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.

Over the next week I’d like to set down my understanding of how going to space works.  Most of this has been gleamed from my academic career as well as having fun in Kerbal Space Program, but I’ve noticed that despite the half century of progress since America first went to the moon, most people I’ve met don’t know how space travel works or why spaceships work the way they do.  So I just wanted to set down my understanding in hopes of helping someone else who might be reading.

Step one of most any space travel is getting into orbit, everything else comes from there.  As XKCD taught us (https://what-if.xkcd.com/58/) getting into space is about speed more than height.  Being in orbit is about moving around the earth fast enough that gravity can’t bend your trajectory back to the earth’s surface, it can only bend your trajectory around the earth.  Don’t go too fast or gravity won’t even be able to keep your trajectory around the earth, instead you’ll fly off into the solar system.

So with that said, the primary necessity of a spaceship is to gain horizontal velocity (relative to the surface) so that gravity will keep them in orbit and not pull them back to the ground.  Spaceships only go up so that they can escape the atmosphere and not have it sap them of all their precious horizontal velocity, so while a spaceship starts its journey thrusting vertically to get off the ground, it quickly adjusts to a more horizontal position in flight such that it continues to gain vertical speed but gains horizontal speed at a much much greater rate.  From there, the key is to just keep gaining horizontal speed until you reach the point where gravity can’t bend your trajectory back towards the ground anymore, and as long as you’re above the atmosphere so it can’t sap you of horizontal velocity then voila you’re in orbit.

From Orbital rendezvous and changing obits

So once you’re in orbit, what do you do up there?  Have a party in your spaceship maybe.  Call your friends to go visit them in their spaceships.  But this gets to the tricky question of how you’d get to their spaceship.  Keep in mind that when you’re in orbit, you’re not stationary.  You’re hurtling around the earth at about thousands of miles per hour.  Let’s say you’re in an orbit that is just 250 miles above the surface, about the height of the ISS.  Your friend is 1000 miles above the surface and you want to visit them.  How would you go about doing that?

First one needs to understand how to change an orbit to begin with.  I’ll start with the most basic of the basic: prograde and retrograde.  When you’re in an orbit, prograde refers to the direction you are moving in at any particular time, and retrograde refers to the opposite direction from prograde.  So if you’re in a spaceship whizzing around the earth, look straight ahead in your direction of travel and you’re looking prograde.  Look behind you and you’re looking retrograde.  These are important because these directions are how we can change an orbit and visit our friend.

Point your ship so it’s front is pointing prograde and its thruster is pointing retrograde, fire the engines and you will give yourself more velocity in the prograde direction.  Doing this will expand your orbit, making you orbit be further away from the body you are orbiting (although it will mostly expand the part of your orbit on the other side of the planet from you).  Fire your engines in the retrograde direction and you will contract your orbit.  This is how you can visit your friend.  If you’re in a circular orbit at 250 miles above the equator, and they are in a circular orbit 1000 miles above the equator, you need to expand your orbit such that at least part of it crosses that 1000 mile mark.  Expanding and contracting your orbit is how you’re going to have to go anywhere in space, it doesn’t really work to aim your rocket *at* a thing and fire the engine, that’s now how space works.

So you finally have an orbit that crosses your friend’s orbit and at the point of crossing you and your friend will be only a few hundred meters from each other, so you can finally visit him in his capsule, right?  Not entirely, there’s one final thing.  At the point of crossing your relative velocities (how fast your moving relative to *each other*) will probably not be zero, and this can cause you to blow past each other at the moment of closest approach (https://youtu.be/CnxpsV_FMsI?t=3181).  If you actually want to get in your friend’s capsure and have a party, you need to fix that.  To do so, during closest approach you need to fire your rockets in a direction that reduces your speed relative to your friend’s spaceship.  This part requires a little math and is hard to explain without visuals, but trust me when I say it’s a necessary part of the procedure.  Reducing your speed relative to your friend’s spaceship will cause the two of you to match speeds, and your orbits will begin to potentially look almost identical to each other (since you’re going the same speed at the same point in space).  Once you have perfectly matched speeds with your friend, you can *now* point your rocket in their direction and fire the engine, because since you aren’t moving relative to each other things finally work intuitively like they do on earth.  You can then use this to dock with their craft, get in, and have your party.

So this has been a fun little trip, we talked about how to get into orbit and how to change an orbit.  This all would be easier to explain with visual aids and in my mind this would work better as a YouTube video, maybe some day I’ll make it one.  For now though this is only part 1 of space travel.  Next up, actually getting from orbit to the moon.