Published 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.