It’s hard enough finding your way around planet Earth, but what do you do when you’re trying to find your way around the Solar System? Today we’ll talk about how spacecraft navigate from world to world.
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Fraser Cain: Astronomy Cast Episode 413, navigating near. Welcome to Astronomy Cast, your weekly facts based journey through the cosmos where we help you understand not only what we know but how we know what we know. My name Fraser Cain. I’m the publisher of Universe Today. With me is Dr. Pamela Gay, a professor at Southern Illinois University Edwardsville and the director of Cosmo Quest. Hey, Pamela, how you doing?
Dr. Pamela Gay: I’m doing well – a bit more than sleepy. We just finished a two day, all hands meeting for Cosmo Quest where we brought in all the new people for funding and then got home to a sick dog, so it’s like I’ve gone three days without enough sleep, actually, much longer than that. So this is going to be the sleepy Pamela episode, so please be kind.
Fraser Cain: Aw, I won’t. I just got back from – yeah, no, the questions gotta come. It’s gotta happen.
Dr. Pamela Gay: It’s true.
Fraser Cain: I have no sympathy, no mercy. Yeah, I just got back from a weeklong trip in Banff Jasper. If you’ve never been to that part of the world, I highly recommend it. It’s so great. It’s unbelievable. What a beautiful, beautiful place. Man, I like road trips. Today’s episode of Astronomy Cast is brought to you by me. Well, it’s actually brought to you by Universe Today, which you’re probably aware is the website that I run – www.universetoday.com. I’ve been doing Astronomy Cast with Pamela for almost ten years now, and I’ve been running Universe Today for more than 17, and in the past, the website was full supported by advertising, and it mostly still is.
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Fraser Cain: It’s hard enough finding your way around planet Earth, but what do you do when you’re trying to find your way around the solar system? There’s three dimensions. Today, we’re gonna talk about how spacecraft navigate from world to world, and next episode, we’re gonna talk about how they get from star to star.
Dr. Pamela Gay: In the future.
Fraser Cain: In the future how it will happen. Okay, cool. Pamela, let’s just start and talk a bit about what methods we use to just navigate here on planet Earth, and then why we can’t scan that up so easily.
Dr. Pamela Gay: Well, once upon a time, it was simple. You said, “There’s a tree over there on a hill. There’s a mountain over there, and back behind me I see the ocean. I’m going to orient between these different things.” Well, you might sometimes screw up because you misjudged your distance to the tree; you generally knew where you were in the grand scheme of your small area. As people’s’ world’s got bigger, as they explored further and further across land, it became a matter of, “I know the sun rises in the east and sets in the West,” and we could get our basic directions off of the stars and the sun with enough guesstimates on time that we could handle things like the Mediterranean.
Now, when people started trying to travel across the ocean, we had to then solve the time problem, travel this far across this completely blank ocean for this amount of time, look at what the stars look like at a given time, and you could figure out where you were, north, south, east, and west.
Fraser Cain: Right, and that was a huge, huge challenge. the knowing where you are, north and south, is relatively straightforward. You just look at the stars, and you can tell where you are. Knowing where you were east to west, as you said, took a really, really precise clock, and there’s a wonderful story about that. What was it, the chronograph?
Dr. Pamela Gay: Yes.
Fraser Cain: The latitude prize.
Dr. Pamela Gay: Yeah.
Fraser Cain: Longitude prize, sorry. Amazing story. Did you ever see it? There was this great television special.
Dr. Pamela Gay: No, I didn’t.
Fraser Cain: I’m not sure who did it. They covered the whole story of the longitude prize.
Dr. Pamela Gay: It’s totally going out – Dava Sobel did a book on it. Go read her book. But here on Earth, basically, if we can figure out north, south, east, west, we’re confined to a surface, so we’re only moving really in two dimensions, so we only need to know where we are along that north and south and that east and west, and we’re good. But when you get into outer space or you when you add the third dimension on the surface of the planet, you suddenly need something else, so GPS, actually, here on the surface of the planet, if you have a good GPS connection, it will tell you how many stories up in a building you are. You need that extra thing in space helping to nail down your position in that extra axes of movement.
Fraser Cain: Although, it’s still clocks, which is kinda fun, right?
Dr. Pamela Gay: It is, but here, now you’re measuring how long it took between when that signal was released from a couple of different spacecraft to when you received it because all those different time lags tell you, “Oh, it was less lag to this spacecraft, more to that spacecraft. Now, I know my distance from these three spacecraft. Now, I know how high above the surface of the planet I am.
Fraser Cain: Right, and so your GPS device is just listening to all of these signals. It locks on to as many GPS satellites as it can and then looks at the time codes from every single one of these satellites and then figures and calculates its position in three dimensions mapped onto the two dimensional surface of planet Earth and tells you were you are. And as you said, you get your altitude as well. So this is all great. Thanks to GPS, we’ve got this great system for navigating ourselves on planet Earth. So once we get up into space, how does it get weirder and harder?
Dr. Pamela Gay: Well, so here on the surface of the planet, we’re only really worried about three dimensions: up, down, left, right, side to side, or north, south, east, west, and altitude above the surface of the planet. To measure your position or to lock in your position in three dimensions, you need three measurements. We nailed that. The problem with the solar system is you now have to add a fourth dimension of time because the planets are constantly moving.
Fraser Cain: Right, but I’m just trying to think about it. So if you were – say you had some spacecraft, and I’m just thinking how I would go about it is I would somehow have a bunch of either signal receivers or cameras on it that were looking for the positions of, I guess, the signal on Earth, the signal of – or at least a way to tell where the positions of the planets are, where the stars are, but things aren’t gonna move very quickly when you’re out deep in space, so how do they do this?
Dr. Pamela Gay: Well, we’re not going too deep in space yet. We’re staying within our own solar system.
Fraser Cain: Right, so the stars aren’t gonna move. They’re all gonna be in their same positions, and it’s not like you’re calculating when they rise and set.
Dr. Pamela Gay: So to first order, you figure out how far you are away from the surface of the planet Earth, and we can do this using the deep space network. We send a signal out to the spacecraft. The spacecraft sends an A-Okay back, or a moral equivalent, and we measure the transition time that it takes from message sent to message received. That tells us where it is, and it can do something very similar to figure out where we are. So now, it knows its distance from the receiver on Earth.
Fraser Cain: Right, but distance, that doesn’t tell you position; it just tells your distance.
Dr. Pamela Gay: Well, it tells you that you’re on a surface of a sphere that is centered on that point that was sending out the signal. So you’ve now confined yourself to the surface of this sphere.
Now, once you’ve confined yourself to the surface of the sphere, that helps. Now, the next thing that the spacecraft will do is, quite often, they can take pictures of the bright stars and figure out relative to the bright stars, okay, so I now know where I’m oriented relative to that other sphere, and between these two different things, you can figure out exactly where you are on that surface. So you get your distance from the Earth, and then you figure out where you are on that sphere by looking at the stars and figure out your orientation relative to the stars.
Fraser Cain: And so you’ve got this calculation, but it’s an imaginary sphere. It’s not necessarily your orbit. It’s like a –
Dr. Pamela Gay: It’s literally.
Fraser Cain: It’s a crystal sphere. It’s an imaginary sphere that your spacecraft if on for this moment, and you also know the orientation of the spacecraft.
Dr. Pamela Gay: Exactly. Now, all this tells you is the where. It doesn’t tell you the how fast bit, which is something that really matters when a spacecraft is in motion.
Fraser Cain: Yeah, and – sorry – just to go back to nautical terms, knots, that was the way they used to calculate their position is that they would put a rope out behind their ship, they would tie a bunch of knots on, and that would tell them how fast the ship was going depending on how many knots were poking up above the water, and then they would calculate and say, “WE traveled in this direction at 30 knots for 17 hours, and so we’re pretty sure we’re at about this position.” But it was a pretty –
Dr. Pamela Gay: Crude.
Fraser Cain: Rough, very crude method, and that’s why they came up with the clock system instead.
Dr. Pamela Gay: And so we don’t exactly have the ability to throw a rope out behind the spacecraft and measure how it’s moving relative to the doesn’t actually exist ether of space.
Fraser Cain: Right. If only the ether existed. That would be so easy.
Dr. Pamela Gay: But this is where Doppler shifting is super useful. So we can look at what is the frequency shift and that signal that we’re getting from the spacecraft. And the other thing is we can actually refine our position by receiving that signal a couple of different places and say if we have a circular planet Earth, okay, this receiver over on this one side of the Earth, it’s getting this Doppler shifted component.
This receiver over on this other place on the earth is getting a different Doppler shifted component. And that starts to get at, what is the velocity in two different dimensional because you know the X and Y components have to add up to be the same for the spacecraft. Since you’re in a different position, you’re going to see part of that X and part of that Y differently for the two different positions.
Fraser Cain: So sorry, just to go into more detail on this then, so the spacecraft is – or say Earth is sending a signal to the spacecraft. The spacecraft receives a signal. It knows the frequency of this signal if both were, I guess, at rest. It knows, what is the frequency of the signal that is outbound? I guess it’s been calculated beforehand or it’s provided information. And then it measures not only – or it provide the timecode – but it actually measures the frequency of the signals that are coming towards it, and says, “Okay, great. I know what the frequency should be. I’m calculating what the frequency is now, so I know what my relative velocity is to that signal.”
Dr. Pamela Gay: Yeah, and –
Fraser Cain: And if I can get two signals and calculate the frequency, then I can see, “Oh, I’m moving a little towards this signal and a little away from that signal, and you can do the math to figure out your exact velocity in this three dimensional space.
Dr. Pamela Gay: Exactly, and one way to think of it is if you have a car that is moving straight away from you, you have pure Doppler shift. If you have a car that’s moving in front of you as it goes by on a road that you’re standing on the sidewalk beside, then you have zero Doppler shift when it’s straight in front of you. But as that angle changes from being off in the distance where it’s close to coming straight at you, but not quite because you’re on the sidewalk and not on the road, that angle, as it changes, the amount of Doppler shifting changes, and then it happens again as it’s moving away. Well, if you have two different people watching at two different points on the sidewalk, they’re going to experience the zero Doppler shift being directly in front of you in the street at different times, and at any given moment, they’re gonna see a different frequency shift.
Fraser Cain: Right. Okay, so now we’ve got distance from the Earth, we’ve got our velocity, and we’ve got a sense of what our orientation and position is. So does that give us all the tools that we need to pretty accurately know where we are?
Dr. Pamela Gay: The velocity is hard to get completely right because with our two measurement example, we’ve now only gotten that velocity nailed down and two different axes. You really want to have three different points to measure it to get your three dimensional velocity. So once you get that three dimensional velocity, measure your three dimensional velocity, measure your three dimensional location, you know where, and you know where you’re going, and that is the important part for not losing your spacecraft.
But beyond not losing your spacecraft, you need to also know all those three dimensional component for where you’re getting to and calculate into the future, how’s my spacecraft moving into the future, and how is the planet going to – or the comet or the asteroid – how is it moving into the future?
Fraser Cain: Right, and so that is the – I guess that’s part of the time component is that with more measurements of these – your distance, your velocity, and the three dimensions, your orientation, you start to chart this line in space that tells you with greater and greater accuracy where you are along – what your position – essentially, you’re calculating what your orbit is around whatever body you’re orbiting, be it the Earth, be it the sun, be it Mars – whatever. And so that’s the point that you really – then the flight controllers really know exactly where that space craft is, give it enough time.
It’s very similar to finding the asteroids. We talk about how scientists have found some asteroid, and we’re not sure if it’s gonna smash into the Earth or not, we just need to take a few more readings, and then we’ll get a sense of where it is. So same thing, right?
Dr. Pamela Gay: Exactly the same thing, and one of the things that is a problem with asteroids, but not a huge problem with asteroids, is you have to worry about, what are the gravitational interactions you’re gonna have with other bodies? So how is Ceres going to yank around smaller asteroids that get too close? We also have to worry about, with spacecraft, as they approach other bodies, how is that gravity going to affect their motion? So we have to think about both, well the spacecraft has its own engines, its own thrusters, and we can use those to change its velocity.
But then gravity is out there exerting this constant force going, “I’m gonna push you,” well, pull, actually. And so the sun is out there just yanking away of the spacecraft. The planets, when you get too close, yanking away on the spacecraft, and this is useful when we use gravity to change the orbits of spacecraft, but all the things you have to keep track of, you have to know where you are, when you are, where you’re going, and what extra forces the universe is going to add to your journey.
Fraser Cain: So let’s talk about how, then, the flight controllers will try to modify. It’s one thing to know where you are and where you’re going, but what you really wanna do is be able to go to different places. And so how do they, then, make their – what kinds of calculations, what do they do, to be able to then change a spacecraft’s orientation?
Dr. Pamela Gay: Well, if you’re in an orbit around a simple body, so a satellite orbiting the Earth, for instance. Then, if you know the where you are and the how fast you’re going, that will allow you to figure out the rest of your orbit, more or less. You want more than one reading just because things change, errors happen. And then to change your orbit, you figure out where in the orbit you need to change your velocity to get the effect you want.
So if, for instance, you launch yourself into a highly elliptical orbit where you’re coming down to, maybe, low Earth orbit, 300 miles up at your closest approach, zipping out to 10,000 miles out on your further approach, if you want to circularize that orbit, you either have to slow yourself down when you’re at that closest approach so that you don’t zip back out and you end up with a tiny circle, so you can go from far out to circularized close in, meet up with the space station. But if you want to circularize yourself out further out, you speed yourself up on that further out point, so you stay out in those outer parts. This is where we talk about Delta V.
Fraser Cain: Yeah, so everything I’ve learned, I’ve really learned from Kerbal Space Program, and what’s really great about that program is you start to realize, you see how everything is just these orbits. They’re all ellipses, and so your spacecraft is just following some circular orbit or some elliptical orbit around some body, and it just goes around and around and around and around, and then if you want to go somewhere else, say you want to go from the Earth to the moon, you don’t just point your spacecraft at the moon and just fire your thrusters. I guess if you had unlimited fuel, you could kinda do that, but what you do instead is you calculate the new orbit that you want to get to.
You calculate your insertion orbit, and then it’s gonna say – it’s gonna come back and say, “Okay, great, so now you need to orient yourself in this direction, and you need to burn your thrusters for a certain amount of time until you’ve reached this new orbit.” And sometimes once you’ve reached the top part of the orbit, you then need to turn around and do a different burn to stabilize the orbit into the new position. That’s just to get yourself to where you can do an orbital insertion. Going back to what you talked about, once you know where you are, where you’re going, what your speed is, then you can make those calculations for the orbital burn that’s then gonna put you into the new position that you wanna be in.
Dr. Pamela Gay: And one of the things that always amazes me is it’s relatively easy to start calculating in the grand scheme of the universe how much Delta V you need in order to move from one orbit to another. But where it starts to get tricky is when you make that Delta V, you’re also changing the mass of your spacecraft. So now, the kind of Delta V that you need to put in, you’ll get a different Delta V with a different amount of force, depending on if you’re heavy or you’re light.
So the amount of firing you need to do to get that same 100 kilometers per whatever unit of time is relevant change in velocity if you’re full up on fuel is gonna take a whole lot more fuel. If you’re lightweight, it takes a whole lot less force, and this is what we saw in The Martian. He knew what Delta V he needed to get, but he knew his spacecraft was too heavy for the amount of fuel he had to get him that Delta V. So if they could remove it, they removed it. Make it smaller, you require less force for the same Delta V.
Fraser Cain: Right. So are we at a place now – I mean, you talk about the deep space network. Are we at a place now where the spacecraft – like there is some kind of navigational system that’s just going on across all the spacecraft in the solar system? I just imagine, is there a GPS version of the spacecraft orienting themselves in the solar system, or is still fairly early days on this?
Dr. Pamela Gay: It’s not early days, but it’s not GPS. It might be safe to say we’re in the early ‘80s. we plenty of receivers on the Earth. It becomes fairly simple to catch the signals that we need to. Mars, we have a bazillion happy little rovers on the surface, by which I mean two, and those are great for sending signals back and forth from the things, orbiting Mars, getting better positions for both things on the surface and in space. We’re getting there. We don’t have the global network we might like that allows everything to be tracked absolutely all the time. There’s just not enough dishes. So we take turns, and we hope things don’t stray too far between when their turn comes up on the deep space network.
Fraser Cain: So then, can you imagine going into the future, like think about The Expanse. I don’t know if you’ve watched The Expanse yet. It’s awesome if you haven’t already. I can imagine a few hundred years down the road when we do have a colony on Mars, when someone has hollowed out asteroids just as expected by Dr. Pamela Gay that we’ve got these spacecraft buzzing around, mining different worlds. What would a future navigational infrastructure look like here in our solar system?
Dr. Pamela Gay: It’s going to be a land of transponders. You walk into a room. You see the holographic display where everything is saying, “I’m this distance from this. I’m this distance from this,” and we’ll probably want to have some fixed points that we work very hard with lasers to make sure that they are our standard reference frame, just like we have the GPS around the earth as a standard reference frame. So you can imagine that there are, at various points, spacecraft that are sitting there going, “I know exactly where I am. I know exactly where I am,” and those are the things that become our solar system wide GPS as they orbit the sun instead of orbiting our Earth.
Fraser Cain: So I’m imagining that there’s almost like buoys. When you’re on the ocean, there’s all these marker buoys, and they’re mostly like, “There’s rocks over here so be careful,” because we just use the GPS when we’re navigating on the ocean, but I can kind of imagine there are these asteroids and moons and, obviously, Earth and places like that, and each one’s gonna have some transponder that maybe can broadcast in a wider field. It’s not directing right at your spacecraft. It’s, instead, maybe doing something that’s sending out a signal in all directions, and then you’re just counting up how many different transponders that you can get all at the same time, and then you’re able to get a signal from six different transponders, and so you can calculate your position, and then you know, “Oh, we wanna get into orbit around Phobos. We’re gonna need – and then you calculate the burn, right?
Dr. Pamela Gay: Exactly. That is very much the future that we’re looking at, and what’s amazing is how much we’ll learn about things as simple as, what are the densities of different asteroids as we’re able to see interactions with things flying past each other, and we measure their exact sizes better. How we’re going to be able to get at the fine details of orbital interactions over time as we see, “Oh, this transponder is one hundredth of a second off of where we expect it to be.” That means there’s some interaction that occurred. We’re gonna learn so much more about the densities of the rocks in our solar system as we drop radio transmitters on them one by one, year after year after year.
Fraser Cain: Right, and eventually, we will have, probably, a transponder on every object out there.
Dr. Pamela Gay: Above a certain size.
Fraser Cain: Above a certain size, and not to mention, a bunch of just artificial ones placed in spots that we’ve created just to help if it’s there’s a big wide space or whatever. It’s pretty exciting to think about that future because it means that we’ve become a true solar system spanning civilization.
Dr. Pamela Gay: Yes, and what’s awesome is all it takes to keep refining that is to use shorter and shorter wavelengths of light until we know where things are within nanometers.
Fraser Cain: That’s amazing. Next episode, we are going to be talking about a similar idea, but how would we scale this up to navigating outside of the solar system. So we’re gonna move into science fiction land. I’m really excited.
Dr. Pamela Gay: Cool.
Fraser Cain: All right, we’ll talk to you next time. Thanks, Pamela.
Dr. Pamela Gay: Sounds great, Fraser.
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Duration: 30 minutes