100 pointsa communications satellite is in a synchronous orbit 22,000 miles above earth’s surface. points b and d in the figure are points of tangency of the satellite signal with the earth. they represent the greatest distance from the satellite at which the signal can be received directly. point c is the center of the earth. 3. how much longer does it take a satellite signal to reach point b than it takes to reach point e? use 186,000 mi/sec as the speed of a satellite signal. round your answer to the nearest hundredth. show your process and explain your reasoning. 4. the satellite is in orbit above the earth’s equator. along with the point directly below it on the earth’s surface, the satellite makes one complete revolution every 24 hours. how fast must it travel to complete a revolution in that time? round your answer to the nearest whole number. show your process and explain your reasoning.

3)

check the picture below.

bearing in mind that the point of tangency, the green one there, is always a right-angle, then we get that much for the distance AB.

since the satellite can emit a signal at a speed of 186,000 miles/second, how long will it be to cover AB?  well, it'll just be AB/186000, which is about 0.1381 seconds.

and how long will it be to cover the distance AE?  well, it'll just be AE/186000, which is about 0.11828 seconds.

of course is quicker to AE since it's closer, so the difference for both distances will be AB - AE, which is about 0.01984121052328095721 seconds.

4)

if the satellite makes a revolution, or 2π, in 24 hours, and we know the satallite is orbiting at 22000+4000 or 26000 miles from the center of the Earth, thus its circular orbit has a radius of 26000, how many miles is that?

well, Circumference of a circle is C = 2πr, if r = 26000, then C = 2π(26000), so on those 24 hours it has covered 52000π miles.

how fast must it travel then?    

now if you need the rate in miles/seconds, bear in mind that an hour has 60 minutes and each minute 60 seconds, thus and hour has 60*60 seconds or 3600, thus its speed in miles/seconds will be 52000π/3600.