Free Fall from Selene

>
> Hi,
>
> Is there an initial velocity and direction from the lunar surface
> that will ultimately lead to capture in LEO? Gut feeling says no,
> but I'm not too sure. If an object is falling toward earth and
> doesn't lose energy somehow, it's just going to whip around real fast
> (too fast) and go right back. (Assuming it doesn't impact.) But, I
> don't how the lunar pull figures in. Can anyone show me that such a
> trajectory doesn't exist?
>

An object released from the Moon towards the Earth will end up in an
Earth orbit
with an apogee of about 250,000 miles.
The apogee does not depend on the direction.

The perigee does depend on the direction.

To get into LEO will require reducing the apogee considerably, this
takes a lot of energy.

> Can it be done with aerobraking?
>

The apogee could be reduced by aerobraking provided the initial perigee
was low enough.

This assumes you do not wish to use rockets for some reason.

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