BackMars, here we are
India's mission to Mars, Mangalyaan, is a fantastic achievement on any number of counts
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Some years ago, I bought myself a radio-controlled toy helicopter. Oh the fun I would have, manoeuvring it here, there and everywhere! Or so I thought. Reality set in quickly. I couldn’t get it to so much as hover, let alone fly forward any distance. That’s how difficult I found it to control the thing, although I’m sure your mileage may vary.
Still, I’m not being facetious when I say that that trivial pursuit gave me some tiny idea of the enormity of something that was achieved this week. I mean the job of guiding a spacecraft remotely across millions of kilometres of empty space. I mean India’s mission to Mars, Mangalyaan, which has now entered into orbit around that planet.
This is a fantastic achievement on any number of counts. Now I realize there’s a team of highly-trained scientists, each far more knowledgeable than me, behind Mangalyaan. I realize they use far more complex technology than my toy helicopter did. I’m just saying this: each time my little chopper crashed futilely into the ground, it was a faint reminder of the infinitely more intricate problem an inter-planetary mission poses.
Leave aside building the actual spacecraft, fuelling it and giving it the communication and other facilities it needs. Consider instead just the task of getting it from this planet to that. Is this about the same as boarding a plane and flying from Bombay to Bagdogra?
Well, not quite.
To start with, there’s the inconvenient reality of gravity. Pretty much everything you choose to fling into the air, spacecrafts included, will fall back to Earth. That’s gravity for you. So for Mangalyaan to actually leave the Earth, it had to accelerate to what’s known as the planet’s escape velocity: the speed at which an object can escape the pull of gravity. This is a well-known and understood number that’s easily calculated once you know a planet’s size and mass. On Earth, it is just over 11km per second. How fast is that? Probably faster than you can throw a ball. But also, about 11,000 times faster than Usain Bolt and about 50 times faster than a Boeing 737. This is why you’ve never seen either Bolt or a 737 barrelling through outer space. For Mangalyaan, though, the first big hurdle was to power it up to that speed. Only then could it leave the Earth and enter space.
Once there, is it a simple matter of setting course for Mars and waiting to crash land there some fixed time later?
Well, not quite again.
Both Earth and Mars are moving through space, and at a pretty fair clip: Earth, at about 30km per second; Mars, at about 24km per second. So think of the Mangalyaan mission as akin to leaping out of a swift train, running towards another swift train and leaping on there. No easy task, and one that naturally needs serious precision. Not least because Mangalyaan’s speed as it leaves the Earth’s gravitational clutches—11km per second—is noticeably less than either of the planets’ speeds through space.
To accelerate the craft even more, scientists used the Earth’s gravity itself in an ingenious way. The escape velocity is actually just enough to put Mangalyaan into orbit around the Earth. But with each orbit, Mangalyaan fired its on-board engine just enough to make the path of the orbit a little larger, to raise its speed a little. Six times Mangalyaan did this, and that was enough to dispatch it into what’s called the Mars transfer trajectory.
To understand this, think of a discus thrower at the Olympics, turning around again and again to build momentum before he lets the discus go. Or think of using a slingshot, whirling it faster and faster around your head before you let the stone fly. In fact, this technique of using each successive orbit to build up the craft’s speed until it can be sent on its way is called a gravitational slingshot. (Actually in this case it’s a powered slingshot because the engine fires with each orbit.)
The Mars transfer trajectory is not exactly a straight line drawn from Earth to Mars at the time Mangalyaan sets out. Following that would mean Mangalyaan would completely miss Mars. Imagine, in football, sending a pass to a teammate who is racing toward the opposing goal. If you aim at where he is when you kick, you’ll miss him. So you estimate where he’ll be a second or two later, and aim your kick there. In the same way, the intrepid Mars craft cruises on a wide curve that swings steadily outward from Earth’s orbit, calculated precisely to intercept Mars in its orbit over nine months later. Because even at a speed of better than 25km per second, which Mangalyaan has averaged on its journey, it takes that long to get to Mars.
On 24 September, just as it was meant to all along, Mangalyaan slipped smoothly into an orbit around that red planet. Wondrous stuff.
Me, I think I’m inspired to try that helicopter one more time.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences.
Comments are welcome at dilip@livemint.com. To read Dilip D’Souza’s previous columns, go to www.livemint.com/dilipdsouza
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