I understand that a central force is one always pointing to the same fixed point, in the same direction (parallel) as the position vector $\mathbf r$, and whose magnitude only varies depending on the magnitude of $\mathbf r$ (the distance to the fixed point).
So am I correct in assuming that gravitational attraction between a planet orbiting the Sun is a central force. I was unsure because the force acts towards the centre of the system but I thought it was perpendicular to the position vector of the planet.
Also, say if you have a ball that you throw vertically up in the air, is gravity a central force in this case ? And the same for a projectile ?