How far above the earth's surface is the satellite's orbit?

Question

Suppose you are at the earth's equator and observe a satellite passing directly overhead and moving from west to east in the sky. Exactly 13 hours later, you again observe this satellite to be directly overhead.

Answer 1

There is a wide range of altitudes at which satellite orbit the earth. Let's talk about the common satellites for communication and television. They are roughly 35,786 km above sea level. That's about 100,000,000 feet. Compared to this, jet planes, at 30Kft, appear crawling on the ground.

Answer 2

the radius of the earth..

Answer 3

This was a bit of a pain, the equation you'd want to use is

T = (2pi*r^(2/3))/squareroot(GM)

which is equals

R = (T*(GM)^1/2/2pi)^(2/3)

Mass of Earth = 5.97E24 kg

Radius of Earth = 6.38E6 meters

G = 6.67E-11 N*m^2/kg^2

Final Equation is

R = (T*(GM)^1/2/2pi)^(2/3) - RadiusofEarth

Keep in mind the orbital period is given in hours so you'll need to convert to seconds i.e. 13*60*60

ALSO keep in mind that the earth is rotating every 24 hours.  So a sattelite going from west to east is going to take less than 13 hours to be directly overhead.  i.e.  13/(1+13/24) = 8.432432432... hours for a full revolution

If you need to do the reverse, simply calculate the sattelite traveling in the opposite direction, which should amount to a long orbital period.

Answer 4

You should use the following formula: http://en.wikipedia.org/wiki/Circular_or...

(If the orbit is circular)

T is 13 hours, corrected for the rotation of Earth. Since satellite is going from west to east, it orbits in the same direction as Earth rotates. I.e. the actual T is shorter.