This is just a series of thoughts leading to a “conclusion”. I would appreciate comments/criticism, please.

1. Velocity is a vector which includes speed and direction.

2. Acceleration is change in velocity.

3. Change of speed with constant direction = acceleration.

4. Change of direction with constant speed = acceleration.

5. A body orbiting at constant speed is constantly accelerating.

6. Gravity is not a force that holds an orbiting body as though it were on a string.

7. Gravity alters the geometry of spacetime such that it becomes (or acts as though) curved.

8. The curve thus formed is a geodesic, and is defined as the most direct path from A to B in curved spacetime.

9. Thus, a geodesic is equivalent to a straight line in flat (non-curved) spacetime.

10. A body travelling at constant speed in a straight line in flat spacetime is not accelerating.

11. It should be reasonable to argue that a body following a geodesic at constant speed is not accelerating.

12. It should, therefore, be reasonable to conclude that an orbiting body is not accelerating.