A communications satellite is in a synchronous orbit 18,000 miles above an alien planet's surface. Points B and D in the figure are points of tangency of the satellite signal with the planet. They represent the greatest distance from the satellite at which the signal can be received directly. Point C is the center of the planet, which has a radius of 3,500 miles.
Satellite diagram with satellite at point A, planet with center c and points of tangency with A at B and D. Radius of planet is 3,500 mi and distance from edge of planet to satellite is 18,000 mi.
Find distance
. Round to the nearest mile. Show your process and explain your reasoning.
m∠BAC = 9.4°. If the circumference of the circle represents the the planet's equator, what percent of the planet's equator is within range of the satellite’s signal? Show your process and explain your reasoning.
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.
The satellite is in orbit above the planet's equator. Along with the point directly below it on the planet's surface, the satellite makes one complete revolution every 36 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.
