What is the Escape Velocity of a Satellite in Orbit?

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SUMMARY

The escape velocity (EV) from a planet, given a satellite's orbital speed of 7080 m/s, can be calculated using the relationship EV = sqrt(2) * v_o, where v_o is the orbital speed. By substituting the known value, the escape velocity is determined to be approximately 10,000 m/s. This calculation utilizes the formula EV = sqrt(2GM/r) and the orbital speed formula v_o = sqrt(GM/r). The mass of the planet and the radius of the orbit are not required for this specific calculation.

PREREQUISITES
  • Understanding of gravitational physics and orbital mechanics
  • Familiarity with the formulas for escape velocity and orbital speed
  • Knowledge of the gravitational constant (G)
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of the escape velocity formula EV = sqrt(2GM/r)
  • Explore the relationship between orbital speed and gravitational force
  • Learn about the gravitational constant (G) and its significance in astrophysics
  • Investigate real-world applications of escape velocity in satellite launches
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Astronomy students, physics enthusiasts, and aerospace engineers will benefit from this discussion, particularly those interested in satellite dynamics and orbital mechanics.

mike91
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Homework Statement


A satellite is in orbit around a planet with orbital speed determined to be 7080 m/s. Find the escape velocity from the planet from this position of its orbit.


Homework Equations


EV=sqrt(2GM/r)


The Attempt at a Solution


With a problem like this, I would just plug in the mass of the planet and its radius, but they aren't given in the statement, and nor is the satellite's position. It seems like I don't have enough information, but I'm likely missing one relevant formula. I've scanned my notes and can't find a solution - just a push in the right direction would be much appreciated.
 
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The orbital speed is given. How is it related to the radius of the orbit and the mass of the planet?

How would you get the escape velocity from a distance R from the centre of the planet of mass M?

ehild
 
So since the satellite is likely much less massive than the planet it is orbiting, the orbital speed can be written as
v_o=sqrt(GM/r)..
EV = sqrt(2GM/r), so I can rewrite that as sqrt(GM/r) = EV/sqrt(2) and I get
v_o = EV/(sqrt(2)).
I have v_o = 7080, so solving for EV I get EV = sqrt(2)*v_o, or EV = 1.00*10^4. Aannd that's right, thanks for the help!
 

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