Question

If the distance between two masses is increased by a factor of 5, by what factor would the mass of one of them have to be altered to maintain the same gravitational force ? Would this be an increase or decrease in the mass ?

Answer 1

F (gravitational force) = ?
G (gravitational constant) = G
M (mass of sun) = M
m (mass of the earth)= m
d (average distance between sun and earth) = increased by 5 times than Rest all variables remain constant
`F = (GM  m)/d^2`
`F = (GM  m)/(5d)^2`
`F = (GM  m)/(25  d^2)`
(NOTE – To maintain the same gravitational force, the mass should be increased by 25 times)
`F = (GM   25m)/(25  d^2)`
`F = (GM  m)/d^2`
There would be an increase in mass .