Date: November 23, 2011
Title: Flying to Mars
Podcaster: Rob Knop
Organization: Quest University Canada
Links: My home page : http://www.pobox.com/~rknop
My Quest page: http://www.questu.ca/academics/faculty/rob_knop.php
Description: In just a few days NASA will launch the Curiosity rover on its way to Mars. In this podcast, I talk about just how it is that we fly from Earth to Mars, and describe the “transfer orbit” that is used when we send spacecraft from our planet to the red planet.
Bio: Rob Knop obtained a PhD in Physics from Caltech in 1997. He then worked with the Supernova Cosmology Project and was part of the discovery that the expansion of the Universe is accelerating. After six years as an assistant professor at Vanderbilt University, he worked in the computer industry for two years. He now teaches physics the new college Quest Unviersity in British Columbia. He gives regular astronomy talks in Second Life in association with the Meta-Institute of Computational Astronomy.
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Transcript:
Hello! I am Rob Knop, professor of physical science at Quest University Canada. Thank you for listening to 365 Days of Astronomy.
In just a few days, NASA is set to launch the next Mars Rover. You may remember the last pair of rovers, Spirit and Opportunity. Both of them launched in 2003, and landed on Mars at the beginning of 2004. They were originally planned to have 90-day missions. Both of them continued operating for years. Spirit got stuck in 2009 and went silent in 2010. However, Opportunity continues to truck along, making observations of the conditions on the Martian surface.
The next generation NASA rover, named Curiosity, is set to launch in a launch window starting on November 25. This is a more advanced rover than the previous pair, although Curiosity has quite a lot to live up to after the stellar and extended performance of Spirit and Opportunity. Whereas Spirit and Opportunity where powered by solar panels, Curiosity will be powered by an RTG, or a Radioisotope Thermoelectric Generator. It has a power core with a radioactive element, the decay of which generates the energy it needs to keep operating. This means that it will not be as dependent on the Sun as were Spirit and Opportunity, and will not have to worry about night, about seasons, or, as much, about dust. This power generator will last for years.
What I really want to talk about, though, is not the rovers themselves, but about getting to Mars. Just why is it that there is a limited launch window in which we can send a spacecraft to Mars? And why does it take every spacecraft we send the same 260 days to get there?
You might think that the most obvious way to get to Mars through space is just to point your engines at Mars and power your way on over there. Indeed, when you watch science fiction movies, for the most part that’s how you see spacecraft moving. They point to where they want to go, and out of their back end emerges gouts of flame propelling them along. And, indeed, this would be a nice way to get to Mars, if we had lots of extra fuel to waste. It still wouldn’t quite be that simple, because we would have to consider the gravity of the Sun, and offset that with our powered orbit. But, if we had enough fuel that we could just keep burning it a high rate all the way over, we could get there pretty quickly. Of course, we might want to turn around and decelerate, so that we don’t just blow by the planet once we get there. It turns out that, again if you have the fuel to burn, the fastest way to get somewhere in space is to accelerate as fast as you can halfway there, speeding up the whole time. Once you’re halfway there, turn your ship around, and fire your rockets in reverse. Decelerate at the same rate that you had been accelerating. That will get you to your destination– assuming your aim is good– just as you slow down enough so that you’ll be at rest when you get there.
However, this way of doing things requires tremendous amounts of fuel, far more fuel than is practical to launch with a spacecraft that we want to send to Mars. Indeed, when we go to another planet in the Solar System, we don’t point our ship straight at that planet and just fly over there at all. Rather we cleverly fall around the Sun in such a way that we get there at just the right time.
“Delta vee” is the way in which we measure our spacecraft’s ability to maneuver. “Vee” stands for velocity, which is speed and the direction in which you’re moving. “Delta” is a standard symbol that is often used to mean “change in”. So, when we say “delta vee”, we mean change in velocity. A spacecraft has a limited amount of fuel. It can spend this fuel to change its velocity. The total amount of fuel it has tells you the maximum amount it can changes its velocity. The cheapest way to get from one place to another place is to minimize the amount of Δv you need to use to get there. Of course, that’s not the only consideration. You also want to get there without spending too terribly much time. Some of the spacecraft that we’ve sent to the outer solar system to visit Jupiter or Saturn have gone through complicated inner-Solar System orbits, passing Earth and Venus to slingshot past them and pick up a little extra speed that way. However, when we go to Mars, we use a pretty direct transfer orbit.
The Earth orbits the Sun in a circle that is one astronomical unit in radius. The astronomical unit is a very useful distance unit for measuring things in the Solar System, as it is just the distance between the Sun and the Earth, or about 150 million kilometers. Mars orbits the Sun in approximately a circle of radius 1.52 astronomical units or AU. While this might lead you to conclude that Mars is 0.52 AU from the Earth, that is only sometimes true. Remember that the Solar System isn’t one dimensional, with all of the planets nicely in a line, even though often art of the Solar System displays it that way. Earth and Mars both orbit the Sun, but not at the same rate. Whereas it takes the Earth 1 year, or 365 days, to make one circuit around the Sun, it takes Mars 1.9 years, or 687 days, to go once around the Sun. Because their orbital periods are different, Mars and Earth are always at different positions of their respective circles around the Sun. Sometimes, Earth passes Mars, and at that point indeed Earth is only about half an AU away from Mars. However, at other times, Earth and Mars are on opposite sides of the Sun, and Mars is more like two and a half AU away from the Earth.
When a spacecraft wants to go from Earth to Mars, it needs to move itself from Earth’s orbit out to Mars’ orbit. It does this by first getting off of the Earth, at which point it’s in a circular orbit around the Sun with a radius of 1 AU, just like the Earth. Then it spends some of its fuel– some of its Δv– to speed itself up. It’s now going too fast to stay in a circular orbit the size of Earth’s orbit, so it will spiral out into a larger, elliptical orbit. If the amount of the Δv is just right, the spacecraft will go into an elliptical orbit that just barely touches the orbit of Mars on the opposite side of the Sun. Were the spacecraft to stay in this orbit, it would continue in an ellipse around the Sun, every one and a quarter years passing at a closest point that is the same distance from the Sun as the Earth, and then, half-way through that orbit, just grazing the orbit of Mars one and a half AU away from the Sun.
For a transfer orbit, however, the spacecraft stops once it gets out to Mars. If all it wanted to do was match orbits with Mars, it would spend some additional Δv to speed it up again, so that it would now have the same speed as Mars in its orbit. Without that additional Δv, it would fall back in and stay in the elliptical orbit I just described. By kicking its speed up a little bit, it matches speed with Mars and is now orbiting the Sun in the same orbit as Mars. However, when we send spacecraft to Mars, that’s not what we really want to do. We don’t just want to match orbits with Mars, we want to orbit Mars, or land on Mars. Curiosity, being a rover, wants to land on Mars. (Hey, if we’re going to name our probe Curiosity, you have to expect me to anthropomorphize it.)
So, instead of spending additional Δv to match Mars’ speed in its orbit, the spacecraft instead wants to go into orbit around Mars, and then slow down enough to land on Mars. Because Mars has an atmosphere, it doesn’t have to do all of this with fuel. It can also use aerobraking– basically, slowing itself down by plowing into the Martian atmosphere.
This transfer orbit I’ve just described is called the Hohmann Transfer Orbit, after the German celestial mechanic who first published a description of it in the 1920’s. Again, let’s try to visualize it. Imagine the Sun, and then imagine two circles around the Sun. The inner circle is the orbit of Earth, and the outer circle is the orbit of Mars. If we are looking “down” on the Solar System– that is, so that we’re looking down on the north poles of the planets– the two planets are going around the Sun in these orbits counter-clockwise. Imagine that the spacecraft leaves Earth just as Earth is at the far right edge of this circle. Inscribe an ellipse, elongated left to right, whose left edge just kisses the outer circle. The upper half of this ellipse represents the transfer orbit. The spacecraft will leave Earth at the right edge and follow the upper half of this ellipse, until it arrives at Mars’ orbit.
The full left-to-right width of this ellipse is called its “major axis”. Half of that major axis is the “semi-major axis”. Were the ellipse a circle– as is very nearly the case for the Earth, and approximately the case for Mars– the semi-major axis would just be the same as the radius of the circle. Because the major axis of this transfer orbit encompasses half of the Earth orbit diameter (on the right) and half of the Mars orbit diameter (on the left), the semi-major axis of this ellipse is the average of the radii of Earth’s and Mars’ orbit. With Earth being 1 AU from the Sun and Mars being 1.52 AU from the Sun, that means that this ellipse has a semi-major axis of 1.26 AU. Kepler’s Third Law is a simple relationship that allows us to calculate the time it takes something to orbit once around the Sun, given the semi-major axis of its orbit. The spacecraft in the transfer orbit takes half one complete orbit to get from the Earth to Mars. Using Kepler’s Third Law, and the knowledge that the semi-major axis of this transfer orbit is 1.26 AU, you can figure out that the amount of time it takes to get from Earth to Mars is about 260 days.
The nature of this transfer orbit also tells us why there are only specific launch windows during which we are able to launch spacecraft from Earth to Mars. Earth and Mars have to be lined up just right in their orbits so that if the Earth is on one side of the Sun at one time, 260 days later Mars will be directly opposite it on the other side of the Sun. The ability to maneuver the spacecraft into slightly different orbits from the one perfect ellipse means that the launch window isn’t just one instant in time, but stays open for a few weeks. However, because Earth and Mars have to be lined up just right, these launch windows only come a little over every two years. That means that if we want to go to Mars, we really don’t want to miss a launch window, because we won’t be able to try to go again for another two-plus years.
It’s worth sitting back and thinking about this orbit. A spacecraft going from Earth to Mars is not flying through space the way they are usually depicted in science fiction movies. Rather, the spacecraft is just falling around the Sun– just like all the planets are falling around the Sun. By cleverly launching it at just the right time, and giving it just the right amount of additional speed over the speed it had from moving along with the Earth, we can send our spacecraft falling around the Sun in just the right way so that it meets up with Mars on the opposite side of the Sun. Think about Curiosity, falling through the Solar System, over the next 8 or 9 months as it makes its way to Mars.
Thank you for listening to 365 Days of Astronomy!
End of podcast:
365 Days of Astronomy
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