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A comment to this question sparked my interest. If we start a rocket from the surface at the equator, it has some angular momentum with regard to Earth. This angular momentum is definitely much too small to reach enough speed for lower Earth orbit or even geostationary orbit. However, sufficiently large orbits have arbitrarily low angular velocities. So, if the rocket did not turn and kept straight ahead¹, would it be possible to reach a stable (circular or elliptical) orbit?

1) The notion of "straight ahead" could mean either "keep pointing towards the same star" or "keep pointing the exhaust towards Earth's centre". An analysis of both possibilities would be welcome.

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M.Herzkamp
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  • If Elon Musk eventually gets his Mars project going, and in order to save fuel, avoids a circular orbit, and heads straight for where Mars will be in say, 10 months time, by your logic it may be necessary to make mid course corrections, to "straighten" the vehicle, and avoid an Earth orbit, which imo, would not be necessary. –  Oct 19 '16 at 08:56
  • @CountTo10: Note, that the acceleration of the rocket is variable. To get to Mars you probably need more acceleration (you reach escape velocity). In order to stay in an orbit you would of course need to keep you velocity below escape velocity. – M.Herzkamp Oct 19 '16 at 09:16
  • What you could do, if you have time, is to check have any probes gone straight to their target, even if it is only for a gravity assist, say Cassini –  Oct 19 '16 at 09:20
  • See Hohmann transfer orbit – Ng Chung Tak Oct 20 '16 at 19:07
  • @NgChungTak: unfortunately, the Hohmann transfer orbit does not meet either definition of keeping the spacecraft "straight ahead" – M.Herzkamp Oct 24 '16 at 09:28

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