Gravitational force is a centripetal force so it provides centripetal acceleration only and no tangential acceleration.

Gravitational Force and Radial Acceleration

Gravitational force is a fundamental force of nature that attracts objects with mass towards each other. It is responsible for keeping celestial bodies, such as planets and moons, in their orbits around larger objects like the Sun. When we consider the motion of objects under the influence of gravitational force, we can distinguish between radial and tangential acceleration.

Radial Acceleration
- Radial acceleration is the acceleration directed towards or away from the center of an object's circular path. It is also known as centripetal acceleration.
- In the context of gravitational force, radial acceleration refers to the acceleration of an object towards the center of the gravitational field, which is typically the center of the attracting object (e.g., the Sun or Earth).
- The magnitude of the radial acceleration is given by the formula a_r = v^2/r, where v is the tangential velocity of the object and r is the distance between the object and the center of the gravitational field.
- Radial acceleration is responsible for keeping objects in circular orbits. In the case of planets orbiting the Sun, the gravitational force provides the necessary centripetal force to maintain the circular motion.

Tangential Acceleration
- Tangential acceleration, as the name suggests, is the acceleration that acts tangentially to the object's circular path.
- In the context of gravitational force, tangential acceleration refers to the change in an object's speed along its orbit. It is responsible for increasing or decreasing the object's tangential velocity.
- Tangential acceleration is not directly provided by the gravitational force but is influenced by it. As an object moves closer to or farther from the center of the gravitational field, the gravitational force changes its potential energy, which in turn affects its kinetic energy and hence its tangential velocity.
- If the gravitational force does work on the object, converting potential energy to kinetic energy, the object's tangential velocity increases, resulting in a tangential acceleration.
- On the other hand, if the object moves against the gravitational force, work is done by the object, converting kinetic energy into potential energy and reducing its tangential velocity. This leads to a tangential deceleration or negative acceleration.

Summary
In summary, gravitational force provides the radial acceleration necessary to keep objects in circular orbits around a larger attracting body. It acts as the centripetal force that continuously changes the direction of the object's velocity towards the center of the gravitational field. However, tangential acceleration, which affects the object's speed along the orbit, is not directly provided by the gravitational force. It is influenced by changes in the object's potential and kinetic energy as it moves closer to or farther from the center of the gravitational field.