Calculate Earth's Gravitational Field at the Moon

[O0ZeRo00]

The Moon's mass is 7.34x10^22 kg, and it is 3.8x10^8 m away from Earth. Earth's mass is 5.97x10^24 kg.

(a) Calculate the gravitational force of attraction between Earth and the Moon.
I already did that. It's 2.01e+20.

(b) Find Earth's gravitational field at the Moon.
This is the part I'm having trouble with. Could someone please explain to me how to do this?

 

[denverdoc]

How do we get 9.8m/s^2 on the earth? Basically I think they want you to ignore the moons mass, and compute a new "g" , not at the Earth's surface but at a distance from the center of the Earth to the moons surface. Here, the distance given from the Earth to the moon will be the quantity you use as accuracy won't suffer too much.

 

[kerimek]

To calculate Earth's gravitational field at the Moon, we can use the equation F = G (m1m2)/r^2, where F is the force of attraction, G is the gravitational constant (6.67x10^-11 Nm^2/kg^2), m1 and m2 are the masses of Earth and the Moon respectively, and r is the distance between them.

Substituting the given values, we get:

F = (6.67x10^-11 Nm^2/kg^2) (5.97x10^24 kg) (7.34x10^22 kg) / (3.8x10^8 m)^2

Simplifying, we get:

F = 1.99x10^20 N

To find the gravitational field, we divide this force by the mass of the Moon (7.34x10^22 kg), giving us:

g = F/m2 = (1.99x10^20 N) / (7.34x10^22 kg) = 2.71x10^-3 N/kg

Therefore, Earth's gravitational field at the Moon is 2.71x10^-3 N/kg. This means that for every kilogram of mass on the Moon, it will experience a force of 2.71x10^-3 Newtons towards the Earth due to gravity.