Lunar transfer trajectory considerations
An efficient transfer into Lunar transfer trajectory, requires the spacecraft to be fired from the negative unit vector of where the Moon would be at the time of landing or simply from the antipode of moon’s position at expected landing time.
It's interesting to note the moon takes exactly 25 hours to cross any given longitude on earth twice, if you assume the spacecraft is injected into the lunar transfer trajectory taking 73 hours to get to the moon - based only on the Earth’s gravity & ignoring Moon’s gravity perturbation. The spacecraft will get there 2 hours too early. Therefore the injection window must account for this time - the actual journey to the moon takes less than the projected time, about 66 hours with 7 hours transit time reduced on account of perturbation of Moon’s gravity.
From the launch pad to the injection point transit time is an additional consideration, typically this varies between 1000-1500secs. When designing the ascent trajectory the Lunar transfer trajectory injection point should ideally be inside the Range safety of the launch vehicle, take its antipode add 2 hours 20 minutes (2.3 hours) to this time and compute the lift off time. The spacecraft can be injected upto 20 minutes after the pre-decided injection point. These considerations when put through additional constraints provides the limits on the injection velocity required, the range for our computations vary from 10.5 km/s to 10.9 km/s.
Next up more about on "launch window considerations".
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