ACTIVITY3

MISSION CONTROL: AN APPLICATION OF ROTATIONAL MOTION AND GEOMETRY
STUDENT ACTIVITY

Your Job on the Mission Operations Team

Think about how many times each day you hear about satellites or make use of satellite applications. Among others, there are communications satellites, weather satellites, global positioning system (GPS) satellites, and satellites carrying research instruments that are advancing our knowledge of the Earth and the universe. Years of work by hundreds of people go into planning, developing, and operating each of these satellites.

Here you will become a member of the FUSE Mission Operations Team. The Mission Operations Team is responsible for sending instructions to the satellite and receiving data from the scientific instrument, so the team must be able to predict the contact times with the ground station. You will estimate the contact time per orbit using concepts from geometry.

Estimating Contact Time

Picture yourself on a satellite looking down on Earth. You can not see Earth's entire surface because you can not see through the planet. In Figure 1, the region of Earth's surface visible to the satellite is shaded. Note that lines drawn to the edge of the shaded region are tangent to the sphere.

This shaded region also represents the only locations that can communicate with the satellite. There can not be communication between points outside the shaded region and the satellite because the satellite’s on-board computer and the ground station communicate by sending signals with antennas. These signals are electromagnetic radiation, like visible light but with longer wavelength, and do not penetrate Earth.

Figure 1. Shaded points can communicate with the satellite. THIS FIGURE IS NOT DRAWN TO SCALE.

1. On a blank sheet of paper draw a scale diagram to show the position of FUSE above the surface of Earth.

a) First draw a circle to represent Earth with radius R = 6360 km and label the center point O.

b) Then draw a point labeled F to represent FUSE 760 km above the surface.

You might be interested to know that FUSE's orbit is higher than a typical space shuttle orbit. Your diagram should give you a feeling for how tenuous Earth's atmospheric layer is; it is a very thin cover for our planet.

2. On your scale diagram, draw the tangents to the circle and label the points of tangency A and B. Draw line segments OF, OA, and OB. Use a protractor to find the measure of angle BOF.

Measure of angle BOF = ____

3. Explain how you know that angle OBF and angle OAF are right angles.

4. Using the numbers given in part 1., fill in the blanks below. Then calculate the measure of angle BOF using right triangle trigonometry.

The real space length of the line segment from O to B = _______km

The real space length of the line segment from O to F = _______km

Calculation of the measure of angle BOF:

Figure 2 NOT DRAWN TO SCALE

5. Explain why the measure of angle AOB is twice the measure of angle BOF.

6. Estimate the time it takes FUSE to pass through an angle equal in measure to angle AOB. Use the fact that it takes FUSE 100 minutes to make one complete orbit around the Earth and that in making one complete orbit FUSE has turned through an angle of 360^o.

7. Your answer to part 6. gives a pretty good estimate for the maximum time the satellite can be in contact with the ground station. Why might the actual contact time be less?

8. If FUSE's orbit was higher, would the contact time be shorter or longer?

Extensions:

Visit http://spacelink.nasa.gov or another source of information about the different types of satellite orbits and then answer the following question:

In which orbit must a satellite be placed in order to have continuous contact with a ground station?

Visit http://fuse.pha.jhu.edu/facts/jhu_team.html and read the biographies of the members of the FUSE Mission Operations Team.What aspects of the job appeal to you? What education and training are needed?
Do a precise calculation of contact time using Satellite Tool Kit.
Go to Technology Notes: Satellite Tool Kit to use a simpler version of the same software used by the FUSE Mission Operations Team to plan a statellite orbit.