Question
Show that gravitational field due to a point m ass M at any point is equal to negative gradient of gravitational potential at that point.
Solution
The gravitational potential due to point mass M at a distance r is,
Differentiating the above equation w.r.t. r,
...(1)
The gravitational field due to point mass M at a distance r is,
...(2)
The negative sign is due to sign convention that gravitational field is directed towards the mass.
Therefore, from equation (1) and (2), we get
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Hence, the result.
Differentiating the above equation w.r.t. r,
...(1) The gravitational field due to point mass M at a distance r is,
...(2) The negative sign is due to sign convention that gravitational field is directed towards the mass.
Therefore, from equation (1) and (2), we get
Hence, the result.
