The European Space Agency’s ExoMars spacecraft is currently cruising down a celestial highway, eight days into its seven-month journey to the Red Planet. We know it’ll land on Mars on October 19, but where will it be in a month? Or the Fourth of July? Its location seemed calculable to me. Given the spacecraft’s acceleration time, cruising speed, and distance from Mars at launch, I figured I could crunch some numbers. This was — I know now — pure hubris. Rocket science is a cultural touchstone, a cliché even, for a reason.
I found this out while trying to find a spacecraft.
Space highways aren’t like terrestrial roads, Michael Khan, Ph.D., a celestial mechanics expert at the ESA’s Mission Analysis Office, explained when I asked for his advice on locating ExoMars. If there’s one thing to keep in mind, he says, it’s this: There are no straight lines in space. In a beautifully written e-mail, he explained why we’ll all have to learn to drive on a curve — and why the future of space travel is infinitely more complicated than we think.
Rather than attempting to summarize his explanation, I’m going to paste it below because it is beautiful.
I fear celestial mechanics, which is the science underlying the calculation of the trajectories of all orbits in space (natural or man-made), works a bit differently from what you seem to be assuming.
An interplanetary transfer from the Earth to another planet (in this case, Mars) is not a matter of flying on a straight line with a given cruising speed like an aircraft would on the Earth, or like a ship that cruises through the ocean, with some changes in direction at given waypoints. That’s not the way it works in the solar system. Because it doesn’t work like this, I don’t think it will be straightforward (or even possible) to make simple, rough and ready calculations as to where ExoMars will be at what time.
Basically, the laws of nature governing the flight of an object through space were by Isaac Newton and Johannes Kepler centuries ago. I’ll simplify just a little bit: Earth and Mars move on orbits that are more or less circular (for Mars, that is not quite true, but that works for starters). Now we have the Earth orbit, a wide circle around the Sun, and the Mars orbit, an even wider circle that also has the Sun in its centre.
The transfer trajectory followed by ExoMars is an ellipse. Where this ellipse is closest to the Sun, it grazes the Earth orbit. Where it is farthest from the Sub, it grazes the Mars orbit. The spacecraft flies from this lowest point to the farthest point. It reached the ellipse by the enormous boost imparted to it by the proton M rocket that was used to launch ExoMars, throwing it so high and fast that the spacecraft actually leaves the Earth gravity with just the right speed and direction to meet the required transfer ellipse to Mars. At this point (Earth escape), ExoMars was quite a bit faster than the Earth on its orbit around the Sun.
On this transfer ellipse, ExoMars’ speed will be decreasing continuously. To understand why this is so, imagine a clock pendulum, As the pendulum swings up, it moves slower and slower. That’s because there are two kinds of energy: potential energy (=height energy) and kinetic energy (=motion energy). The spacecraft orbit has a certain total energy. This was imparted by the launcher. This energy doesn’t increase. It’s like pocket money or a salary, we just have to make it last.
If the rocket had not given it enough energy, the ExoMars orbit would not have reached out to the Mars orbit. Conversely, if the rocket had imparted too much energy, the spacecraft orbit would have gone way beyond the Mars orbit. So we wanted (and got) exactly the right amount of energy, not too little, but not too much. This is different from pocket money or a salary, where too much definitely is better than too little.
Now, on the elliptical transfer, the spacecraft it climbing away from the Sun towards the Mars orbit, and the Sun is holding on to to the spacecraft with its gravity. So as ExoMars is climbing, its height energy increases. Therefore, the motion energy must decrease. The total energy stays the same. So on its flight to Mars, ExoMars continuously gets slower and slower.
To compute the transfer, the one thing one absolutely has to take into account is the gravitational attraction through the sun. There are also other effects such as the very small pressure of light on the solar arrays and the gravity of the planets in the solar system, and of course we have to take into account every time we use the rocket engines aboard ExoMars to change the orbit. But all this has a much lesser effect than the solar gravity.
Essentially, we use a computer to calculate the trajectory of the spacecraft taking into account all factors that affect the trajectory, and we can also measure where spacecraft is and how fast it is travelling from the time the signals take to travel from the Earth to the spacecraft and back and by the way the frequency of the signal changes over time.
In a later e-mail, he added:
The most important thing you see is that the ExoMars trajectory, like all trajectories in space, is distinctly curved. There are no straight lines in space. Once you have bodies that have mass, such as stars and planets, you have gravity, and in the presence of gravity, everything will fly on curves. Curves are natural, straight lines are not. The distance covered following the curved red line from Earth to Mars is about 500 million kilometres, to put that into perspective. Half a billion kilometres.
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