After launching in February, that road car becamethe first in the cosmos, carrying a towel and blasting David Bowie. It was a heck of a spectacle, sure, but the car isn't justlost to the void now. We know exactly where it is. All an enterprising super villain would have to do then is get to it, and I'm not saying I'm one of those or that you should do it, I'm just saying thisis how you could do it, very very important distinction there.
First, it's not like government agencies or Musk himself is goingto help us nab a space car that's already traveledthe equivalent of 37 times all of the world's roads put together, no. So, we're gonna have totake a quick crash course in orbital mechanics and maneuvers. Probably not the bestchoice of words there. And don't you worry abouthow we're actually going to intercept and thenreturn the Tesla to us. I so happen to have a Tesla capture device that I cons... that I found at a yard sale. What we really need is a planand a pathway through space. When should we launch? How long will it take usto get to the Roadster? What will the trajectory look like? Oo, it's all coming together, he said innocently (laughs maniacally).
A rendezvous in space isn't as easy as just point and then thrust it and that's because everythingin space is moving. Gravity is everywhere,it affects everything and so, in effect,everything in the universe is always falling around something else, whether that be the earth around the sun or a galaxy around another galaxy, and so any orbital maneuver inside our solar system, for example, has to take into accountthis omnipresence of gravity.
For example, if youwanted to launch a rocket from Earth to Mars, andyou just point and shoot without gargantuan thrust, you're gonna miss. So instead, bending to gravity's whim, we're gonna want to takesome kind of curved path, not a straight one, that will take us, not just to where Mars is, but to where Mars will be when our rocket gets there millions of kilometers later. This kind of orbital maneuveris one of the simplest and easiest, in terms of fuel and it's called a Hohmann Transfer. So, we're gonna wanna learn the mechanics of this kind of transfer if we're gonna pull offgrand theft strato...sphere. Stra...
So, let's learn by doing and return to the examplethat we just laid out. How would we really geta rocket from Earth, where it would launch from, to Mars, where there's definitely not a subterranean base of mine, for sure. We know we have to take somekind of curved path again, but we have to be exact orelse we're going to miss Mars, where something is definitely not being constructed right now, don'teven worry about it at all. So, let's get more technical. The idea during a Hohmann Transfer is to take some kind of elliptical path to your destination,but when you get there, you have to remember that a celestial body or a planet or what have you, has a lot of velocity on it's own. So, when you get there, you're gonna have to matchthat velocity in some way, and so, this kind of maneuverwon't just take one burn to launch you off of a planet like Earth, it's actually gonna take two, one to launch you off of your planet and then, a second to match the new orbit of the thing you are trying to intercept. When performed correctly, this kind of maneuver looks like this.
How'd you do? Using the exact same reasoning, look up the distancebetween the sun and Mars and solve for theorbital velocity of Mars. I'll wait. (elevator waiting music) The correct answer is 24 kilometers per secondaround the sun, C. How did you do? Did ya get it? Because now, it's time toget a little bit more-- (phone rings) complicated. Ssh, say I'm not here. (Over the phone) I know you're there! If you wanted to find outthe total amount of energy of a body orbiting something like a star, you would need it's energy of motion, it's kinetic energy and you'd also need it's gravitational potential energy, which is the same energy as anything has sitting in a gravitational field. Anyway, the total amount of energy of an orbiting body is also equivalent to half the gravitational potential energy at the average distancebetween two bodies, and this is really important because this will enable us to calculate how much velocity we will need to both enter and exit an elliptical path between two points. We can use this relationship to solve for velocity here, too, and we get the velocity that we need to both enter and exit ourelliptical transfer orbit based on R being the distance between the sun and Earth and the sun and Mars, and remember, that Ahere is those distances added together and then divided by two. Pop quiz!
Using the distance betweenthe earth and the sun as our first, what velocity do we need to initiate our transfer orbit? (elevator waiting music) The correct answer is A,33 kilometers per second. Did ya nail it? I bet you did, you nerds. Now, use the distancebetween Mars and the sun to find our exit velocity, pop quiz! (elevator waiting music) The correct answer is B,21 kilometers per second. Did you get it? Because if you did, thatdeserves one gold skull. We don't give out starsfor this kind of mission. So, now that we know all of our numbers, what is the total amount of velocity that we need to give our rocket to make it from Earth to Mars? This is a critical calculation in any orbital maneuver called Delta V, pop quiz, what is it?!
We want the absolute distance between all of these velocities. How much velocity will take us to launch off of Earth to get us into that elliptical orbit and then, how much will it take us to speed up or slow downto exit from that orbit and match Mars' orbit? Take a shot at it right now. I'll wait again, ah! (elevator waiting music) Did you get 6 kilometers per second? Well, let's check our work. You can find Delta V maps for real interplanetary travel pretty much anywhere on the internet. So, if we look at the pathway, you would need to take,in terms of velocity, from Earth to Mars andyou add all those up, what do we get? Well, I got 5.7 kilometers per second. Look how close we were with six. We calculated a space mission kinda. That deserves one gold skull, maybe even two, kinda, yeah!
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We did the basic calculations, sure, but to steal a space car, we might need some help. We already know the Tesla Roadster's exact location in space. We also know that it'sgoing 40 times faster than a Bugatti Veyron. Thanks to the laws of physics, we should be able to accurately track the position of thisspace car for centuries. Now, while we could do the same kind of Hohmann Transfercalculations that we just did to get to this space car, as you can see, the orbit of this car is not quite as nice and circular and centered on the sun as Mars is. So, I'm not gonna lie, these calculations we just went through aren't really gonna cut it and the math would be a littlebit above our pay grade. So, instead of going through a bunch of complicated math andthen, getting it wrong, why don't we, instead, play around with a very specific andspecifically helpful calculator? (rock music) Sup, nerds? Welcome back to anotherLet's Play, of course.
Today, we're checking outPlanetary Transfer Calculator, which you can go and check out at http://www.transfercalculator.com. As you can see here, we have the orbits, the standard orbits thatwe're looking at here. We have the earth orbiting around the sun and we have Mars orbiting out around here and what's cool about Transfer Calculator is that you can actuallyadd other minor bodies and we can add star man. So, let's turn that on right here. So, now, we see star man's orbit in red. Now, what this calculator does, is make hundreds of Hohmann-liketransfer calculations. It iterates them down to findthe simplest best transfer, the lowest energy transfer from anywhere you wanna go to another place.
So, we can actually now calculate our path using a lot of mathematical help from the people who created this, our path from Earth to, let'ssay, the Tesla Roadster. I'ma set the time to whenI'm filming this Let's Play, (chuckles) as we always do streaming. Yeah, am I right? So, I'ma set the time to now and then, I am going to go aheadand calculate our transfer. I get, if we launch next February, which is the best time to launch, according to this calculator, it looks like it'll take us just about 16 1/2 months to interceptthe Tesla Roadster and then, it would takeanother 16 1/2 months to get back to Earth, presumably, and with a Delta V of about4 1/2 kilometers per second.
So, this is a much longer transit time, as you can see here, to the Tesla Roadsterthan it would be to Mars, but it's a much lower Delta V. So, with all these numbers, we should be able to set oursuper villainy plan in motion. This is all we need. We can see the ship comingwithin intercept range of the Tesla Roadster now injust a couple months time. That's pretty cool. I like Transfer Calculatorquite a bit, all right. Ah, Bearcat comes in witha five dollar donation. If we use this specific trajectory, within a few years, we should be able to get our hands on the only road car thathas ever existed in space, and when our undisclosed Teslacapture spacecraft lands, we will have an awaiting semi-truck to whisk it away to super villain auction.
Of course, we probably won't be able to make back even one percent of the mission costs from the car sale, but hey, it's the supervillain principle of the thing, which I'm not and I'm notsaying you should do this and don't tell Elon. So, if you're a super villain and you have millions of dollars burning a hole in your pocket and staff and infrastructure and rockets and the knowledge of orbital mechanics, there is a relatively simple trajectory towards carjacking the star man and if you do pullsomething like this off, now that I support or condone it, tell them it was, "Because Science." (Chuckles) Space car. (Upbeat electronic music) You know what might actually be more impressive than a super villain stealing a space car, is if Elon Musk did all of this himself.
If he launched it into space and then, with hisreusable rocket technology in a couple years, wasable to successfully return a space car back down to Earth, and then, he restored it, and then, he was driving it around headquarters in Hawthorne, now that would be impressive, and it would improvehis rocket technology, and I guess I just gave hima great idea for some PR. You're welcome. (electronic music)
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