Get equation for velocity of a satellite

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SUMMARY

The discussion focuses on deriving an equation for the velocity of a satellite orbiting Earth, given the gravitational constant (G = 6.67 x 10^-11 nm^2/kg^2), Earth's mass (ME = 5.98 x 10^24 kg), and the orbital period (T = 1.20 x 10^4 s). Participants emphasize the need to eliminate the radius (r) from the equations V = √(GM/r) and V = 2πr/T. The solution involves rearranging one equation to express r and substituting it into the other, thus deriving a velocity equation that does not require a numerical value for r.

PREREQUISITES
  • Understanding of gravitational physics and orbital mechanics
  • Familiarity with the gravitational constant (G) and its application
  • Knowledge of the mass of Earth (ME) and its significance in orbital calculations
  • Ability to manipulate algebraic equations for derivation
NEXT STEPS
  • Study the derivation of orbital velocity equations in gravitational physics
  • Learn about Kepler's laws of planetary motion and their applications
  • Explore the concept of centripetal force in relation to satellite motion
  • Investigate the implications of varying orbital periods on satellite velocity
USEFUL FOR

Students in physics, aerospace engineers, and anyone interested in satellite dynamics and orbital mechanics.

rcrx
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Derive an equation for the velocity around Earth. Satellite has no mass. Radius not given. Only period, G, and ME (earth)

G = 6.67X10^-11 nm^2/kg^2 | Earth = 5.98x10^24 kg | Period = T = 1.20x10^4s

I know I can find radius, and then find velocity. But I am supposed to derive an equation to suit the given information.

Homework Equations


V = √GM/r
V = 2πr / T

The Attempt at a Solution


I'm not positive about my ability to cut r from the equations and merge them?
 
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You say that you know that you can solve for radius and then find velocity, but you're supposed to derive an equation to suit the given information.

Well, solving for radius and then velocity is in a way doing what they asked, except just don't solve for r numerically!

Re arrange one of the equations so it's r = [...] and then put the [...] in as r for the other equation.
 

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