Smile in the sky

Venus, Jupiter, and the Moon, to light up your night.

Image courtesy Martin Cooper in Bangkok, Thailand, published on the BBC website. Original here

Chandrayaan-1 enters lunar orbit

(This is a link to the website of ISRO -- the Indian Space Research Organisation. It features a graphic animation showing how the earth orbit was boosted, how it transferred to an elliptical lunar orbit today, and how it will eventually settle into a circular lunar orbit.)

Galileo's experiment on the moon

Aristotle (384-322 BC) was one of the great Greek philosophers, who speculated on many fields of human experience, including motion. Although one of the most important names in western philosophy, his scientific thinking was sometimes fatally marked by a lack of experimental work. This led him to make curious blunders, such as the assertion that the human male has more teeth than the female! However, he laid the foundations of logical reasoning, made some rigorous observations of marine creatures, and is rightly regarded as one of the great thinkers of all time.

Such was his fame that for nearly 2000 years, if anyone disagreed with Aristotle, their ideas never took root. The earth was accepted as being at the centre of the universe, even though some of Aristotle's contemporaries believed otherwise. Again, according to Aristotle, a falling objects gains speed, based on its weight. A heavier object will fall faster, and a lighter one will fall slower.

Sometime around 1589, an Italian scientist named Galileo Galilei advanced a theory that contradicted Aristotle, and stated that "the velocity of moving bodies of the same composition, but of different weights, moving through the same medium, do not attain the proportion of their weight as Aristotle decreed, but move with the same velocity."

Essentially, what he meant was that bodies of different weights would fall at the same velocity. Bodies of different materials, though, initially fell at slightly different rates, but attained the same velocity. Galileo is then believed to have gone on and dropped a cannonball and a musket ball from the Leaning Tower of Pisa, demonstrating the truth of his theory.

Apparently Galileo was not the first to challenge Aristotle. But he was the first to muster both theory and experiment in his cause. As for Galileo's observation about objects with different densities, there are two points of view. One is that denser objects would be less affected by air. The second is that human error while holding and dropping a heavy load would ensure that the heavier object was dropped slightly after the lighter one.

Whatever the exact truth, Aristotle's assertion now belonged only in scientific history.

If you try this experiment with the lighter object being something like paper or a feather, air resistance would slow it down severely. So what would happen in a vacuum? Theory, as well as experiments in vacuum chambers tell us that a feather and a steel weight would fall at the same rate. Imagine then, the excitement when this experiment was tried on the Moon which, as you know, has no atmosphere!

Transcript of broadcast from the lunar surface, on 2 August, 1971

Commander David R Scott: "Well, in my left hand I have a feather; in my right hand, a hammer. And I guess one of the reasons we got here today was because of a gentleman named Galileo, a long time ago, who made a rather significant discovery about falling objects in gravity fields. And we thought: 'Where would be a better place to confirm his findings than on the Moon?'

[Camera zooms in on Scott's hands. One is holding a feather, the other a hammer. The camera pulls back to show the Falcon the Apollo 15 landing craft and the lunar horizon.]

Scott: "And so we thought we'd try it here for you. The feather happens to be, appropriately, a falcon feather for our Falcon. And I'll drop the two of them here and, hopefully, they'll hit the ground at the same time." [Scott releases hammer and feather. They hit the ground at about the same time.]

Scott: "How about that! Mr Galileo was correct in his findings."

How Chandrayaan-1 is raised to higher orbits

(an article by R. Prasad in The Hindu on October 30, 2008)

Chandrayaan-1 could have been fired to reach the moon, which is about 3,84,000 km from earth, in one shot. But that was not done. Instead the spacecraft is being moved towards the moon in increasingly elliptical orbits with an apogee (farthest point from the earth) increasing many times more than the perigee.

“We could have done it one shot, but there is a possibility of missing the moon,” said M. Annadurai, Project Director of Chandrayaan-1 to this Correspondent. “So we have adopted an incremental increase in the orbits’ perigee.”

That probably explains why the Indian Space Research Organisation (ISRO) has decided to settle for five increasingly elliptical orbits before Chandrayaan-1 reaches the moon’s sphere of influence. Why is the firing always undertaken at the perigee position?

Firing at perigee
“To increase the apogee, we must fire at the perigee [position]. And firing should consume less energy. So the firing is done at the perigee,” Dr. Annadurai explained.

One more reason to fire at the perigee is to ensure that the spacecraft can be tracked by 3-4 ground stations. “The spacecraft is allowed to complete one or more orbits till such time 3-4 ground stations can track it. But we will fire it at the earliest opportunity,” he said.

But not always can one assume that the firing will happen as planned. So any change in this will in turn affect the apsidal line (imaginary line that connects the apogee and perigee). This should be corrected and maintained if the rendezvous with the moon is to happen.

Increasing the apogee
And what ensures that the apogee increases many hundred kilometres after every firing while the perigee changes by only a few kilometres? “When the firing is done exactly at perigee, the velocity increases and the apogee keeps increasing. There will be no change in the perigee position,” he said.

But firing the spacecraft exactly at the perigee position is only theoretically possible. This results in a small change in the perigee altitude.

Duration of firing
“It is not an instant firing [at the perigee]. It takes a few hundred seconds to complete the firing,” he said. But great effort is however taken to centre the firing around the perigee position.

For instance, the first firing to take Chandrayaan-1 from the initial orbit to the first orbit (with an apogee of 38,000 km) took about 1060 seconds to complete. The second firing to take the spacecraft to the nearly 75,000 km apogee took 920 seconds. And the third firing to raise it to about 1,65,000 km apogee took 560 seconds.

The fourth firing to take Chandrayaan-1 to 2,67,000 km will take about 190 seconds and finally the last raise to 3,80,000 will take 150 seconds.

Though the original plan was to reach 2,00,000 km apogee in the third orbit, ISRO could only raise it to 1,65,000 km. So will that lead to any problems? “This can be made up for in the next firing,” Dr. Annadurai said.

Use of propellant

Will the change in the orbit-transfer strategy from five-and-half days to nearly a fortnight lead to increased fuel consumption and hence reduced mission life? “The amount of propellant required to fire the spacecraft to 4,00,000 km is less, whether it is done in one shot or in stages. And the propellant is used only for changing the orbits and not for orbiting around the earth,” he explained.

Orbiting around the earth is mainly through the gravitational force of the earth. But the gravitational influence of sun and moon would still play a role, though minor. Since the spacecraft goes around only for a few days in each orbit, there will not be any change in the orbits and hence the need to use propellant to correct the orbits would not arise.

But that will not be case when Chandrayaan-1 orbits the moon for two years. “There will be a need to correct the orbit once in two weeks to maintain a 100 km circular orbit,” said Dr. Annadurai.

Less energy required
While earth’s gravitational force will exist even when the spacecraft moves further and further away from the earth, the force will decrease with distance. “So firing it to the fourth and fifth orbit will require less energy,” said Dr. Annadurai. “Since some propellant is already used in the previous firings, the overall mass would come down. So the effort required to fire reduces.”

Reverse firing
Five-and-half days after the fifth firing, Chandrayaan-1 will have its rendezvous with the moon. Chandrayaan-1 will get nearer to the moon on November 8 when it reaches the 3,81,000 km apogee.

Though the moon’s influence will be predominant, the velocity of Chandrayaan-1 has to be reduced to enable the moon to capture it. Else, it can fly past the moon.

Once captured by the moon’s gravity, the velocity of the spacecraft has to be reduced to help it reach its final destination of 100 km circular orbit around the moon.

This is achieved by reversing what was done to raise its orbits.

“First, the firing is resorted at both perigee and apogee positions. And the firing takes place only after the orientation of the spacecraft is reversed — turned 180 degrees,” he said.

While the momentum of the spacecraft allows it to move in the same direction, the reverse firing helps it to reduce the velocity. The reduction in velocity is again undertaken in an incremental manner to reach the predetermined 100 km circular orbit around the moon.

© 2008, The Hindu