Ep 484: Transfer Orbits and Gravitational Assists

This episode was recorded on Tuesday, March 20 at 8 pm EDT / 5 pm PDT / 0:00 UTC Wednesday.
If you want to get around in the Solar System, you’ll want to take advantage of natural gravitational speed boosts and transfer orbits. Whether you’re heading to the outer Solar System or you want to visit the Sun itself, the planets themselves can help you in your journey.
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Show Notes

Gravity Assist – only possible with a moving object
Gravitational Assist tutorial paper (Thanks W.Bacon for reference!)
Missions using gravity assists:
Mariner 10 was first.
Voyager 2 was biggest one – sling-shooting around Jupiter and shooting out past Neptune towards Uranus
Voyager 1 took another look at Jovian moons
Galileo studied Jupiter and moons by going by Venus and Earth
Ulysses from ESA used Jupiter to sling around and study polar regions of the Sun
MESSENGER used one flyby of Earth, two flybys of Venus, and three flybys of Mercury before finally arriving at Mercury
Cassini passed by Venus twice, then Earth, and finally Jupiter on the way to Saturn.
NASA’s Parker Solar Probe mission, scheduled for launch in 2018, will use multiple gravity assists at Venus to remove the Earth’s angular momentum from the orbit, in order to drop down to a distance of 8.5 solar radii (5.9 Gm) from the Sun. Parker Solar Probe’s mission will be the closest approach to the Sun by any space mission.
Transfer Orbits
Hohmann Transfer
Bi-elliptic transfer


Podcast Transcription provided by GMR Transcription
Fraser: Astronomy Cast Episode 484: Transfer Orbits and Gravitational Assists.
Welcome to Astronomy Cast, our weekly facts-based journey through the cosmos, where we help you understand not only what we know, but how we know what we know. I’m Fraser Cain. I’m the publisher of Universe Today. With me – as always – Dr. Pamela Gay, the Director of Technology and Citizen Science at the Astronomical Society of the Pacific and the Director of CosmoQuest. Hey, Pamela. How are you doing?
Pamela: I’m doing well. How are you doing, Fraser?
Fraser: Good. I really feel like I don’t have a long enough title though. That’s for sure.
Pamela: You know, when I was in undergraduate school, I was told that you have increased amounts of power according to how many keys you have to a point at which the fewer keys you have, the more power you have. So, the person who has one key to unlock all the things has the most power.
Fraser: Right.
Pamela: That may be you.
Fraser: If a person has no title, do they have the best title? Good question.
Pamela: Possibly.
Fraser: Right, sounds good. I have no news this week – nothing super interesting. You’re on the road like crazy. We’re recording this in just this brief moment in between wheels down and wheels up.
Pamela: It’s true. I am just home from Israel where I got to hang out with Yoav Landsman – one of the friends of both of our shows. And I’m getting ready to leave for Japan where I’m going to see all the good folks behind the International Year of Astronomy back in 2009 and we’re gonna be working on planning new and exciting things. And then I’m back for like a week and I go to San Francisco.
Fraser: Whew.
Pamela: Yeah. But I can record Astronomy Cast from San Francisco.
Fraser: That’s true, yup. Speaking of, if you want to get around in the Solar System, you’ll want to take advantage of natural gravitational speed boosts and transfer orbits. Whether you’re heading to the outer Solar System or you want to visit the Sun itself, the planets themselves can help you along in your journey. Alright, Pamela. Now, I mentioned this sort of before the show the fact that people love the idea of gravitational assists. It’s like – I don’t know – it’s like free money. It’s like winning the lottery and they love the idea.
So, let’s get into gravitational assists and transfers. Now, we talked about gravitational assists a long time ago and this was one of those times when I legitimately didn’t understand how this worked and you explained it to me in a way that I finally understood. And so this idea of gravitational assists right – and I think this is where a lot of people have the problem understanding it – is that it makes sense. Let’s say you’re flying yo8ur spacecraft to Jupiter. It makes sense that your spacecraft is flying towards Jupiter and – as it falls down into Jupiter’s gravity well – it speeds up and speeds up and speeds up.
But then as it flies away from Jupiter, it’s being pulled back towards Jupiter and so it’s gonna slow down and slow down and slow down. And so when you think about this sort of dropping into a gravity well and back out, you would expect that the speed boost that you would get would then be cancelled out by the speed un-boost. How does a gravity assist work?
Pamela: I love how you do like 90 percent of the explanation and then you’re like, “And what’s the final ten percent?” So, it turns out the gravitational assists only work if you’re working with a moving object. So, for instance, within our own solar system, we can change our direction using the Sun, but we can’t boost our orbital velocity using the Sun because relative to the rest of the Solar System, for all intents and purposes, the Sun is not moving. Now, Jupiter. Jupiter is moving and the fact that it’s moving makes all the difference in the world.
So, if you sneak up on Jupiter – which isn’t hard because it has no observational abilities – if you sneak up on Jupiter as it’s orbiting in the same vague-ish direction that it’s moving around the Sun, you will spend more time as you’re catching up to Jupiter getting pulled into Jupiter – and pulled along the orbit with Jupiter – than you spend running away from Jupiter. It’s that excess time as you’re moving in the same direction as Jupiter where you’re gaining from its orbital speed and getting to add some of that to your own speed.
Fraser: But the further you go from the Sun, the planets are orbiting more slowly.
Pamela: Yes.
Fraser: So, if you’re orbiting the Earth – and say the Earth is going, I don’t know, 30 kilometers per second – and then you leave the Earth on this big, long trajectory. You fly past Jupiter. It’s going more slowly. How does that give you a boost?
Pamela: It’s the amount of time that you’re falling into its gravity well. So, as you’re catching up to it, it’s going, “Come on. Come on. You can do it” pulling you in with gravity. That pulling you in with gravity over the long period of time that it takes for you to catch up, each moment that you’re working on trying to catch up to Jupiter, it’s pulling you a little bit further and pulling you a little bit further and then it’s as you race away and you spend much less time racing away. It’s that integrated time that’s longer catching up than it is running away.
Fraser: And so something has to pay the terrible price for this, right?
Pamela: Well, Jupiter – in theory – slows down a little bit and it actually happens in reality, but not at a level that we can measure because let’s face it, the mass of a spacecraft is awful tiny compared to the mass of Jupiter. So, while Jupiter does give up some of its momentum, that loss is not a huge concern to that giant planet.
Fraser: So, the most famous example of spacecraft that used gravity assist were the Voyagers. Tell me about that.
Pamela: So, Voyageur II is perhaps the best example. It left Earth. It was on a nice, happy journey through the Solar System, caught up to Jupiter and turned almost a right angle as it slung shot around Jupiter and made its way straight off towards Saturn, where it made another massive turn to get flung off towards Uranus. And from Uranus it was almost a straight line. We had this glancing blow past Uranus with only a slight turn coming and then it headed out towards Neptune.
And it was this amazing alignment of the worlds that Voyageur II was taking advantage of and Voyageur I took advantage of it as well. It was this amazing alignment of the worlds that was what caused them to race to get the Voyageur program done when they got it done. Had the worlds not been aligned so beautifully in their orbits allowing all of these different gravity assists to take place, Neptune would not have been on the possibilities list and we would never have had one spacecraft be able to make such a grand tour through the Solar System.
Fraser: You’ve probably seen the animations of them doing this, right? Where the Voyageurs go past Jupiter and then you can see the slingshot. They go faster. Then they take another trajectory around Saturn. Voyageur II heads off to Uranus and Neptune and Voyageur I just sort of heads off into deep space. Interesting side note; I don’t know if you knew that Voyageur I could have made a trip to Pluto?
Pamela: And they decided not to because they needed to get a little bit better of a look at those moons.
Fraser: Yeah. They wanted to get a look at Titan and the horrible irony is that Titan was too foggy for the Voyageur spacecraft to see it and so Cassini had to be the one that did it.
Pamela: We did learn something. We learned it has an amazing atmosphere. It was just – with sadness – that we learned that it has an amazing atmosphere at the cost of Pluto.
Fraser: Yeah, alright. So, that’s a good example of a spacecraft that that’s a very famous mission, but others have sort of done famous gravity assists – not because they wanted to go really quickly, but they wanted to be able to get there at all. And a good example of that was the Galileo mission.
Pamela: Right. So, launched back in 1989 on the space shuttle Atlantis, it was originally planning to do what’s called a Hohmann transfer orbit. This is how we normally get to Mars. This is where you hit your nice, circular orbit around Earth, then boost your velocity such that our position on Earth is the closest point on the orbit to the Sun and that furthest point from the Sun is going to be when they hit that next world that we’re planning to get to.
And in the case of a few Mars missions, I mean hit that world quite literally, but ideally you get there and you slide straight into orbit and the original plan for Galileo was to slide right into orbit, but there was problems. Our ability to use the space shuttle changed between when they designed the Galileo spacecraft and when they launched the Galileo spacecraft. And we were no longer taking space shuttles to as high an orbit and – with these changes – the energy just wasn’t quite going to be the same.
So, they basically visited more objects than seems rational in our Solar System, by which I mean they got to Jupiter by way of Venus, which is not a path anyone would ever really expect.
Fraser: Right, and explain that, right? So, like that simple idea of the Voyageur flying out, picking up a speed boost from Jupiter and then Jupiter paying the terrible price and getting slowed down a tiny, little bit and then it sling-shotting out into space. How could it use something that’s closer to the Sun? It used Earth as well, but it launched from earth. What?
Pamela: Right. So, it launched from Earth. It was in an orbit around the Earth. It then increased the size of its orbit so that it went out past Venus. So, that is bigger than going around the Earth. It got a gravity assist from Venus – which slung it a little bit faster, moved it along – and so now it’s in this orbit that started at Earth, including Venus. It’s not heading back towards Earth. It got some more gravity assist from Earth and then continued off on its way until it eventually – very far in the future – ended up slowly making it to Jupiter.
Fraser: Right. I’m still – you know. We’ll probably need to move on, but I think for a lot of people how you can get that sort of stealing of momentum from an inner planet is the part where their easy understanding of how this works starts to go sideways.
Pamela: So, the way to think of it is while you should push a swing just after it hits its highest point to add velocity as it goes down, you can add velocity to it at any point and you’re still gonna increase how high the swing goes, as long as you’re pushing in the same direction the swing is already going.
Fraser: Right.
Pamela: So, with Venus, we’re going along in our orbit and – because its gravity pull pulled us in the direction it was moving, in the direction we were moving – that extra pull was just like running along as someone’s on the swing, giving them a little bit of extra force the entire time. It’s not a lot. It’s not ideal, but it totally gets the job done.
Fraser: So, what is sort of the theoretical limits of what this technique can give you? Could you just keep going back and forth in the Solar System ping-ponging around until you’re going the speed of light? What are the limits?
Pamela: Well, no. The fullness of time doesn’t quite allow you to get there. You can continue to increase your speed until you’re going the speed of the objects that you’re stealing energy from.
Fraser: Compared to the sun?
Pamela: Well, okay, it’s more complicated than that.
Fraser: See.
Pamela: Yeah. So, you start out usually going faster than the objects. It’s the whole momentum thing. You can’t steal all of an object’s momentum. And momentum is mass times velocity. So, the thing that makes gravitation assists work is spacecrafts have little, tiny mass. Planets have big mass. Spacecraft have large velocity. Planets have not as large a velocity, but still large compared to me sitting in my chair.
And that velocity that they’re going around the Sun, as long as we’re moving with that and not at a right angle – right angles don’t work – we’re good. If we’re going against it, we can slow ourselves down. Now as you’re ping-ponging around, you have to be careful of a couple different things. One, don’t launch yourself out of the Solar System. So, you can’t exceed the escape velocity of the Solar System and not have a plan for turning yourself around and keep ping-ponging around.
Fraser: Right.
Pamela: So, just that’s a mathematical difficulty.
Fraser: And just to give people some context, the escape velocity of Earth is about 8.5 kilometers per second and the escape velocity of the Solar System is about 16 to 17 kilometers per second. So, that’s your window. Could you scale this up even further though? Could you use another star? Could you use a black hole? What are the limits of this?
Pamela: There’s no limit as long as the other object is moving. That’s the whole catch. If it’s stationary relative to the system you’re flying through, it’s not going to help you. So, if you’re flying around inside our galaxy, you’re not going to be able to gravitationally assist yourself around the black hole in the center. You can change your direction. You’re not going to gravitationally assist yourself. But all the little stars all over the place, those are totally useful. All of the stellar mass black holes all over the place, totally useful. You just have to – well, gravitationally assist yourself out of the Solar System first.
Fraser: Right. Now, you can use gravitational assists in reverse as well, which is that you can use them to slow yourself down. I think a good example of what that is is the upcoming Parker Solar Probe. I don’t know if it’s exactly slowing itself down, but it’s getting itself to a very difficult orbit, which is very close to the Sun. So, how would this process work in reverse?
Pamela: Well, in this case, you simply go against traffic. You fly in the direction so that your motion looks like you’re heading towards a head-on collision with a planet and then you miss. And as you’re getting accelerated towards that head-on collision, you’re getting accelerated into the planet’s gravitational field. But the amount of time it takes you to get there – since it’s a head-on collision – is shorter than the amount of time it takes you to go, “Oh, my gosh. I didn’t actually get hit” and fly away. So, as you’re flying away with it behind you, you moving past it, this amount of time is prolonged and that’s where all of the slowing down takes place.
Fraser: Right. And so in this case, you’re actually speeding up its orbit.
Pamela: Yes.
Fraser: And it is doing the reverse. It is slowing. So, you’re kind of giving it a push, which is awesome.
Pamela: And it’s all about the momentum in this case. Physics requires momentum to always be conserved and you can do all sorts of remarkable things this way, but what’s cool is that you’re also changing the angles on everything. So, while we often think about the speeding up and the slowing down, every time you see Voyageur II making that almost right hand turn as it makes a bank shot around Jupiter, it’s also changing the direction of the orbit. And this is key when we start thinking about what happened in the early Solar System as we boosted various moons, various asteroids, all sorts of things into all sorts of different orbits. It was all this same principle.
Fraser: Right. So, this is kind of half of the conversation. The other half is to talk about transfer orbits and you mentioned briefly the Hohmann transfer?
Pamela: Yes. This is the most common type of transfer orbit that we think about because it’s – in a lot of ways – the lowest energy kind of transfer. You fire your engines once when you’re at that closest point to the Sun if Earth is where you’re starting and you’re trying to move outwards and then you fire them again to move into orbit as necessary once you get to your furthest from the Sun point at either Mars or Jupiter or Saturn.
And it’s this simple, change your orbit once, set yourself going, and then just correct your orbit when you get where you want to be that makes it so simple to do, such a low energy orbit. Now, the thing with the Hohmann transfer orbit is you do have to remember that you’re actually slowing yourself down if you want to go to an inner orbit. So, you can use it in both directions. We can use the Hohmann orbit to get to Mars. We can use it to get home. It’s just slow. Slow happens.
Fraser: The trick with the Hohmann transfer is that it is your slowest, but the least amount of propellant that you have to use. As you said, right, you’re firing your thrusters when you’re in orbit around Earth say at this perfect time.
This is the key is that you need this window and then you fire your thrusters and this puts you on a new essentially orbit around the Sun that intersects both Earth and the target that you’re trying to get to – say it’s Mars – and then when you get to Mars, you fire your thrusters again to get caught and go into orbit around the planet and you’ve used the minimum amount of propellant as you said. And this is why we can only fly to Mars every couple of years.
Pamela: And it’s one of our great frustrations with everything in the Solar System because the alignment we got with Voyageur I and Voyageur II isn’t an alignment we’re going to get again in our lifetime. So, there’s certain exploration missions that we just can’t wait for the planets to get back where they are and we can only launch in so many windows to get to Mars and it’s just a huge frustration because alignments are fairly rare. But we do what we can and keep a constant eye out for when is that prime time to get to Jupiter? When is that prime time to get to Saturn or Mars?
Fraser: And when is that prime time when you can fire a spaceship past the four giant planets in the Solar System? Oh, not again for another couple of hundred years, unfortunately.
Pamela: But luckily they got it done when they needed to get it done.
Fraser: Yeah. The amazing thing about that mission was that they didn’t even know that they were gonna be doing that full grand tour until they kind of already launched. They knew it was possible and they raced to get that timeframe, but they didn’t know that they were gonna for sure do it. And so, in the end, they did get the green light and were able to extend the mission to add Uranus and Neptune, which is always so fascinating.
Now, you talked a little about Hohmann transfer, which is this really – and again tons of animations on the internet. I apologize that this is a podcast because this is the kind of thing that, for example, if it was the Guide to Space, we’d show you a pretty animation. But just imagine you leave Earth and you fly on this big, long sort of circular orbit and you reach Mars. Let’s talk about some other transfer orbits. The one that I love is the free return trajectory from the Moon.
Pamela: Really?
Fraser: I think it’s the most – It saved Apollo 13. Oh, yeah, I love that transfer, that trajectory.
Pamela: Okay. So, do tell. I was ready to talk about bi-elliptical, but it sounds like this one is your heart and soul.
Fraser: It’s not. I just love it. But this was this idea that when you fly to the Moon, there is – as one extra layer of safety – is that you can follow a trajectory where you’re able to return back to Earth. You sort of do this figure eight around the Moon and are able to come back and you sort of catch the Earth where it’s moved a little further in its orbit and the Moon has moved around a bit in its orbit and you can kind of make everything lined up.
And it’s a safety valve if there’s a problem with your mission and they used it in Apollo 13. They weren’t able to go down. They weren’t able to land. They used the free return trajectory. They went around the Moon, used it as a different kind of slingshot to kind of get thrown back towards the Earth and were able to return the astronauts safely. And if they hadn’t built that trajectory into account, they probably wouldn’t have gotten those astronauts back safely from that mission. So, I really love that free return trajectory. But let’s talk about your next transfer orbit.
Pamela: So, one of the orbits that has always left me going, “That makes absolutely no sense but it still gets used” is the bi-elliptic transfer orbit. This is an orbit where say you start off in a fairly low Earth orbit – nice and happy circular – and you want to get yourself into a slightly larger circular orbit. It turns out one of the ways to do this is to put yourself into a giant elliptical orbit. So, you start off small, circular orbit, fire your engines. The point where you fire your engines becomes your closest point to the planet Earth. You’re now launched off into an elliptical orbit. You will return to the same distance you start at.
But say you don’t want to return to the same distance you started at? Say you want to return to a slightly further out orbit, but not a lot further out of an orbit. When you’re at your new point in your elliptical orbit – furthest from the Earth – you just fire your engines a little bit and – as you fall back to Earth – you’ll fall back, but not back to your starting point – to a point further out than your starting point.
Fire your engines again to circularize things. This is one of the lowest energy ways to move yourself between two circular orbits and it actually can require less change in velocity than the Hohmann transfer maneuver which, to me, does not intuitively make sense. But the math makes sense and my stomach yells at my brain and the brain wins.
Fraser: Right. Well, I think the most fascinating one – and it’s sort of the longest – like if you’ve got nothing but time that you want to take the interplanetary transport network – Have you looked into this?
Pamela: I haven’t.
Fraser: So, it’s essentially it’s this idea that you can sort of make your way up to the Lagrange point around a certain object. So, you want to go Earth, Sun, L2 Lagrange point. And at that point, you’re kind of drifting away from the Earth at that point. And then you can sort of slowly make your way – with very little propellant – and get caught by the Mars Sun Lagrange point and you sort of drift your way in.
And you can actually go from world to world throughout the entire Solar System – either direction – with almost no propellant. The only downside is it takes a ludicrous amount of time. So, if you want to go from Earth to Mars, you could do that for free if you can get up to the Lagrange point. It just takes 10,000 years – and longer if you want to go from Mars to Jupiter and Jupiter to Saturn. It’s crazy.
Pamela: Let’s maybe not do that.
Fraser: Right.
Pamela: But be in total awe of the first person figured out the mathematics on that.
Fraser: Yeah. There’s a researcher at NASA JPL and there’s this great graphic of the interplanetary transport network and everyone’s super excited about it until they find out how long everything takes. It has been used a couple of times because there’s sort of smaller versions of it that you can use if you’re trying to go to asteroids that are close to Lagrange points that are already available to us.
So, if you want to go and visit various near-Earth asteroid or things like that, you can do it within a couple of years with almost no fuel. But even that is way too long. You could just take the Hohmann transfer and be there relatively overnight. But if you got nothing but time and you don’t have fuel, then you can follow the interplanetary transport network. But one of the interesting ideas about that is just that there is material that could be flowing from world-to-world because of the way these gravitational balances work out.
Pamela: And that’s kind of amazing and, at the end of the day, the magic of all of this is – and by magic I mean the sufficiently advanced science of all of this – is if you have all the time in the universe, you can get anywhere with very little energy requirement. The trick is this ping-ponging around doing the gravity assists takes time and if you want to get somewhere fast, the way you do it is you accelerate constantly and then deaccelerate constantly. And that at least gives you gravity.
Fraser: Yeah. Awesome. Alright. We got one more episode in this series and that’ll be next time.
Pamela: Sounds great, Fraser.
Fraser: Alright. See you then, Pamela.
Pamela: Okay. Bye, bye.
Announcer: Thank you for listening to Astronomy Cast, a nonprofit resource provided by Astrosphere New Media Association, Fraser Cain, and Dr. Pamela Gay. You can find show notes and transcripts for every episode at astronomycast.com. You can email us at info@astronomycast.com, tweet us at Astronomy Cast, like us on Facebook, or circle us on Google Plus. We record our show live on YouTube every Friday at 1:30 p.m. Pacific, 4:30 p.m. Eastern, or 2030 GMT. If you missed the live event, you can always catch up over at CosmoQuest.org or on our YouTube page.
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[End of Audio]
Duration: 28 minutes

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