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In the 1960s, the space race was well under way.

Â Both the United States and

Â Russia were trying to figure out how to put people on the moon.

Â Another obvious place to compete in space is to send the first space craft

Â to another planet.

Â It sounds a little complicated, to send a space craft to another planet,

Â but I'm actually here to tell you a, a dirty little secret.

Â The dynamics, the orbital dynamics of sending a space craft to another planet

Â are actually pretty simple.

Â And the reason they're pretty simple is because all you have to deal with

Â is gravity.

Â And when you're in, flying through interplanetary space,

Â all you have to do with, deal with, is the Sun's gravity.

Â Eventually you get close to Mars, you have to deal with Mars' gravity.

Â You have to leave the Earth, you had to leave, deal with Earth's gravity.

Â But once you've done those two things, that flight through space is pretty easy.

Â It's efficiently easy that we can at least calculate some simple things about it

Â just right now.

Â First question you might ask yourself is how would you get from Earth to Mars?

Â Well let's remember that, here let's put the sun here in the middle again.

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Earth is here. Mars is out here.

Â And let's actually write down the distances because these

Â are going to be important.

Â The distance from the Sun to the Earth, average distance, is defined to be one AU.

Â One astronomical unit.

Â And in these same units, in these same units,

Â Mars is 1.524 astronomical units.

Â So, Mars is about 50% further away than the Earth is.

Â Is this when you launch your spacecraft?

Â Well, okay. Let's figure out how you do it.

Â You launch your spacecraft here and you head straight towards Mars.

Â But of course Mars has moved along this way.

Â And so maybe you should launch in this direction and

Â eventually intersect with Mars.

Â If you start to iterate this long enough you realize that the easiest thing to do,

Â the least energetic solution is actually not to launch towards Mars at all,

Â but to launch perpendicular to the Earth's orbit,

Â with just a slightly higher velocity than the Earth's orbit.

Â Let's look at how that looks.

Â If this is the Earth's orbit, I'm going to draw the whole thing now.

Â Here is the orbit of Mars.

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The way you get from Earth to Mars using the least amount of energy and

Â using the least amount of energy is important because you have this

Â large spacecraft that you're trying to get to Mars,

Â usually your limiting factor is how much energy you can generate from his rocket.

Â So the least energetic way to get form the Earth, Earth is right here,

Â to Mars is a flight that goes, just barely hits the orbit of Mars.

Â And if it continued on, didn't stop at Mars, it would come back to the Earth.

Â Now, you could do a lot more things.

Â You could say, I'm going to go faster, and I'm going to try to go this way.

Â But imagine what you've done now.

Â You have intersected Mars, and

Â you still have a high velocity as you're going through here.

Â So you would take yourself way out through here to the outer part

Â of the solar system.

Â And back in, if you continued on after Mars.

Â To get on an orbit like that requires a lot more energy than this one that's just

Â barely leaving the Earth's orbit, and just barely getting to Mars.

Â As you might remember, from orbital mechanics, or just some basic physics.

Â The important things that matter in an orbit are the semi major axis.

Â And the excentricity of the semi major axis, this is an elliptical orbit now.

Â The semi major axis is the average of the closest and

Â the furthest points from the orbit.

Â The closest points of the orbit is called the parhelion,

Â furthest point from the orbit is called the aphelion and

Â they're simply related mathematically by q parhelion.

Â And this is the typical thing we call use for

Â parahealian is a the semi major axis times 1 minus the eccentricity,

Â and Q, it's terrible that astronomers use this notation, but they do,

Â is, which is the appelline is a times 1 plus e.

Â So, if you know the semi-major axis you can figure out the eccentricity.

Â If you know the locations where these parahelia and aphelia are, and, in fact,

Â you do, because you want the parahelian to be Earth's orbit, which is one AU, so

Â that is going to be 1AU.

Â You want the aphelion to be the Martian orbit, which is 1.524AU.

Â You can solve these two for the semi major axis.

Â Of course we know the semi major axis is just the average of these two.

Â So the semi major axis of your new orbit that you're putting this thing on is AU,

Â is 1.262AU.

Â So you have added energy to the orbit by moving it to a higher semi-major axis.

Â As you might remember from basic physics, orbital mechanics,

Â adding energy to an orbit causes the semi-major axis to increase.

Â Decreasing energy causes it to crease, decrease.

Â And so, you see that this orbit is the one where you add the least amount of energy

Â and still make it to Mars.

Â Again, you could do this orbit sure, but

Â now you're semi-major axises is much larger and

Â your energy is much larger, which means you need a huge rocket to get there.

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The benefit is you get there faster.

Â That has never been an important enough benefit that anybody's ever

Â done it that way.

Â Instead, every single mission to Mars has taken an approach that moves from here

Â over to here, lands at that point.

Â How long does that flight take?

Â Well, it's, it's half of the orbital period of this new orbit of the rocket.

Â The orbital period of an object is equal to the semi-major

Â axis to the three-halves power.

Â This is simply one of Kepler's laws, one of Kepler's three laws.

Â The semi-major axis of the Earth, and this is, of course,

Â in, semi-major axis in AU, orbital period in years.

Â Here's the semi-major axis of the Earth is one AU, and so the period is one year.

Â That's nice.

Â Semi-major axis of Mars as you remember is 1.524.

Â So it takes Mars 1.88 years to go around the sun.

Â And the semi-major axis of this is 1.262 so it takes this object that,

Â your spacecraft, about 1.4 years or

Â 17 months to go all the way around the Sun.

Â But you don't go all the way around the Sun.

Â You go to Mars.

Â So you're only doing half of your orbit.

Â So it takes you about eight and a half months to get from the Earth to Mars.

Â And if you're ever paying attention to Martian flights.

Â The next one is not going to be for a while so

Â you had to've been paying attention recently.

Â But they always launch something like nine months before they get there.

Â They take about that long of a time to get there.

Â So when do you launch?

Â You don't launch when the Earth is right here and Mars is right here.

Â Because, then in nine months, what's going to happen?

Â Well, in nine months your spacecraft is going to be here,

Â but where is Mars going to be?

Â It will only have gone about 40% of the way around it.

Â It'll be around right here.

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And your space craft will fly by and say Mars wasn't here.

Â So instead, you launch when Mars is about right here.

Â The Earth has not quite cut up, caught up with Mars yet, and

Â then Mars is right here when the spacecraft arrives there.

Â Or if you think about it, the spacecraft is actually moving slower then Mars at

Â this point which is why its going to start to fall back towards the sun.

Â And so its not really that Mars is there when the spacecraft arrives,

Â the space craft is there when Mars arrives.

Â And how do you actually do it,

Â really all you do is you have the the rocket is in orbit.

Â Getting into orbit, okay, that's a little bit complicated.

Â I told you that the orbital dynamics is easy because all you have to worry

Â about is the sun.

Â Rockets, going through the Earth's atmosphere?

Â Much more complicated.

Â We're not going to worry about that.

Â We're going to assume that somebody else takes care of that and

Â we are now in orbit around the Earth.

Â Once you're in orbit around the Earth, all you do is calculate the velocity that you

Â need to have, and you know the direction you need to go,

Â perpendicular to the sun, and then that's all you do.

Â You, you blast your rocket, it gives you that exact velocity, and you coast.

Â The spacecraft moving to Mars, we sometimes think of them as,

Â burning their rocket the entire time, but they don't.

Â It's easier to think of it as they do one blast of the rocket, and they coast for

Â nine months until they get there.

Â In practice, somewhere around in here, they take a look where they are, and

Â they say, oh you know, I'm off by a little bit this way, a little bit this way, and

Â they do a mid-course correction or two to perfectly align themselves.

Â But other than those small corrections, they're really just coasting.

Â They're really just resting and waiting until Mars grabs them.

Â And then they have to do something else because of course, if they got here, and

Â nothing else happens, well, if we, if we, aimed perfectly we would smash right

Â into Mars which would be entertaining but not very scientifically useful.

Â We've actually done that before a few times.

Â