The distance from the sun affects a planet's velocity because of Kepler's laws of planetary motion. Kepler's first law states that planets move in elliptical orbits with the sun at one of the two foci. This means that as a planet moves closer to the sun, it speeds up, and as it moves away from the sun, it slows down. This variation in velocity is related to the changing distance between the planet and the sun, which influences the gravitational force between the two bodies. The combination of the planet's velocity and the gravitational force determines the shape of the planet's orbit.