# Calculate Earth's Gravitational Field at the Moon

• O0ZeRo00
In summary, the Moon has a mass of 7.34x10^22 kg and is 3.8x10^8 m away from Earth, while Earth's mass is 5.97x10^24 kg. The gravitational force of attraction between the two is 2.01x10^20, while the gravitational field at the Moon can be calculated by ignoring the Moon's mass and using the distance from the center of the Earth to the Moon's surface.
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?

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.

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.

## 1. How do you calculate Earth's gravitational field at the Moon?

To calculate Earth's gravitational field at the Moon, you can use the formula F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of Earth and the Moon, and r is the distance between them.

## 2. What is the gravitational constant?

The gravitational constant, denoted by G, is a fundamental constant in physics that is used to calculate the force of gravity between two objects. Its value is approximately 6.67 x 10^-11 N*m^2/kg^2.

## 3. How is the gravitational field different from the gravitational force?

The gravitational field is a measure of the force per unit mass exerted by a massive object, while the gravitational force is the actual force exerted on an object due to the presence of another object's mass.

## 4. Why is the gravitational field at the Moon different from that at Earth?

The gravitational field at the Moon is different from that at Earth because the Moon has a much smaller mass and radius compared to Earth. This means that the force of gravity exerted by the Moon on an object is significantly weaker than the force of gravity exerted by Earth on the same object.

## 5. Can the gravitational field at the Moon change?

Yes, the gravitational field at the Moon can change depending on the position of the Moon in relation to other celestial bodies, as well as any changes in its mass or radius. However, these changes are usually very small and not easily detectable.

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