This is the second post in my weeklong series about space travel.  Yesterday’s post can be found here and in it I explained the basic mechanics of getting from the ground into orbit.  To summarize, getting into orbit is all about getting enough horizontal velocity (relative to the ground) such that gravity pulls your journey around the body you’re orbiting and not back into the body’s surface.  To do so you need to get above Earth’s atmosphere (where atmospheric drag would sap you of velocity and allow gravity to pull you back in) which is why spaceships start their journey by going up, but most of the energy will be expended gaining the horizontal velocity.  Secondly I discussed changing an orbit, in particular how firing your rockets (“burning” for short) in the prograde direction expands your orbit, while firing them in the retrograde direction contracts your orbit.  These will be important concepts for getting to the moon.

So if we’re in a spaceship in orbit around the earth, how do we get to the moon?  Well the moon is just a body that orbits the earth at a very long distance, so in principle there’s not much difference between going to the moon and when we visited our friend’s spaceship in Part 1.  Let’s assume that like last time, our orbital plane is the same as the moon’s orbital plane, so again all we have to do is burn prograde to expand our orbit to a point where it comes close to the moon.  In reality the calculations for this are diabolical, especially with the hand-calculation used by NASA in the 60s.  The prograde burn turns a circular orbit into an elliptical one with its periapsis (the point of the orbit which is furthest from the earth) hopefully intersecting the moon’s orbit at a point when the moon will be close to it.  But if done correctly, then at the furthest point of our spaceship’s orbit we will come close to the moon, having crossed over into its gravitational hill sphere several hours beforehand.

But we’re not done yet.  Just getting our ship close to the moon isn’t enough, we’ll likely just pass right by it and continue on our orbit around the earth.  We need to get into orbit around the moon.  Again from Part 1: an orbit is just when you’re moving fast enough relative to a body that gravity can’t pull your trajectory back down to the surface, but not so fast that you fly off into space.  If we got to the moon by burning from the earth, then we’ll have so much velocity relative to the moon that we can’t just get into orbit, we need to slow down relative to the moon so that its gravity can bend our trajectory back into an orbit.  And if burning prograde speeds you up, then burning retrograde slows you down.  In this case retrograde will be in relation to our speed relative to the moon, rather than relative to earth, but retrograde we must burn if we are to create an orbit.

So finally we are in orbit around the moon.  We burned prograde from our earth orbit to extend it outwards towards the moon, then once close to the moon we burned retrograde relative to the moon in order to slow down and get into a moon orbit.  Now orbiting the moon we would be able to look down at the lunar surface and pick out a landing site.  Getting down onto the moon is now just the opposite of getting up off of the earth.  For earth we burned vertically at first to gain height and then horizontally to gain horizontal momentum and create an orbit.  For the moon, we first burn retrograde to lose horizontal momentum in order to decay our orbit to the point where it intersects the ground, then as we fall towards the moon we will gain vertical momentum from gravity pulling us down.  As we approach the lunar surface we can perform a final burn to slow both our horizontal and vertical moment to zero, or as close to it as possible before final touchdown.  Congratulations, we have landed on the moon.  

You’ll notice this explanation has so far been missing a few pieces that you might remember from the Apollo program: there’s no discussion of a separate lunar module and leaving a crewmember behind in space, for instance.  Those will all be discussed in a later post where I talk about weight and fuel requirements.  For now, I’d like to enjoy a game of lunar golf, and tomorrow we can discuss getting back to earth.