Question

Suppose that Planet Q exists such that it is an identical planet to Earth yet orbits the sun at a distance of 5 AU. How does the amount of gravitational force exerted on Planet Q by the sun compare to the amount of gravitational force exerted on Earth by the sun

Answer 1

Force on planet Q =
`(1)/(25) F_e`

Step-by-step explanation:

given,

Planet Q is identical to planet Earth.

Distance of the planet Q is 5 AU

distance between earth and sun = 1 AU

to calculate the gravitational force on the Q by the sun in comparison with the gravity on earth.

we know the equation of gravitation force between two bodies

`F = G(mM)/(r^2)`

as planet Q is identical so mass will be same.

so from the above equation we can clearly see that the force is inversely proportional to square of distance.

force on earth (F e)=
`F = G(mM)/(1^2)`

force on planet Q =
`F = G(mM)/(5^2)`

on comparison

Force on planet Q =
`(1)/(25) F_e`