Exploring Our Universe: From the Classroom to Outer Space II. The FUSE Satellite Activity #3 Solutions

2.  The measure of angle BOF should be about 27^o. Student answers will vary.

To construct the tangents to the circle from point F:

1. Mark the midpoint of line segment OF.
2. Draw a circle centered at that point with radius equal to half the length OF.
3. The two points where this circle intersects the original circle are the points of tangency.


To see this construction, visit:  http://www.intermath-uga.gatech.edu/tweb/gwin1-01/wilson/tancir/tanconstr.htm

3.  The tangent of a circle is perpendicular to the radius of the circle drawn to the point of tangency.
 

4.

The real space length of the line segment from O to B = ___6360____km

The real space length of the line segment from O to F = ___6360 + 760 = 7120____km

Calculation of the measure of angle BOF: angle BOF is the angle whose cosine is 6360/7120 = 26.7^o

5.
Angles BOF and AOF are congruent because they are corresponding parts of congruent triangles. Triangles OBF and OAF are congruent triangles because they are right triangles (see 3 above) and in which hypotenuse and leg are congruent. Legs OA and OB are congruent because they are radii in the same circle and OF is the hypotenuse of both triangles.
 
 
 
 
 
 
 
 

6.

Let x = The time it takes FUSE to pass through an angle equal to the measure of angle AOB.
The measure of angle AOB is 2 ( 26.7^o )  = 53.4^o

x / 100 minutes =  53.4^o  /  360^o                     x = 14.8 minutes
 

7.  This calculation assumes that the satellite will pass directly over the observing station which is not necessarily the case. To get a feel for the planning of a satellite orbit go to the extension activity. In fact the path of the satellite changes with each orbit.

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

Extension:  A satellite must be placed in geosynchronous orbit to maintain continuous contact with a ground station.