Mass of object in Escape velocity

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SUMMARY

The escape velocity does depend on the mass of the escaping body, but its effect is negligible for practical purposes. The equation for escape velocity is given by v_e = √(2G(M+m)/r), where M is the mass of the central body, m is the mass of the escaping body, G is the gravitational constant, and r is the distance from the center of the central body. For Earth, the escape velocity from Low Earth Orbit (LEO) is approximately 11 km/s, and the mass of the escaping object must be around 10^15 kg to measurably affect this velocity, which is impractical for current space missions.

PREREQUISITES
  • Understanding of gravitational physics
  • Familiarity with the gravitational constant (G)
  • Knowledge of the concept of escape velocity
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of escape velocity equations
  • Explore gravitational effects on different celestial bodies
  • Learn about the implications of mass in orbital mechanics
  • Investigate the engineering challenges of launching massive payloads into orbit
USEFUL FOR

Aerospace engineers, physicists, students of gravitational physics, and anyone interested in the mechanics of space travel and orbital dynamics.

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Why doesn't the escape velocity depend upon the mass of body?
 
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asmalik12 said:
Why doesn't the escape velocity depend upon the mass of body?
Why doesn't the height reached by a tossed ball depend on the mass of the ball? Same thing. (As is often the case when dealing with gravity, the mass drops out.)
 
asmalik12 said:
Why doesn't the escape velocity depend upon the mass of body?
It does. The correct equation is

[tex]v_e = \sqrt{\frac{2\,G(M+m)}r}[/tex]

The capital M denotes the mass of the central body, the little m, the mass of the escaping body.

Now think about how big that little m needs to be to make any measurable difference in the velocity needed to escape Earth orbit. Escape velocity from LEO is about 11 km/s. Suppose we can measure velocity down to the micrometer/second range, or 10 significant digits. That corresponds to a mass of 1015 kg, or the mass of about 100 mountains.

We aren't going to launch a 100 mountain mass out of Earth orbit any time soon.
 

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