A Satellite Phone Call

vendredi 28 février 2014

1. The problem statement, all variables and given/known data

A communications satellite is in a synchronous orbit that is 3.33×107 m directly above the equator. The satellite is located midway between Quito, Equador, and Belem, Brazil, two cities almost on the equator that are separated by a distance of 3.30×106 m. Calculate the time it takes for a telephone call to go by way of satellite between these cities. Ignore the curvature of the earth.

2. Relevant equations

Time= Speed / distance

Speed of Sound: 340.29 m/s

a^2 + b^2 = c^2

3. The attempt at a solution

So, I started by drawing what was going on and it turned into a equilateral triangle which I made into two right triangles.

I divided the distance between Quito and Belem in half (3.30 E 6)/2 = 1,650,000 m and I solved for the distance between Quito and the Satellite by using Pythagorean theorem: c^2=b^2+a^2

c^2 = (1,650,000)^2 + (3.33 E 7)^2

c^2 = (2.72 E 12) + (1.108 E 15)

Sqrt(c^2) = Sqrt((2.72 E 12) + (1.108 E 15))

c = 5.49 E 13 m

C is the distance from Quito to the Satellite and so then, the distance from the Satellite and Belem would also be 5.49 E 13 m. Which would mean the total distance that the call would have to travel is 1.0989 E 14 m.

The formula for Speed is Speed=Distance/Time which can be rewritten as Time=Distance/Speed. The speed of sound constant is 340.29 m/s.