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

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SUMMARY

The discussion focuses on calculating a satellite's altitude above the Earth's surface, given its orbital speed of 5.1 km/s. Using the gravitational constant G (6.67259 x 10^(-11) Nm^2/kg^2) and Earth's mass (5.98 x 10^24 kg), the formula v^2 = (G * Mearth) / r is applied. The correct altitude calculation results in approximately 8970.99 km after adjusting for Earth's radius (6370 km). The initial error stemmed from a unit conversion oversight.

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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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