Escape velocity question - constant is wrong....

In summary, escape velocity is the minimum speed required for an object to break free from the gravitational pull of a celestial body. It is calculated using a formula that takes into account the body's mass and distance from the object's starting point. Escape velocity is not a constant value and varies depending on the mass and size of the celestial body. It is directly proportional to the mass of the body, meaning that as the mass increases, so does the escape velocity. It is incorrect to assume that escape velocity is the same for all celestial bodies, as it can vary even on different points of the same body. Escape velocity plays a crucial role in space travel and rocket launches, as it determines whether a spacecraft can successfully leave Earth's orbit.
  • #1
maxelcat
32
3
Homework Statement
A planet of mass M and radius R rotates so quickly that material at its equator only just remains on its surface.
What is the period of rotation of the planet?

This is a multiple choice question. I must be doing something wrong.9
Relevant Equations
V=-GMm/R=0.5mv^2
This is a multiple choice question. I assumed that this is an escape velocity question. I have been going round and round...
Here's what I have done:
1663239000057.png
 
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  • #2
It is not an escape velocity question. You do not require escape velocity to just orbit at a fixed radius.
 
  • #3
Also you made an arithmetic error. Your answer should be wrong by √2
 
  • #4
yes - found that.
 
  • #5
and yes, it is not an escape velocity question. D'oh - I see that now.

Thanks
 
  • Like
Likes berkeman

1. What is escape velocity?

Escape velocity is the minimum speed required for an object to escape the gravitational pull of a celestial body, such as a planet or moon.

2. How is escape velocity calculated?

Escape velocity is calculated using the formula v = √(2GM/r), where v is the escape velocity, G is the gravitational constant, M is the mass of the celestial body, and r is the distance from the center of the celestial body to the object.

3. Why is the constant in the escape velocity formula considered wrong?

The constant in the escape velocity formula, G, is not considered wrong but rather it is an approximation. The actual value of G varies slightly depending on the location and composition of the celestial body.

4. Can escape velocity be achieved by any object?

Yes, any object can achieve escape velocity as long as it has enough energy and is not hindered by external forces such as air resistance.

5. What happens to an object that reaches escape velocity?

An object that reaches escape velocity will continue to move away from the celestial body it was launched from and will eventually enter into a stable orbit around it or travel into space.

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