Subject: linear speed
Name: Naomi
Who are you: Student

If the linear speed of a satellite in synchronous orbit is 1000 mi/h, how high is the satellite above the earth?


Hi Naomi.

"Synchronous orbit" is an orbit where the satellite stays located exactly above the same spot on the ground all the time. That means that its angular velocity is the same as the angular velocity of the point on the ground. The angular velocity of any point on the ground is 1 revolution per day, obviously. So that means the angular velocity of the satellite is also 1 revolution per day.

Angular velocity (call this A) is linear speed (call this L) divided by the circumference (call this C) of the orbit. That means: A = L/C which is the same as C = L/A

From the circumference, you can calculate the radius and if you know the mean radius of the planet, you can calculate the altitude of the satellite.

Remember to watch your units! You need to make sure you convert from days to hours!
Stephen La Rocque.

PS: The numbers in your question are very odd, Naomi. I calculate a negative altitude, so check your question and make sure it really says 1000 miles per hour.