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We are told right from childhood that space is just vacuum and so I wondered if the space is empty then how come satellites accelerate in space. Newton's third law is applied, to accelerate any body but if there is no matter in space then what gives an equal and opposite force to satellites?

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Satellites accelerate in space mainly

  • through the action of gravity, both from the Sun as well as the planets, and
  • by firing rocket engines or other similar means of propulsion.

In the first case, Newton's third law demands an equal and opposite reaction, and this is exerted on the Sun (or planet / moon / whatever), where its effect is negligible. In the second case, the reaction is exerted on the rocket exhaust, which ends up moving much faster (but with lower mass) in the opposite direction.

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