Velocity needed to escape gravitational potential

In summary, the conversation discusses using conservation of energy and angular momentum to determine the direction and behavior of an asteroid's velocity as it approaches infinity. The conclusion is that the velocity will point radially outward at infinity and the angular velocity will tend to zero, but this is not enough to guarantee the direction of travel. The need for considering angular velocity is questioned.
  • #1
Fibo112
149
3
I am solving a problem where I need to decide if an asteroids velocity is high enough to escape the planets gravitational pull. The way I did it was use conservation of energy and angular momentum to find an expression for the radial velocity and show that it remains positive as r tends to infinity. In the solution all that was done was argue that the sum of potential and kinetic energy is positive. I can see how this would work if v0 is pointing radially outward but I don't see why is holds generally. Does it and if so why.
 
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  • #2
At infinity, what direction does the [other end] of the velocity vector point?
 
  • #3
The velocity will point radially outward at infinity
 
  • #4
Fibo112 said:
The way I did it was use conservation of energy and angular momentum to find an expression for the radial velocity and show that it remains positive as r tends to infinity.
That is a good approach. You can probably use the same approach to find an expression for the angular velocity. What does it tend to?
 
  • #5
Well the angular velocity will go to zero in any case where r goes to infinity
 
  • #6
Dale said:
That is a good approach. You can probably use the same approach to find an expression for the angular velocity. What does it tend to?
An angular velocity that tends to zero is not sufficient to guarantee that the tangential velocity also tends to zero. It may be better to reason based on conservation of angular momentum that the tangential velocity must tend to zero.

Further, an angular velocity that tends to zero is not sufficient to guarantee the existence of a limiting direction of travel.

But then I am not completely certain why @Dale is asking you to consider angular velocity in the first place.
 

1. What is the formula for calculating the velocity needed to escape gravitational potential?

The formula for calculating the velocity needed to escape gravitational potential is v = √(2GM/r), where G is the gravitational constant, M is the mass of the object exerting the gravitational force, and r is the distance between the two objects.

2. How does the mass of an object affect the velocity needed to escape gravitational potential?

The mass of an object has a direct relationship with the velocity needed to escape gravitational potential. As the mass of the object increases, the velocity needed to escape also increases. This means that larger objects require more velocity to escape their gravitational pull.

3. Can an object have a velocity greater than the escape velocity?

Yes, an object can have a velocity greater than the escape velocity. In this case, the object will continue to move away from the gravitational source, but its velocity will decrease due to the gravitational force acting against it. However, if the object's velocity is equal to or less than the escape velocity, it will follow a parabolic or elliptical path around the gravitational source.

4. How does the distance between two objects affect the velocity needed to escape gravitational potential?

The distance between two objects has an inverse relationship with the velocity needed to escape gravitational potential. As the distance increases, the velocity needed to escape decreases. This means that objects farther away from each other require less velocity to escape their gravitational pull.

5. What are some real-life examples of the velocity needed to escape gravitational potential?

Some real-life examples of the velocity needed to escape gravitational potential include rockets launching from Earth, satellites orbiting the Earth, and comets passing by the Sun. These objects must reach a certain velocity in order to overcome the gravitational force and escape the gravitational potential of their respective sources.

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