Calculating Gravitational Potential

[TalliThePrune]

Homework Statement

:[/B]
"Calculate gravitational potential at point Z, which is 8.10 x 10⁷m away from a planet of mass 1.08 x 10²³. "

(This point is between the planet and a moon, where the gravitational field strength is zero. I'm not sure if that makes a difference. The moon's mass is 4.8 x 10²² and point Z is 5.4 x 10⁷m away from it.).

Homework Equations

V = - G M / r

The Attempt at a Solution

V = - (6.67 x 10^-11) x (1.08 x 10^23) / (8.1 x 10^7)
Therefore
V = - 8.89 x 10^4 J/kg

Is this correct?

Many thanks in advance.

- Talli

 

[PeroK]

Homework Statement

:[/B]
"Calculate gravitational potential at point Z, which is 8.10 x 10⁷m away from a planet of mass 1.08 x 10²³. "

(This point is between the planet and a moon, where the gravitational field strength is zero. I'm not sure if that makes a difference. The moon's mass is 4.8 x 10²² and point Z is 5.4 x 10⁷m away from it.).

Homework Equations

V = - G M / r

The Attempt at a Solution

V = - (6.67 x 10^-11) x (1.08 x 10^23) / (8.1 x 10^7)
Therefore
V = - 8.89 x 10^4 J/kg

Is this correct?

Many thanks in advance.

- Talli

Why can you ignore the gravity of the moon?

 

[TalliThePrune]

Why can you ignore the gravity of the moon?

Whoops! Sorry moon. Does this mean I calculate V for both the planet and the moon, and add the two?

So for the moon...
V = - (6.67 x 10¹¹) x (4.8 x 10²²) / (5.4 x 10⁷)
V = - 5.93 x 10⁴

 

[PeroK]

Yes. It's good that you wanted to add them and not subtract them!

 

[TalliThePrune]

Yes. It's good that you wanted to add them and not subtract them!

Wonderful! I won't say I didn't consider it for a minute... But that would imply one field disappears with the presence of another, so no!

So V_Planet + V_moon:
- 5.93 x 10⁴ + - 8.89 x 10⁷ = - 1.429 x 10⁸

Thanks so much for your help.