Last 15 minutes are the longest
Source: By Dilip D’Souza: Mint
India’s own Chandrayaan-2 lifted off from Sriharikota on 22 July 2019. It’s now somewhere in space, heading for the Moon. Correct?
Well, yes and no, and that’s actually why this is such a fascinating exercise. Chandrayaan-2 is indeed somewhere in space. If all goes as planned, it will land on the Moon in September; so in that sense it is indeed going to the Moon. Yet, if you knew nothing about Chandrayaan-2 and were somehow able to watch it right now, as you read this, the phrase “heading for the Moon" would not come to mind. Because what it is doing right now is quite different from what that phrase suggests: It is orbiting the Earth. Yes, orbiting—like plenty of satellites and the International Space Station and, when it was in operation, the Space Shuttle.
Why, instead of setting a course for the Moon is Chandrayaan-2 whirling around our planet?
Let’s start by answering another question. When a technical snag of some kind aborted Chandrayaan-2’s planned launch last week, the new launch date was Monday, 22 July. Not just that, it was going to happen at 2.43pm. Not just that either, some reports mentioned something very interesting about this chosen moment. There was a small “launch window" around that particular moment, lasting just a couple of minutes. If Chandrayaan-2 could not take off during that window, it might have had to wait as long as a few months, for another launch window to open up.
Why this small window, why this precision? The short answer might be that anything as intricate and difficult as a Moon mission needs precision. But the longer answer is far more satisfying.
Apart from the verb, shooting for the Moon is nothing like shooting at a target on a firing range. At the range, you’re not moving and the target isn’t moving. You aim, you fire and, if your aim is true, you hit the target Simple.
But what if the target is moving? We quickly learn what to do then as well: Aim just slightly ahead of it, in the direction it’s moving, and if your aim is true, you hit the target again quite simple.
But what if the target is far away? So far off that your bullet has no hope of reaching there without some meaningful nudges on the way? Not only do you have to figure out how to do such nudges, you also have to ensure they don’t send the bullet off target.
But what if you’re moving, too? Now you have to account for your own motion as you aim, because it will affect the path the bullet takes. And, if your target is rotating around you, and if you and the target are together rotating around a vastly larger object which is itself a tiny component of a gigantic spinning spiral conglomeration… well, exactly how do you take aim? In fact, what does it mean any more to take aim? You see, now we’re getting closer to a sense of the complexity of the Earth-Moon dance, the complexity that gets us into thinking about such things as launch windows.
With both the Earth and the Moon following their particular paths through space, working out a path from one to the other is a matter of serious mathematical theory and calculations. To get an idea of this, consider this very simplified comparison. Suppose we have two chances to launch our rocket to the Moon. The first, at a time in the Moon’s orbit when it is at its farthest point from the Earth, called the apogee and second when the Moon is at its closest, or perigee. Which of these moments would you choose for a launch?
Naturally, you think the second. For on the face of it, that will be a shorter trip that will likely need less fuel than the other. In reality, of course, things are not quite as simple. Taking into account the time for the journey and weather conditions on Earth, for example, might just lead you to conclude that it’s better to launch while the Moon is approaching and some distance away from the perigee. Taking into account where the launch site is in relation to the Moon during a given launch window — facing the Moon? The opposite side of the Earth — might call for still more calculation, more changes in the path.
And then, there’s the need to escape Earth’s gravity, and yet use the same gravity to propel the craft. If that sounds contradictory, bear with me.
When we launch a rocket, it has to reach “escape velocity"—a speed that will free it from the clutches of gravity here on Earth. But even so, that’s really only good enough so that it doesn’t fall back to Earth, but instead goes into orbit around the Earth, one that gets increasingly elliptical. As the Beresheet mission, spacecrafts use their orbit around the Earth—indeed, Earth’s gravity itself—as a slingshot.
They pick up speed as they zoom close to the planet and past, then use that speed to range further out, before coming back again. Do this over and over, orbit after orbit, and eventually the spacecraft gets so far from Earth that it is essentially out of the reach of Earth’s gravity—and in this case, it is drawn into the Moon’s gravitational field.
In fact, the various intrepid crafts we’ve sent coursing across the solar system—Voyager, Pioneer, Mariner, Cassini—have very deliberately taken advantage of such “gravitational assists" not just from the Earth, but from the giant outer planets as well. In 1981, for example, flying past Saturn boosted Voyager-2’s speed from 16km per second to nearly 35km per second. Neptune accelerated it similarly in 1989. This is how Voyager-2 has successfully journeyed past the outer edge of our solar system, into the unimaginable vastness beyond. Fuel alone could never have taken it as far.
So, if your favourite Moon mission has the time to execute these ever-expanding ellipses around the Earth, it is actually the most fuel-efficient way to reach the Moon. It builds momentum for the trip by using gravity rather than fuel. On the other hand, for the Apollo missions with their perishable human cargoes, time was critical. So, they needed to fly more directly towards the Moon than gradually stringing ellipses together into a gravitational slingshot.
For these reasons and plenty more, Chandrayaan-2’s path to the Moon—like Mangalyaan’s to Mars a few years ago, like Beresheet’s earlier this year—looks like a child’s doodle: Two sets of ellipses joined by a long, loopy line. And, this is why, where Apollo took about four days to cover the approximately 350,000km that separates us from our satellite, Chandrayaan-2 will need over six weeks and will probably have logged a few million km by then.
When it does get there in September, what will ensue also needs a whole lot of complex calculations and careful manoeuvring. Chandrayaan-2 will start orbiting the Moon, preparing for its lander, Vikram, to execute a “soft landing". Put it another way: Vikram had better not crash on landing. Apart from instruments for various experiments, it’s carrying Pragyan, a rover that is expected to roam the lunar surface for 14 days.
So, at some point, Vikram will separate from the orbiting craft and start descending towards the surface. Once it gets close, it will fire directional thrusters to orient itself in relation to the ground, and its main engine to slow its descent. Why so? If it doesn’t fire its engine, Vikram will fall like a stone and shatter on impact. Fire it too powerfully, and it might just float back into space. This entire engine jockeying, then, while trying also to make sure Vikram’s “feet" are pointing at the ground, that they will make contact simultaneously so the craft stays upright, that the engine shuts off on touchdown. The whole descent should take about 15 minutes. You know it will likely be the longest 15 minutes in the lives of all the members of the team at the Indian Space Research Organisation (Isro).
Will Chandrayaan-2 manage all this? Considering that it’s somewhere up there already, getting its gravitational assists on cue, there’s every reason to believe it will also nail that soft landing. Yet even if it doesn’t, to me the effort itself—the science, the mathematics, the imagination and vision of this, or any mission into space—already makes the mission a triumph. Still, it’s going to be a long 15 minutes in September.
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