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