Question

The International Space Station (ISS) is inan approximately circular orbit 400 kilometersabove the surface of the Earth. If theground station tracks the space station whenit is within a 45° central angle of thiscircular orbit above the tracking antenna,how many kilometers does the ISS coverwhile it is being tracked by the groundstation? Assume that the radius of the Earthis 6400 kilometers. Round to the nearestkilometer. SHOW YOUR WORK

Answer 1

The key to the question is: If the ground station tracks the space station when

it is within a 45° central angle of this circular orbit above the tracking antenna,

how many kilometers does the ISS cover while it is being tracked by the ground station?

We need to get the arc of the circumference that corresponds to this 45 degrees. This is the "kilometers the ISS cover while it is being tracked by the ground station".

We have the radius of the Earth is 6400km.

The circumference is:

C = 2 * pi * r = 2 * 3.141592 * 6400km

C = 40212.38km

What is the arc of the circumference that corresponds to the central angle of 45 degrees?

The whole circumference is 360 degrees.

Then, the arc is

(45/360) * C

(45/360) * 40212.38km

5026.55km

So, the number of kilometers the ISS cover while it is being tracked by the ground station is 5026.55km