How Strong is the Moon's Gravitational Pull on a 1-kg Mass on Earth?

[needhelp83]

A 1-kg mass at the Earth's surface is gravitationally attracted to Earth with a force of 9.8 N. Calculate the force of gravity with which the 1-kg mass on Earth is attracted to the moon. (The moon's mass is 7.4 x 10^22 kg)

Would this be setup correctly?


F=(G me mb)/r^2

F=(6.67*10^(-11))(7.4*10^22 kg)(5.98*10^24 kg)/(3.84*10^20)^2=1.99*10^20 N

F=ma
F=(1kg)(1.99*10^20 N)=1.99*10^20 N

 

[Doc Al]

Do you really think that your answer makes sense? That an object right on the surface of the huge Earth feels a force of about 10 N towards the earth, but also feels a force a gazillion times bigger pulling it to the smaller and more distant moon?

Hint: You need the gravitational force between Object and Moon, so the only masses involved would be that of the object and the moon.

 

[kyle8921]

Yes, this setup is correct. The force of gravity between two objects can be calculated using the formula F = (G * m1 * m2) / r^2, where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of their masses. In this case, m1 is the mass of the 1-kg object on Earth and m2 is the mass of the moon. The distance between the centers of their masses is the distance between the Earth and the moon, which is approximately 384,400 km (3.84 x 10^8 m). Plugging in the values, we get a force of approximately 1.99 x 10^20 N, which is the force with which the 1-kg mass on Earth is attracted to the moon. This is significantly larger than the force of 9.8 N that the 1-kg mass experiences due to Earth's gravity, showing the strong gravitational pull of the moon.