Solving for gravitational pull

[jaff]

How far from Uranus must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances Uranus's pull?


Fg=Gm1m2/r^2


Would m1 be the sun's mass and m2, Uranus' mass. then what would Fg be?

 

[SammyS]

How far from Uranus must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances Uranus's pull?

Fg=Gm1m2/r^2

Would m1 be the sun's mass and m2, Uranus' mass. then what would Fg be?

Hello jaff. Welcome to PF !

If m₁ is the sun's mass and m₂, Uranus' mass,

and also of r is the distance Uranus is from the sun, then F_g=Gm₁m₂/r^2 is the force the sun exerts on Uranus.

 

[jaff]

thank you,

but its asking for the distance (km)

 

[SammyS]

thank you,

but its asking for the distance (km)

Then one piece of information you will need is the distance that Uranus is from the sun.

Other information you will need are the masses of the sun and Uranus, or at least the ratio of their masses.

You will need to express the force that Uranus exerts on the probe.

You will need to express the force that the sun exerts on the probe.

You will need to equate those two forces.

 

[Nickie]

Yes, in this equation, m1 would represent the mass of the Sun and m2 would represent the mass of Uranus. Fg stands for force of gravity. To solve for the distance, r, at which the Sun's gravitational pull balances Uranus's pull, we would need to set the two forces equal to each other. This would result in the equation:

Gm1m2/r^2 = Gm1m2/d^2

Where d represents the distance from Uranus to the space probe. We can then solve for d by rearranging the equation:

d = r * √(m1/m2)

Therefore, the distance from Uranus to the space probe would need to be r * √(m1/m2) along the line towards the Sun in order for the Sun's gravitational pull to balance Uranus's pull on the probe.