Determine the Altitude of a Satellite above Earth Given it's Constant Speed

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SUMMARY

The discussion centers on calculating the altitude of a satellite in a circular orbit with a constant speed of 8.2 x 10^3 m/s. The relevant equations include the centripetal force equation (Fc = FG) and the gravitational force equation (mv^2/r = GMm/r^2). The user initially calculated the radius (r) as 5,931,975 m but encountered a negative number when subtracting the Earth's radius (6.38 x 10^6 m). The correct approach involves using the gravitational parameter (μ = G*M) to derive the altitude, resulting in an altitude of approximately 5948 km.

PREREQUISITES
  • Understanding of circular motion and centripetal force
  • Familiarity with gravitational force equations
  • Knowledge of the gravitational constant (G) and Earth's mass
  • Ability to perform unit conversions between meters and kilometers
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  • Study the derivation of gravitational force equations in orbital mechanics
  • Learn about the implications of centripetal acceleration in satellite motion
  • Explore the concept of gravitational parameters (μ) in orbital calculations
  • Practice solving problems involving satellite altitude and speed using real-world examples
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Students in physics or engineering, satellite communication engineers, and anyone interested in orbital mechanics and satellite dynamics.

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Homework Statement



A remote-sensing satellite travels in a circular orbit at a constant speed of 8.2 x 10^3 m/s. Determing the altitude in kilometres of the satellite above Earth's surface.

Homework Equations



Fc = FG

The Attempt at a Solution



mv^2/r = GMm/r^2
v^2 = GM/r
r = GM/v^2
r = (6.67 x 10^-11 * 5.98 x 10^24)/(8.2 x 10^3)^2
r = 5931975 m - radius of Earth (6.38 x 10^6 m)
r = NEGATIVE NUMBER

Why am I getting a negative number? Is there a mistake in my conversions or am I completely off as to how to solve this? Any help will be greatly appreciated. :)
 
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Using μ = G*M ≈ 400,000 (if you keep things in km), I get V2= 400,000/(8.2)2 = 5948 km.

Maybe it's a fast Earth worm?
 

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