Nope. Not even the gravity felt by a satellite as it passes over the surface of the Earth is consistent. That's why corrections are needed for their orbit calculations. This correction is built into the GPS constellation, for example, by using ground stations to reference by.
Earth has different densities from place to place on the surface, you see.
The gravity at the Moon is different from the gravity at the Earth.
The gravity at any point in space is a combination of all particles in space, along with the distance to them.
Even Newton has shown that gravity is not consistent. His theory of gravitational attraction has never been falsified.
F=G(m1*m2)/r^2
where F = gravitational force in Newtons,
G is a constant (6.674 * 10^-11),
m1 and m2 are two masses,
and r is the radius between them (their centers of mass), in meters.
This equation works anywhere on or in the Earth or in space.
F is the sum of the effect of all particles at any point in space.
It is why Jupiter can cause a 'tide' on the Sun.
It is why the Moon doesn't orbit the Earth. They orbit each other around a point called the barycenter (about 2900 miles from the center of Earth, just 1050 miles below the surface).
The inconsistent gravity is what causes the tides to rise and fall twice a day.
Even the land has a 'tide'. It rises and falls due to the inconsistent gravity twice a day, just as the sea near a shoreline does...just not as much.
And Earth does the same to the Moon. The only difference is that the Moon has no ocean.
There are five points called Lagrange points, where the gravitional forces between Earth and Moon are balanced. A satellite place there will stay there. Two of them require no fuel to stay there at all (like being at the bottom of a valley). The other three can stay there, but require continuous small course corrections due to other forces pushing them away (like balancing on top of a peak).
Gravity is inconsistent. It is not the same everywhere.