Objects stay firmly on the ground, objects will always fall to the ground, and satellites are kept in orbit due to the planet's gravitational field strength
The weight of any body and the value of the gravitational field strength (g) differs between the surface of the Earth and the surface of other bodies in space, including the Moon, because of the planet or moon's mass
The gravitational field strength on the surface of the Moon is less than on the Earth, meaning it would be easier to lift a mass on the surface of the Moon than on the Earth
The gravitational field strength on the surface of the gas giants (e.g. Jupiter and Saturn) is more than on the Earth, meaning it would be harder to lift a mass on the gas giants than on the Earth
On such planets as Jupiter, an object's mass remains the same at all points in space, but their weight will be a lot greater, meaning for example, a human will be unable to fully stand up