From Rita: A surveillance satellite circles Earth at a height of h miles above the surface. Suppose that d is the distance, in miles, on the surface of Earth that can be observed from the satellite.
(a) Find an equation that relates the central angle theta to the height h.
(b) Find an equation that relates the observable distance d and theta.
(c) Find an equation that relates d and h. Answered by Penny Nom.
From Naomi: If the linear speed of a satellite in synchronous orbit is 1000 mi/h, how high is the satellite above the earth? Answered by Stephen La Rocque.
From Jessica: A satellite is orbiting the earth at an altitude of 100 miles. If the angle of depression from the satellite to the horizon is 50 degrees, what is the radius (to the nearest mile) of the planet? Answered by Harley Weston.
From David: Let us suppose some companies have collaborated to place several satellites in orbit. Let us call the set of all satellites that a given company helped place in orbit a network. Finally let us assume the following 4 rules.
There are at least two distinct satellites.
For each pair of satellites there is exactly one network containing them.
Each network contains at least two distinct satellites.
From Katherine Shaw: I have read your information on 'Why are satellite dishes parabolic", and I know the reciever should be placed at the focus of the parabola. Could you test this with lights beams and a parabolic mirror, or would light beams behave differently. Thanks. Answered by Jack LeSage and Harley Weston.
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Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
