Author Archives: theusernamewhichismine

Update: I’m learning Unity

I’ve always enjoyed video games and wanted to create my own.  I may never actually make one but at least this is a way to exercise my creative side.  My wish is to make a game called something like “Build the Biggest Boom.”  It would be a game all about the chemistry of fire and explosions.  It would start by teaching the player how explosions work, how they can be shaped to send their force in a specific way, and why some compounds explode while others don’t.  There would also be an element of simple engineering to create the devices which would how explosive charge and to detonate.  The game would proceed similarly to Kerbal Space Program where instead of trying to build rocket ships to go to the moon, you build bombs to create the biggest boom.  You do simple research which teaches you the basic chemistry of explosions and then put parts and molecules together in such a way to create bigger and bigger booms, both by creating better explosive materials (for instance nitroglycerin instead of gunpowder) or by making things explode more effectively (ex the shape of the bomb).  There could also be an element of designing explosives to fulfill a specific purpose, such as proximity fuses to only explode when near something or waterproof fuses to explode underwater.

That’s all well and good, but so far I’ve done only the following:

-Make a cube that goes up when space bar is pressed

-Make a box that creates cubes when return is pressed

-Spawn a bunch of going-up cubes with return, then send them up with space bar

-Created a ceiling to stop things from going up too far.  Turns out that to create a ceiling, you have to create a floor upside down.  Who knew

So I want each “cube that goes up” to eventually be a particle in an explosive reaction.  Instead of just going “up” I want them to gain a force proportional to all the other particles near them (as an analogy for every molecule releasing explosive energy) and therefore “explode” outward when the space bar is pressed.  From there I can do the stuff of having different particles have different explosive energies, and having shape charges and stuff.

Game design: should AIs play to win, or play for the player to lose?

I’ve been playing a lot of Sid Meier’s Civilization recently and have thought about this conundrum: should AIs in video games play to win, or just play to make the player lose?  These are two different strategies mind you, if each AI is playing to win they will act in their own rational self-interest to pursue their own goals.  But if they are just playing for the player to lose, they may instead act against their own self-interest in order to hurt the player.  I feel like I see this “play for the player to lose” strategy a lot in games against the AI but I don’t know if it’s accurate or just my imagination.

Consider for instance the early phase of the game: settling.  The player and AIs all are scouting and settling in an attempt to claim as much land as they can to grow and become stronger.  I often appear to see AIs make baffling settling decisions, settling on terrible land with zero fresh water, and their decisions only seem to make sense if they are simply trying to box the player in, not actually win themselves.  Settling is an expensive process requiring a lot of food and production, so you want to settle as good a city as you can.  On the other hand giving the player a lot of land for themselves lets the player grow stronger and be more likely to win as a result. 

The compromise seems to be that in games I have played, the AIs nearest the player will settle on marginal lands in the direction of the player, boxing the player in and preventing them from expanding.  Other AIs will then have more room to settle good land and actually attempt to grow stronger and win the game.  In this way the game becomes more difficult for the player, even though some AIs are making choices that aren’t actually in their own rational self-interest.

To be blunt, I don’t like this.  I think AIs make the most sense when they act in their own self-interest, rather than having a secret alliance against the player in particular, I think it makes the most sense and more accurately represents how a player would play as well.  But like I said I don’t have any hard evidence that the AIs act this way, maybe they settle bad spots because they’re just poorly coded in general.  But it sure does feel like they’re all in on it.

I can tell you a game that DEFINITELY has an anti-player bias and that’s the Total War series, which is part of why I stopped playing them.  In the Total War series, every AI that borders the player in any way is just a short step away from war.  This was fine and fun in Rome and Medieval Total War, where the economics of the game made world conquests like this fun, but in Empire and later Warhammer Total war it just gets tiring and unfun. 

To give an example: Empire Total War takes place starting in 1700s Europe.  France and England both have colonies in North America, and there’s a Native American tribe, the Huron-Wyandot in central Canada.  If the player plays as Britain, this tribe will inevitably attack Britain and stay peaceful towards France.  If the player plays as France, this tribe will attack France and stay peaceful with Britain.  This again isn’t so fun.  Like I said, the economics of this game make world conquest a boring slog rather than a fun romp like in previous interactions, but also this is a historical strategy game that in certain ways does attempt to model diplomacy and agency of historically relevant peoples and nations.  Shouldn’t it be possible for France to attempt an alliance with Native American peoples to counter Britain, just as France did in real life?  I think the game would be a lot more fun that way instead of being railroaded into an “everyone against the player” scenario no matter what country you play as.

Anyway those are my thoughts on AIs, anyone else know of a game that seems to have a strong anti-player AI?

I’ve been playing Pillars of Eternity, and I just wanted to tell someone about it.

Pillars of Eternity (1 and 2) is a fantasy RPG duology made by Obsidian.  Now everyone I’ve known always tells me Obsidian always has the best writing, but honestly I’ve never seen it to be true myself.  I remember booting up Fallout:NV (seen by some as their magnum opus) and thinking “THIS is the bad guy factions?  A bunch of technologically illiterate spear-wielding Roman cosplayers is supposed to be a scourge of the wasteland?”  And the game never did enough to justify to me that these cosplayers were indeed deserving of their status as world-conquerors in a universe where GUNS are plentiful. Instead the game just wants to go into excruciating detail of their evil deeds like it’s written by an edgy teenager, and then I read afterwards in interviews and the like that Fallout:NV was supposed to be “morally gray,” like wtf? 

So I’ve never played an Obsidian game for the writing, the way I’d play an Atlus game for the writing or a Bioware game for the writing.  Obsidian to my mind is best at making interesting systems and gameplay loops that I want to interact with, OR by using someone else’s assets to make a follow-up sequel. They’re good at those, but I don’t expect them to be the best writers.

So with Obsidian’s first wholly new IP since Alpha Protocol (criminally underrated and overrated simultaneously) I jumped into Pillars of Eternity.  How would Obsidian fair when they don’t have a publisher breathing down their neck? 

It turns out publishers aren’t evil and all Obsidian’s bad habits reared their ugly heads.  Let me start by saying I do like this game (I’m replaying it) but I don’t think anyone besides me would ever like it and I can’t think of a single person I know who I’d recommend the game to.  I like it because it is an extensively deep Dungeons and Dragons-type game with real-time-with-pause combat.  I LIKE that. 

But there’s FOUR different saving throws and EIGHT different damage reductions, plus about two dozen weapons and a hundred different status ailments that can occur to your character.  Are you charmed?  Confused?  Dominated?  Those are all different.  Are you hobbled, dazed, dizzy, sickened, weakened, fatigued? The list goes on and on and each one does a different thing using a different skill targeting a different saving throw. 

You can specialize in 1-handed weapons, sword n board, two handed weapons, and dual-wielding and they will all force you to build your character a little different.  And if you want to play a barbarian I hope you know that Intelligence increases the range and duration of ALL abilities meaning a dumb barbarian will rage for mere seconds and then get slaughtered while a barbarian with a PhD in Barbarity can rage for days slaughtering his enemies before him.  Obsidian doesn’t like dump stats so every single stat does something for everyone, a wizard needs high Strength or his spells do no damage, a priest needs high Strength or his heals heal almost nothing, etc.

With all that said it’s the type of game that takes hours just to understand the combat systems and if you’re not the type of person who will read every tool-tip and check both the in-game manual AND the forums to understand how everything fits together, then you are going to have a rough time of it and won’t even know why you’re losing battles until you’ve already replayed them a dozen times. So while I like the combat I can’t imagine how most people would.

But the writing in this game is just not good.  There’s too much of it and every character will talk your ear off at the slightest opportunity without saying much more than “our village of Schitzville is so morally gray that by solving all our problems you’ve just creating new ones.”  The game is a lot less smart than it thinks and that runs through both the first game and it’s sequel. 

It also feels like a game written by teenagers that is so desperate to show you how mature it is that in the sequel half the characters will end every one of their sentences with a sex joke or innuendo.  I’m an adult, most of my friends are adults, sex has not been a common topic of conversation since we were teenagers (or when most participants are blackout drunk).

Finally it makes me sad that although I like Pillars of Eternity 1, Obsidian basically made me never want to play another Obsidian game when they released Pillars of Eternity 2. 

For as long as I’ve known them, fans of Obsidian have said that Obsidian makes the best games but gets screwed by publishers and forced to release buggy, unfinished messes.  Well Obsidian was given a big crowd-funded budget with no publisher to answer to, and they were tasked to follow up on their own IP. And in the end, they made a buggy, unfinished mess.  Combat just didn’t work, the story went nowhere and was a blatantly unfinished sequel hook to drum up interest for a third game that will now never come.  I remember getting to the end and audibly said “that’s it?” when the credits rolled.  Nothing happened and nothing mattered, and now I just don’t care to play new Obsidian games.

Did credit rating agencies make Italy’s borrowing costs go up all on their own?

Yesterday I discussed how credit rating agencies work and why they are a healthy part of a mature bonds market. To recap: credit rating agencies like Moody’s, Fitch, and S&P rate the creditworthiness of nations based on economic and political indicators, and publish those ratings to investors. Investors in turn pay for these in-depth credit ratings to decide exactly what bonds they should invest in and how much. Investors are willing to invest in lower credit-worthy bonds, but will only do so if they can get a higher interest rate due to the higher risk involved. That’s why it is big news when a ratings agency cuts their rating of a country’s bonds, such as Italy. This should directly translate into the market seeing Italy as a riskier investment and thus demanding higher interest rate to buy Italian bonds, forcing the Italian government to spend more and more money servicing its debt and deficit.

That’s the simple part but it doesn’t always work like that. Here for instance is the “spread” between Italian bonds and German bonds, it can be seen as how much more Italy has to spend to service its debt than Germany does. Germany’s bonds did not have any cut in outlook so they should be fairly stable, while Italy’s outlook was cut so it should have even more expensive bonds, right? Well not in this case, Italy’s outlook was cut on August 5th and since then Italy’s borrowing costs have gone down relative to Germany’s. Now I don’t want to ascribe too much to any one thing, analysts have a tendency to over-analyze market moves, but there is a sort of pattern that is often called “buy the rumor, sell the news.” In this case, investors expected Italy’s credit outlook to be cut, so they expected Italy’s bonds to get more expensive. They thus invested in such a way that the price of Italian borrowing went up prior to the actual cut, and then went down after it happened. Regardless, even with this messy pattern it’s hard to say that Moody’s alone was responsible for any increase in Italian borrowing cost, there’s clearly more to it than that.

And that’s an important caveat to the bond markets, Information from Moody’s and other ratings agencies are of course used by investors to inform their decisions, but they aren’t the only thing used. Indeed, Moody’s can sometimes seem reactive rather than proactive, it cuts a country’s credit rating after the country’s borrowing cost has already gone way up due to other economic or political news. Moody’s and the credit agencies are I think a big easy target for financially illiterate commentators because they’re easy to blame. The big bad American ratings agencies cut our credit score and made it more expensive for us to borrow. But these agencies are just one cog in the much larger bond market, and the individual actions of thousands of investors big and small is what causes the change in borrowing costs. If no one trusted Moody’s they wouldn’t have any effect on the bond market, and if they weren’t seen as trustworthy raters of bonds then no one would trust them. But Moody’s doesn’t have the kind of power and authority that its detractors ascribe to it, and Italy’s borrowing costs are expensive for many, many reasons that would not be fixed by Moody’s giving them an Aaa credit rating.

Do credit ratings agencies have too much power?

Recently, the credit ratings agency Moody’s reduced its outlook for Italy from “stable” to “negative”.  For those of you who don’t remember, ratings agencies were some of the key “villains” of the Eurozone crisis of the 2010s.  A ratings agency is simply a company who does research into the creditworthiness of people, organizations, or governments and then sells this information to lenders and investors.  Moody’s is one of the “Big 3” ratings agencies and so its ratings carry a lot of weight, whenever it cut its rating of Italy, Spain, or Greece, lenders would take notice and would consider those countries to be less creditworthy.  This in turn made it harder for those countries to borrow money to cover their expenses, just as an individual with a low credit rating has a harder time getting loans and has to pay higher interest on what loans they can get.  And for countries that were already saddled by high debt, this could be catastrophic.

Whenever Moody’s or another ratings agency cuts its ratings for European debt, the cries arise from various places that these ratings agencies are bad actors who must be reigned in.  People say that they are untrustworthy, they are profit-seeking, and worst of all they are American.  Because of all these things, they should not have this much power over the borrowing costs of European countries.  I think that while there are multiple criticisms to be made of ratings agencies (and I will try to address them later), at least some of this criticism comes from a place of ignorance and I’d like to address this.  

Let me first give a very brief explainer of how a ratings agency like Moody’s works in the context of government bonds.  A bond is basically a loan to a government, when you buy a bond you hand the government some money in exchange for their promise to pay you back over time.  So in a bond market you have the bond sellers such as Italy, and the bond buyers such as the banks and money funds.  Like any loan a bond has an inherent risk, a country that is more likely to not pay back its debts is seen as a riskier investment and must pay higher interest rates in order to sell its bonds on the market.  A government might confidently believe that there is zero risk in their bonds and thus they should only give the absolute minimum of interest rates, but if the market disagrees then no one will buy that government’s bonds and they won’t be able to raise money this way.  But how do the bond-buyers know which governments are less or more likely to pay back their debts?  Ratings agencies like Moody’s look at both the political and economic situations of the governments and come up with a rating, that rating says how risky the bond is and thus how likely it is to be paid back.  That in turn informs the market actors, who will demand higher interest rates for riskier bonds then for less risky bonds.

First of all, ratings agencies aren’t evil entities who make borrowing expensive for the lols, they are simply an element of the division of labor of modern finance.  Financial organizations, be they banks or pension funds or what have you, want to invest in stable, high quality bonds.  But if every bank and fund needed an entire team of analysts to assess exactly which bonds were high quality and which were not, there would be a lot of wasted labor as competing banks paid different people to find the same information.  Instead, banks outsource a lot of this investigation to the ratings agencies like Moody’s, then buy the information provided by Moody’s and use it to understand which bonds they want to invest in.  That in turn is a money saver and so the expenses of the bank or fund are a lot lower than they otherwise could be.  This division of labor is a godsend to modern finance, and to remove it for no reason would not be wise.  Moody’s provides a genuine service, it researches the economies and outlooks of almost every major government and investible corporation, and it has built a reputation of trustworthiness over its long history.

Second of all, ratings agencies have a lot of power in part because the market gives it to them.  Market actors such as banks and funds trust Moody’s and the rest of the Big 3 because of their long history of accurate ratings, or at least being more accurate than their competitors.  Those market actors use the information Moody’s provides to inform their investments, but Moody’s isn’t forcing anyone to raise the price of Italian borrowing, the market actors demand higher costs for Italian bonds in part because they trust Moody’s ratings and Moody’s says Italy’s outlook is not as good as it once was.  If you create a new organization, it wouldn’t necessarily change anything because a new, unproven organization would not be trusted.  The market would still trust Moody’s ratings more and thus Moody’s ratings would inform the price of bonds, this new organization wouldn’t.  You can’t really force every market actor to not use information from Moody’s.  I mean you can try, governments can always write laws, but enforcement of this kind of information ban would be a nightmare and would probably only cause bond-buying entities to flee from the EU bond market altogether because they wouldn’t want to fall afoul of new laws but also don’t want to buy a bond that they don’t know if it’s trustworthy or not.

Thirdly, trying to replace Moody’s is not an easy task and I’m not sure most of the detractors are up to it.  As I said, they only have power because the market gives it to them, so let’s say you put together a “European Moody’s” let’s call it Euddie’s (pronounced YOO-dees), then what?  Euddies won’t have the long track record of Moody’s, it won’t have the trust of the market, and so no one will buy their ratings or use their ratings to inform decision makings.  Instead they’ll just keep using Moody’s ratings and there will be no change to the borrowing price for European countries.  Furthermore, who will run Euddies?  If it’s a private company like Moody’s then you run into the exact same criticisms that people have for Moody’s ie it’s profit focused and shouldn’t have this much power over governments.  The only difference would be the nationalist complaint that Moody’s is American and Euddies wouldn’t be.  On the other hand if Euddies is an EU-level government entity, then who outside the EU would trust them?  EVERY government in the world says it is perfectly creditworthy up until the moment it defaults, so why would investment organizations trust an entity that is controlled by the very governments it is supposed to be rating?  In all likelihood without stringent ring-fencing between Euddies and the governing bodies of the EU, it would be seen as just another government agency like the ECB, without the trust that Moody’s has.  Finally, I don’t think Euddies will solve the problems that Moody’s detractors think it would, nations like Italy are still heavily indebted with poor economic outlooks, any reasonable credit agency will not give them AAA credit rating no matter where the agency is based or who runs it.  There is every reason to believe for instance that Moody’s ratings are as much reactive as proactive, oftentimes borrowing for a country will get more expensive before Moody’s even cuts their outlook.  So I don’t think that a Euddie’s organization giving preferential treatment to European government bonds would really change their borrowing costs when Japanese, American, Chinese, and all non-EU investors will continue to believe that those governments are not as creditworthy as they claim to be.

In conclusion, Moody’s and other credit rating agencies are not bad actors in the market, they are performing a legitimate service for other financial institutions and cannot be simply removed or replaced without serious consequences.  Tomorrow I will try to touch on the differences in borrowing costs between Italy and Germany, and how Moody’s ratings have fit into that.

I want to learn to code, but it’s hard to learn on my own

I’ve described before how I want to make video games.  I’m a self taught coder in a few “academic” languages like R and Matlab and a little Java, but I’ve never worked on anything with graphics so I don’t even know how to start coding for video games.  Over the past year I’ve on-again-off-again tried to get into programming with Unity and I just can’t force myself to stick with it.  I’ll go in, make a block, make a room, and then tap out for weeks or months at a time, it’s just so hard to learn when I don’t have someone to learn from.  I don’t like video tutorials either, I work best with written tutorials, but those seem to be a dying art so I can’t find any.  I was wondering if anyone else had tried to self-teach themselves Unity and knew of any good tutorials for it?  Especially for something very simple and if at all possible turn based.  I don’t think I want to make the next Minecraft, but just having an outlet for my creativity would be nice.

Most of LinkedIn seems like a scam, how do others filter the wheat from the chaff?

As a white collar professional I am occasionally required to use LinkedIn either for job searching or networking, and during these occasions I am astounded by how scammy it feels.  When I attempt to apply for jobs, about half or more seem to be fake postings posted by someone who doesn’t actually represent the company, and is probably just resume trawling to get hired as a recruiter.  Many postings are clearly sourced from somewhere besides LinkedIn because although they may have a flashy “easy apply” button, the text indicates that applications should be sent to a specific email address, or indicates that the post comes from off-LinkedIn in some other way.  And finally my messaging inbox is inundated with all sorts of people desperately asking for a 5 minute call so they can demand I let them represent me as an applicant to some company I have no interest in, or in many cases they refuse to name the company and want to represent me anyway.

I’ve come to feel that a lot of LinkedIn is a scam.  It always sounds great to allow employers and employees to find each other organically from the comfort of a computer, but without strict moderation these types of things always fall into scam territory.  

If anyone is reading this: how do you find the non-scams on LinkedIn?

A Practical Guide for going to space.  Final thoughts.

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.

A Practical Guide for going to space. Part 4: fuel-saving designs for an easier round trip

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.

A Practical Guide for going to space. Part 3: from the Moon back to Earth

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.