Writing this series has been, for me, very therapeutic.  I’ve always been interested in space and space travel.  There’s still a lot more to talk about, for instance SSTOs (single stage to orbit) and why many think they’re the future of space travel.  Or the particular difficulties of landing on any planet with an atmosphere.  But overall I wanted this to be a fun little introduction to how space travel works and how it was done in the Apollo program.  Once I learned how it worked I started noticing how basically no movies or games (besides Kerbal Space Program do it justice.  I can’t tell you how many times I’ve noticed that most spaceships in movies or games don’t actually orbit anything, they just float around relatively motionless compared to whatever body they are near.  The International Space Station for its part is moving incredibly fast, with an orbital rate of about once every two hours.

Still it was fun to get this all out there and in one coherent place.  Thank you for taking the time to read and learn with me.

In the last three days I’ve made a series of posts detailing in a general sense how a space mission can go from the Earth to the Moon and back.  On Monday I discussed how to get into orbit and how orbits work generally.  On Tuesday I discussed how to go from an Earth orbit to a Moon orbit, and how to go from orbit to landing on the surface.  And on Wednesday I discussed the return journey from the Moon to Earth and how atmospheric drag can be used to help land on Earth.

Today I’d like to touch on the things I didn’t mention, the things NASA spent a lot of time and money to achieve because they were crucial to mission success.  In particular, NASA spent a lot of time and money figuring out how they could get the greatest amount of mass to the moon using the least fuel and the smallest rockets they could.  Rockets and fuel are big, expensive, and difficult to handle so the less of them you have to use the better.

This weight-saving starts in the first ascent when the spaceship is getting into orbit.  The rocket that launched from Kennedy space center was 363 feet tall and looked like THIS while the orbiting modules that went to the moon was about 37 feet tall and looked like THIS.  Where did all the rockets go?  Well the Saturn V rocket itself was big and heavy, and once all its fuel was expended it was detached from the orbiting modules and fell back to earth, allowing the modules to get into orbit on their own.  This in turn made getting to the moon cheaper and more fuel efficient because getting those little modules to the moon costs way less fuel than getting a giant Saturn V PLUS those modules to the moon.  This idea of saving weight by detaching from expended rockets was used all over the Apollo and Soviet programs, and will be discussed again shortly.

Next, once the modules got into orbit around the moon, we can save weight again by having only 1 module descend to the lunar surface while the other remains in orbit.  This significantly reduces the amount of weight we need to get on and off the Moon, and that in turn reduces the fuel usage.  Finally, once on the Moon the Apollo module would detach from some of its rockets yet again, leaving them on the Moon and sending only a small part of the lunar lander back to orbit, similar to how booster rockets were jettisoned during Earth ascent.

In all these above cases, fuel can be saved by simply taking less mass from one place to the other. Detaching from the rockets to take less mass from Earth orbit to Moon orbit, detaching the lunar module to take less mass from Moon orbit to Moon Landing, and then detaching from some lunar module rockets to take less mass from Moon Landing back to Moon orbit. All of these save the weight you have to move and thus save fuel, and one of the biggest difficulties in going into space is you fuel usage so this is a big help. Originally NASA didn’t want to detach a lunar module to detach from the command module for lunar landing, they wanted to land the entire module on the moon. This was because detachment and landing would have to be followed by an in-orbit rendezvous to get the astronauts back together for the return-to-earth part of the mission, and they didn’t know if in-space rendezvous were feasible. But the fuel-savings from this method were obvious so several missions were launched to test our ability to perform rendezvous, and once successful the lunar-module version of the mission was given the go-ahead.

The last trick is something I’d like to make clear about the physics of getting into and out of an orbit.  When I watched the Giant-Bomb let’s play of Kerbal Space Program, one of the commenters posed the question: “It’s easier to get down from orbit than back into orbit, it must be easier because you have gravity helping you, right?”. This is in fact a misunderstanding, to get from in orbit around the body to being stationary on a body requires the same amount of force as to do the opposite. You can get down from orbit more cheaply if all you want to do is crash, in that case you can simply shrink your orbit and crash into the body at a few hundred meters per second, saving you a lot on fuel (this is called lithobraking and was used to land the NASA rovers Spirit and Opportunity, although to protect the robots their fall was cushioned by inflatable airbags). So it will always take the same amount of energy to get from the ground into orbit as it takes to get from orbit to the ground, however importantly this does not take into account the atmosphere of a planet. The atmosphere of a planet creates drag which will slow down down any craft moving through it, and we can use that to our advantage when we try to land on Earth by letting the atmosphere slow our descent instead of needing to use rockets to slow ourselves like we did on the Moon. This is the final big fuel-saving for our trip and is why the Apollo capsules landed without their rockets, because they didn’t need those rockets to slow themselves and it would only make descent harder as they’d need a bigger parachute to slow themselves upon final descent to the ground.

All in all, saving fuel and weight is of primary importance to any space mission, and many of the techniques we take for granted had to be calculated and figured out by NASA before they became standard. Everything the Apollo rockets did had hundreds of pages on data and savings behind them, even if they aren’t immediately obvious to us, but they were all necessary to get to the moon.

This is the third post in my weeklong series about space travel.  Yesterday’s post can be found here and in it I explained the basics of getting a spaceship from low Earth orbit to the surface of the moon using the simple concepts of a prograde and retrograde burns.  Remember that burning prograde means firing your rockets in such a way that you increase your velocity in the direction of your motion, relative to the body you are orbiting.  Burning retrograde decreases your velocity in that direction.  If you are orbiting around the Earth’s equation, burning prograde means pointing your rocket in the direction or your current motion and executing a burn to gain more velocity in that direction.  

Now that we’ve been to the surface of the moon we can play a few holes of moon golf, and then once finished we can leave the surface of the moon and return to Earth.

The trip from the moon’s surface to low lunar orbit is much like the trip we took in Part 1 from the surface of the Earth to low Earth orbit, only this time there’s no atmosphere to drag us down.  So we only need to gain enough altitude to clear any lunar mountains, then burn horizontally from the lunar surface until we have enough horizontal velocity that gravity bends our trajectory around the planet and into an orbit.  If we have too little horizontal velocity, our trajectory will be bent back down to the planet’s surface, and if we have too much horizontal velocity we will escape the moon’s orbit.  Escaping the moon’s orbit is actually our next step though, so once in orbit we can burn prograde to gain velocity relative to the moon and escape its orbit.  

Once we escape the moon’s orbit, where will we be?  Back in orbit around the earth.  Remember that the moon itself orbits the Earth, and so anything orbiting the moon is also itself orbiting the Earth.  Escaping the moon’s orbit will likely bring us to an elliptical orbit with Earth as its focus.  We gained a lot of velocity relative to both the moon and the earth in order to escape the moon, but we still haven’t escaped the Earth’s orbit.  That’s actually good, we don’t want to escape the Earth (yet), personally I need to get back home.  So now that we’re out of the moon’s orbit and back into an Earth orbit, how do we get back to Earth?  Simply burn retrograde to reduce our velocity relative to Earth.  Doing this will shrink our orbit, just as burning prograde expanded our orbit in part 2.  And once we’ve shrunk our orbit to the point that our orbital trajectory crosses into Earth’s atmosphere, we’re basically guaranteed to get home.  The Earth’s atmospheric drag will slow our craft down, sapping it of horizontal momentum, until our trajectory no longer maintains an orbit but instead is bent towards the planet’s surface by gravity.  

This was something we couldn’t do on the moon because the moon doesn’t have an atmosphere, but it does bring back the Apollo 13 dilemma that I discussed all the way back in Post 2.  To recap: the Apollo 13 dilemma was about how Apollo 13 would navigate the Earth’s atmosphere to ensure it got home safely.  The astronauts needed to burn retrograde to lose enough velocity such that Earth’s atmosphere would slow them down and they would land on Earth with their parachutes, but how much should they slow down?  If they slowed down too much, they would take a steep plunge through the atmosphere, the intense heat from re-entry might destroy their capsule, and even if it didn’t the steep trajectory might not give their craft enough time to slow down enough for a safe landing.  However if they slowed down too little, then they would take a very shallow trajectory.  This shallow trajectory would mean they would not pass through enough of earth’s dense atmosphere, meaning they would not be slowed down significantly by the atmosphere, meaning their trajectory would not be bent into a surface-crossing one.  As they passed through the atmosphere, they would be slowed down, but it would not be enough and they would continue on their elliptical earth orbit.  Their orbit would still cross Earth’s atmosphere, and so each time their obit passed through the atmosphere the craft would be slowed more and more until their trajectory was bent into a surface-crossing one and it hit the ground.  The problem for the Apollo 13 astronauts was by then it would be too late.  Their elliptical orbit took days to complete and they didn’t have enough food, water or oxygen to survive for that long.  They needed to come down to earth in a single pass.

This dilemma is similar to the one we would face coming back from the moon, we need to burn retrograde such that we will pass through the earth’s atmosphere and let it take enough of our momentum so we can safely land with our parachutes.  Again the calculus for figuring this out is diabolical, and it’s the reason NASA employed so many people just to do calculations during the Apollo program.  But once we are slowed down enough by the atmosphere, our trajectory will be bent into one which crosses the surface of the earth, and from there it’s simply a matter of deploying a parachute at the right time and our craft can gently float down to land on the surface.  Mission accomplished.

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.