parameters and graph the new orbit
  • Use the circle command to plot the surface of the earth
  • Solve the differential equation


  • Hohmann Transfer Orbit:
  • Calculate the parameters and plot the hohmann transfer orbit needed to go from a low-earth shuttle orbit to a geosynchronous orbit
  • Compute the two changes in velocity needed (by rocket booster) δv1 and δv2
  • Compute the total period time for the transfer orbit
  • Plot the transfer orbit using the circle command


  • An Orbit Near Lagrange point:
  • Enter the set of differential equations that model the movement of the earth, moon, and an artificial satellite
  • Verify the stationary point for this system
  • Change settings to view the resulting trajectory


  • A Trip From Near Earth to Near the Moon:
  • Set initial conditions and store location of the earth and the moon to create lists
  • Use stat scatter plot to mark location of two larger bodies
  • Plot the restricted three-body trajectory
  • After the Activity

    Students complete the problems on the exercise page.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary