Translunar Flight
Vehicles sent on lunar or planetary missions are generally not launched on a direct trajectory, but first put into a low Earth parking orbit; this allows the flexibility of a bigger launch window and more time for checking that the vehicle is in good condition for the flight. A popular misconception is that escape velocity is required for flight to the Moon; it is not. Rather, the vehicle's apogee is raised high enough to take it to a point (before it reaches apogee) where it enters the Moon's gravitational sphere of influence (though the required velocity is close to that of escape.) This is defined as the distance from a satellite at which its gravitational pull on a spacecraft equals that of its central body, which is:
where D is the mean distance from the satellite to the central body, and mc and ms are the masses of the central body and satellite, respectively. This value is approximately 66,300 kilometers (35,800 NM) from Earth's Moon.
A significant portion of the vehicle's flight (other than immediate proximity to the Earth or Moon) requires accurate solution as a three-body problem, but may be preliminarily modeled as a patched conic.
Read more about this topic: Flight Dynamics (spacecraft)
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