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Particularly for things orbiting us, the gravitational pull of the Earth is by far the most prominent force keeping these things in orbit. Aside from that, many satellites close to us experience significant gravitational effects from Venus and the Sun.
However, at a very, very fine level, gravity-based models break down, which indicates different forces acting on satellites. Here are a few of them.
- satellites emit radiation, and if it's not evenly distributed across the surface area, Newton's third law kicks in.
- Photons from the sun, for example, can collide with the satellite, sending it off course by a whopping several nanometers.
- Although probably not going to mean much on Earth, satellites can experience rogue forces if the body it's orbiting has a strong enough magnetic pull.
- A meteor hitting a satellite is sure to perturb a satellite's motion, but even drag forces from other particles in orbit can change its motion.