Determining the satellite's altitude above the surface of the Earth

AI Thread Summary
To determine a satellite's altitude above Earth's surface, the orbital speed of 5.1 km/s is used along with the gravitational constant and Earth's mass. The formula v^2 = (G * Mearth) / r is applied, leading to a calculated radius of approximately 15,340,985.32 meters. After subtracting Earth's radius of 6,370,000 meters, the altitude is found to be about 8,970.985321 kilometers. The initial confusion arose from a unit conversion error, which was resolved during the calculation process. Accurate unit conversion is crucial in orbital mechanics calculations.
torquey123
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Homework Statement



A satellite moves in a circular orbit around the Earth at a speed of 5.1km/s.
Determine the satellite's altitude above the suface of the Earth. Assume the Earth is a homogenous sphere of radius Rearth= 6370km, and mass Mearth=5.98x10^24 kg. You will need G=6.67259x10^(-11) Nm^2/kg^2. Answer in units of km

Homework Equations



v^2=(G*Mass of earth)/(radius)


The Attempt at a Solution



(5100 km/s)^2 = (6.67259x10^(-11))(5.98x10^(24))/r

26010000r=3.990190282e14

r= 15340985.32 - 6370000= 8970985.321m = 8970.985321km

i think its wrong, but i don't know where i made the mistake..
 
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never mind...i figured it out when i typed it out...i didnt convert back to km :o
 
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