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What is the value of theta for a satellite not falling back to the Earth if it is launched from the direction tangent to the surface of the Earth? I have found the escape velocity which is 11.18km/s, and initial speed for the satellite which ensure it doesn't fall back to Earth, which is 7.4km/s. Shall I solve the questions using conservation of angular momentum? Or centrifugal force? It is an elliptical orbit.

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    $\begingroup$ An object in an orbit will always returns to the point where it accelerated last. So when you try to launch a craft with a single, instant impulse, the craft will always return to the start location. To reach an orbit from a surface, you either need progressive acceleration or you need at least two impulses (like with a hohmann transfer) $\endgroup$ – Philipp Jul 10 '14 at 8:11
  • $\begingroup$ Hi phillipp. Yea i have searched about the Hohmann Transfer however i cant really relate the calculations to the angle of the launch of satellite where it does not fall off. $\endgroup$ – Chee King Jul 10 '14 at 8:23
  • $\begingroup$ As I said there is no such angle or vector, because any trajectory you can reach through an instant impulse from the ground will either escape, crash into the ground or would return to the exact start location (when there would be no atmosphere - with atmosphere you would also get a crash). $\endgroup$ – Philipp Jul 10 '14 at 8:36
  • $\begingroup$ Yes there is a literal value of angle for this case just that the theory behind it is not understood.Anyway the atmospheric friction is not taken into account.So how do we relate the angular momentum and the angle? $\endgroup$ – Chee King Jul 10 '14 at 8:40
  • $\begingroup$ (showing a complete lack of knowledge about orbital mechanics) Does the launch azimuth (relative to Earth's rotation), combined w/ Coriolus effects, allow for the possibility of settling into an orbit? $\endgroup$ – Carl Witthoft Jul 10 '14 at 12:00

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