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Would required $\Delta V$ for a lunar soft landing differ if the landing site is selected either on the near or the far side of the Moon? If there is a difference, how big would it be and what would be the reasons for different $\Delta V$ requirements?

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There should be no discernible difference - the radius of the Moon compared to the distance to the earth means that at touchdown, it's effect is negligible.

The Moon is in a stable orbit at around 385,000 km. It's radius is around 1800 km, so the gravitational effect of the Earth will change by about 0.002%.

As Andrew Thompson pointed out, moon landers typically go into a low lunar orbit around the moon prior to landing - around 100 km (62 mi) altitude or less above the mean surface of the Moon.

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    $\begingroup$ Given the craft typically go into orbit around the moon prior to touch-down, I cannot see how there would be any difference.. The only difference in that case would be the time they left the lunar orbit to descend to the surface. $\endgroup$ – Andrew Thompson Dec 14 '13 at 18:23
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If we assume soft-landing from a direct ballistic trajectory and do a trans-lunar injection (TLI) burn immediately following the launch with no intermediate parking orbit around Earth or the Moon (latter might be useful to target a landing site further from lunar equator, Like Chang'e 3 did), then your launch window will be slightly earlier for a landing site on the far side of the moon, but your delta-v doesn't change because of it, as has Rory already answered.

Why? Because your $\Delta V$ requirements stem from the need to break free of Earth's gravitational influence (Hill sphere) and this has little to do with your target orbit around the Moon that would change depending on which side of it you'd like to land, but a bit more with your launch window, i.e. timing. Once the Moon's gravitational influence prevails, you're Δv-free and only need to worry about not crashing into it or missing it enough to later crash back into the Earth. By keeping the Moon with your launch window on average on your side as it rotates around the Earth (in direction of your vector), you'd be able to somewhat lower your minimum $\Delta V$, since you'd be faster in region where its own gravity prevails over Earth's. But delta-v isn't really the most interesting aspect of launching to the Moon as far as total thrust (force per wet mass) requirements are concerned, what matters a whole lot more is your total payload mass that will define them. Let's split hairs a bit;

Strictly technically speaking, you will require either two launches or a single one launching a heavier two module lander-orbiter for a landing on the far side of the Moon, since you'd need an additional orbiter to relay communications between your lander and the Earth. Since the Moon is tidally locked with Earth, this means that what we call the far side of the Moon is always turned away from the Earth with no direct communications possible. So you would require either an additional orbiter in lunar orbit to relay communication prior and post each occultation when the orbiter would have both the lander and the Earth in sight, or an additional communications satellite stationed in a $L_2$ (Lagrange point) halo orbit relaying communications to the Earth via another satellite, parked in a Geostationary Orbit (GEO) when the two would be in direct line of sight to each other.

Far side of the Moon is also much more mountainous than the near side, so you should likely assume you'd require more propellant for any additional landing trajectory course corrections. All this adds weight to your launch vehicle, but there's arguably a plus side that your lander wouldn't require as strong communications antenna, since it would only have to reach a much closer orbiter / L2 halo orbit satellite with it, so some of its onboard equipment would be lighter, and with it also requiring a bit less fuel for the deorbit burn. So all in all, your $\Delta V$ requirements mightn't change by much, but you'd be launching a lot heavier payload for the far side of the Moon soft landing. At least, if you also want to communicate with it. Anyway, I did warn you I'll be splitting hair, didn't I?

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  • $\begingroup$ Higher landing point = less fuel to land there. Quite a bit of splitting hairs, though. $\endgroup$ – Loren Pechtel Dec 15 '13 at 19:26
  • $\begingroup$ @LorenPechtel Heh yes, welcome to the club :) Anyway, I forgot to mention that Δv remains the same because the Earth's Sphere of Influence doesn't change, which is where Δv requirements come from. The rest is just making sure you don't crash... but yes, mountains would be a bit closer place to crash... ermmm... land on LOL $\endgroup$ – TildalWave Dec 15 '13 at 19:30

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