What is the gravitational potential due to a point mass m at a distance from it? (G = gravitational constant)
Question 1 Report
What is the gravitational potential due to a point mass m at a distance from it? (G = gravitational constant)
Answer Details
The gravitational potential due to a point mass m at a distance r from it is given by the expression:
- -Gm/r
Here, G is the gravitational constant which has a fixed value, m is the mass of the point source and r is the distance between the point source and the point at which we want to calculate the gravitational potential. The negative sign indicates that the gravitational potential decreases with an increase in distance from the source.
This expression is derived from the equation for gravitational potential energy, which is given by:
- U = -GmM/r
where M is the mass of the object that is being attracted by the point source. The negative sign indicates that the potential energy of the system decreases as the two masses move closer to each other.
The gravitational potential is the potential energy per unit mass, so dividing both sides of the above equation by M, we get:
- V = U/M = -Gm/r
Therefore, the gravitational potential due to a point mass m at a distance r from it is -Gm/r.
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