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Supposedly launching to different orbital inclinations is quite difficult, with launchers trying to launch from different launch sites to using mid air launches to avoid geographic restraints. If a satellite is dispensed perpendicular to the launcher, will the satellite be injected in an orbit that is 90 degrees more than the one that the one it injects to axially. How much of a push is required? Can low energy thrusters(electric propulsion) do the job?

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No, a small push will not change a satellite's inclination by 90°.

Remember that, when in low Earth orbit, a satellite is already travelling some 7-8km/s. A small push of only some m/s will leave the satellite with almost exactly the same trajectory, changing its inclination by only a small fraction of a degree.

In order to change your inclination by a full 90°, you first need to rid yourself of those ~7km/s and then provide a further 7km/s at 90°. Pythagoras will allow you to cut this down to around 10km/s if you use a single manoeuvre, but that is still an enormous change.

The further out we go, the smaller the velocity change required. However, we'd need to go out ~100 times further than the Moon, where other gravitational influences in the Solar System dominate, before our small push can change our inclination by an appreciable amount.

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