The satellite moves under the influence of the Earth's gravitational force, which is a central force always directed towards the centre of the Earth. According to Newton's Second Law, the acceleration is in the direction of the net force; thus, the acceleration of the satellite is always directed towards the centre of the Earth.

Regarding the other options:

1. Since the gravitational force passes through the centre of the Earth, the torque about the centre is zero. Therefore, the angular momentum is conserved (constant in both magnitude and direction).
2. The gravitational field is conservative, so the total mechanical energy (kinetic + potential) remains constant.
3. In an elliptical orbit, the speed of the satellite varies (fastest at perigee, slowest at apogee), so the magnitude of linear momentum ($p=mv$) is not constant.