A satellite of mass 150 KG launched 3000km above the earths surface What is the speed?
A satellite of mass 150kg is launched 3000km above the earths surface. A. What is the speed of the satellite in its orbit? B. What is providing the centripetal force on it? What is its value? C. What is the time period of the satellite?
Please capitalize Earth. It’s a proper noun, just like London or Mexico.
It’s not clear in this problem how many significant digits of accuracy we are dealing with, but 3 digits would be generous. We should keep at least 5 digits during our calculations and then round off our answers to 3 digits.
At 3000km above Earth’s surface, the satellite is 9370km from the center of the Earth. Its weight at that height is 150*9.80*(6370/9370)^2 = 679.387 Newtons. This is the centripetal force, the force of gravity. Now we can use F = mv^2/r to find the orbital velocity.
F = m * v^2 / r
note: we need the radius in meters, not km
679.387 = 150 * v^2 / 9370000
42439042 = v^2
6514.5 = v
This is the orbital velocity in meters per second.
The total length of its orbit is 2*pi*9370 = 58873km, or 58873000 meters.
Divide this number by 6514.5 and we’ll know how many seconds it takes to complete 1 orbit.
58873000 / 6514.5 = 9037.2 seconds
so the answers are:
A) 6510 m/s
B) gravity. 679 N
C) 9040 s