Somewhere between Earth and the Moon, gravity from these two bodies on a space pod would canel. Is it closer to the Earth or the Moon? why?
force on pod proportional to mass of object/distance squared
mass of earth >>mass of moon
therefore distance from moon must be smaller to get same force magnitude from each.
It is closer to the moon because the moon has less mass. For the two forces to be equal and opposite, you must have
Mearth/Rearth^2 = Mmoon/Rmoon^2
Therefore Rearth/Rmoon
= sqrt(Mearth/Moon)
which is greater than 1
To determine whether the cancelation of gravity between Earth and the Moon would occur closer to the Earth or the Moon, we need to compare the strengths of their gravitational forces.
The force of gravity between two objects depends on the mass of the objects and the distance between their centers. The formula to calculate the force of gravity is F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
The mass of Earth is much larger than the mass of the Moon, which means the force of gravity from Earth is stronger. However, the distance between the Earth and the Moon is much larger than the distance between the space pod and either body, which means the force of gravity from both the Earth and the Moon decreases as we move away from them.
For the gravity from Earth and the Moon to cancel out, the force of gravity from each body must be equal. Since the force of gravity from Earth is initially stronger, there will be a point between the Earth and the Moon where it will weaken enough to become equal to the force of gravity from the Moon.
In this case, the cancelation of gravity occurs closer to the Earth because the gravitational force from the Earth initially dominates and gradually decreases as we move away from it.