Every action has an equal and opposite reaction. The force of attraction between a satellite and the Earth is due to the gravitational force of attraction between two bodies. This is equal to `F = (G*m_1*m_2)/r^2` where `m_1` and `m_2` is the mass of the bodies, r is the distance between their center of gravity and G is a constant.
The force with which the satellite is attracted by the Earth is the same as the force with which the satellite attracts the Earth. The difference in the the effect of this force on the two is due to the fact that the mass of the Earth is much greater than the mass of a satellite.