[SF5 7.P.36.] What is the satellite's altitude above the surface of the Earth?

Question

(NOTE: The satellite moves in a circular orbit around the Earth at a speed of 4114 m/s.)

_____ meters

This question is from my Web Assignment from http://www.webassign.com/.

Answer 1

This involves equating the centripetal force of the satellite to the gravitational force due to the Earth. Here, you're assuming things like the Earth being round, no other gravitational forces having an effect etc

We know the centipetal force Fc = (mv^2)/r
and the gravitational force Fg = GMm/r^2

where m = satellite mass
v = satellite velocity
r = Earth-satellite distance (altitude)
M = Earth mass
G = gravitational constant

Need to equate the two, as the satellite is in equilibrium:

GMm/r^2 = mv^2/r
so GM/r = v^2
rearranging: r = GM/v^2

using standard values of G and M (you can get these from somewhere like Wikipedia if you need to site references), but be careful with units (if v was in km/s, G would need to be converted, for example)

G = 6.67E-11
M= 5.97E24

so r = 6.67E-11*5.97E24/(4114^2)
r = 2.35E7 m
or approx 23,500 kms

(compare to a geosynchronous orbit, where r = 42,164km)

Answer 2

The satellite's orbit can vary from 200 to 35,000km above the surface of the earth depending upon the type of satellite.
At an orbital altitude of 200 km (120 mi), a satellite will likely last from a week to three months. At 300 km (190 mi), a satellite may stay in orbit for two years or more. Satellites that orbit above 1,000 km (620 mi) will stay aloft for thousands of years.
There are generally three types of orbits. They are:

1]Geostationary Eqatorial Orbit - The altitude of GEO is about 5.6 times the radius of Earth, or about 35,800 km (about 22,200 mi).

2]Low Earth Orbit - A satellite in low Earth orbit (LEO) orbits at an altitude of 2,000 km (1,200 mi) or less.

3]Medium Earth Orbit - Medium Earth orbit (MEO) satellites orbit at an altitude about 10,000 km (about 6,000 mi)

Answer 3

David M almost has the answer, except he gave you the satellite's radius instead of its altitude above the Earth's surface.

All that's left to do is to subtract the Earth's radius (6378 km) to get the altitude above the surface of the Earth.