Chandrayaan: Moon Mission 1

D. Indumathi, The Institute of Mathematical Sciences, Chennai
(Compiled from Various Sources)

On 22 October, 2008, India launched an unmanned mission to the moon from Sriharikota. India is the sixth country to do so, after Russia, the U.S., the European Space Agency, Japan and China. It takes three weeks for Chandrayaan-1 to reach its final destination, which is an orbit of 100-km around the moon. This is expected to occur on November 15, and you will be reading this article shortly thereafter!
The unmanned lunar exploration mission includes a lunar orbiter and an impactor. As the name indicates, the orbiter will take data on the moon as it is orbiting the moon in a circular orbit of 100 km radius. The impactor will be released after the orbiter is in the final orbit. It will crash-land on the surface of the moon and take data from there.

The launch
All satellites and space probes need to be launched into space. Chandrayaan was launched by the Polar Satellite Launch Vehicle, PSLV C-11, built by the Indian Space Research Organisation (ISRO).
The first PSLV was built in the early 90s when it launched a remote-sensing satellite, IRS-P2. PSLV has proved its reliability by scoring continuous successes, including several satellites and a recoverable space module. That is why it was chosen as the launch vehicle for Chandrayaan.
PSLV has four stages, using solid and liquid propulsion systems alternately in each stage. There are 4 additional strap-on motors in the first stage to provide extra thrust required during take-off. Since the pay-load (weight of the object to be launched which is 1380 kg) was more than usual, PSLV was upgraded by having 6 strap-on motors (this version was called PSLV-C11). These motors are longer than normal as well.

BOX Escape velocity
Everything that goes up, must come down, or so we experience in every-day life. We learn that this is due to gravity that pulls every body down to Earth.

Throwing a ball
Speaking more technically, if you throw a ball upwards, it has kinetic energy because of its velocity (KE = mv2/2). So it can overcome the gravitational force and keep going upwards. As it goes up to a height h above the ground, the gravitational potential energy (PE = mgh) becomes more and more. Since total energy of the body is conserved, its velocity keeps on decreasing. At some point, its velocity falls to zero, at which height all its kinetic energy has been converted into potential energy. At this point, it starts to fall back to the ground. 
Consider a cannon firing a ball at a very great height above the Earth. It falls back on Earth with a path in the shape of a parabola. See the path A in the figure.

As velocity increases
Suppose you give the ball more initial velocity; clearly the ball will go further. This means that the parabolic path of the ball is much longer. See path B in the figure. You can see that if you give more and more velocity, the parabola becomes larger and larger until a critical point is reached.
At this point, the ball acquires a velocity where it simply starts to go into orbit around the Earth! One way of understanding this is that the ball keeps falling back to Earth and keeps missing it! This is because the ground curves away from the ball at least as much as the ball falls, so the ball never hits the ground. 
The ball takes the circular path C shown in the figure. As the initial velocity is further increased, the path becomes an elliptical orbit around the Earth as for example path D in the figure.
As the velocity increases even further, the ball's kinetic energy is equal to the gravitation potential energy. This is called the escape velocity. Any object thrown with a speed larger than this value will simply escape from the gravitational attraction of the Earth. This is the path E in the figure.
On the surface of the Earth, the escape velocity is about 11.2 kilometers per second (over 40,000 km per hour), which is approximately 34 times the speed of sound (mach 34) and at least 10 times the speed of a rifle bullet. However, at 9,000 km altitude in "space", it is slightly less than 7.1 km/s since gravity is much smaller there.
Because of the effect of the Earth's atmosphere, it is not easy to give an object near the surface of the Earth a speed of 11.2 km/s (such an object would simply burn up because of friction caused by "rubbing" with the air).
For an actual escape orbit a spacecraft is first placed in low Earth orbit and then accelerated to the escape velocity at that altitude, which is a little less -- about 10.9 km/s. The required acceleration, however, is generally even less because from that sort of an orbit the spacecraft already has a speed of 8 km/s. Note that the object has a smaller velocity near the turn-around points of the orbit when it is furthest from the Earth.

Description of the Spacecraft 
The spacecraft is cuboid in shape of approximately 1.5 m side. It weighed 1380 kg at launch. After several firings of the rockets to achieve the final orbit, it will weigh 675 kg at lunar orbit. It accomodates eleven science payloads.
It can rotate slowly around its own axis. This is very important for making sure that it is on the right path. For example, when it is transferred from an Earth orbiting path into a lunar transfer orbit, it has to be accelerated sufficiently in order to escape out of Earth's gravity. For this, the rocket thrusters must be rotated into the right direction before firing them. Otherwise, it may simply return to Earth! It has several gyroscopes to stabilise this rotation.
A single-sided solar array provides power during all phases of the mission. The panel generates 750W of peak power. During eclipse, spacecraft will be powered by Lithium ion (Li-Ion) batteries!
The spacecraft has an X-band, 0.7m diameter parabolic antenna for payload data transmission. The antenna has a special mechanism to track the earth station when the spacecraft is in lunar orbit.
The propulsion system carries required propellant for a mission life of about 2 years. Its on-board computers also have the capacity to store sufficient data acquired during this time.

The Scientific Goals
Chandrayaan carries 11 scientific experiments, called payloads. Five of them are Indian and six are from different international partners. Apart from testing some of the instruments, there are specific scientific studies proposed.
The Chandrayaan-1 mission is aimed at high-resolution photography of the moon in the visible, near infrared (NIR), low energy X-rays and high-energy X-ray regions.
It will also make a three-dimensional atlas of the moon (both its near and far side). Apart from searching for water (ice), it will map the moon for the chemicals and minerals it contains. For example, it will search for aluminium, magnesium, silicon, calcium, iron, and titanium, uranium and thorium.
The mission also has a basic sciences programme, to understand the evolutionary history of the moon.

Tracking of Chandrayaan
Deep space describes space beyond 1,00,000 km from Earth. So this is India's first foray into deep space. In order to have an effective programme, scientists at the ground-base must be in continuous contact with Cahndrayaan and be capable of controlling its flight path and its scientific pay-loads.
This is made possible by the Indian Deep Space Network (IDSN). This consists of an 18-m and a 32-m antenna at a new campus in Byalalu near Bengaluru.
Whereas existing tracking stations routinely control India's and other satellites, the new antennae will perform the tracking and control functions, and real-time downloading of information from the scientific instruments over the much greater distances of over 4,00,000 km involved in the lunar mission. More importantly, while the 18-m antenna is tailored specifically for Chandrayaan-1 mission, the state-of-art 32-m antenna can also support other planetary missions, for instance to Mars.

Sequence of the launch
An artist's sketch of the launch is seen in the figure on the next page.
Chandrayaan was placed in its first orbit around Earth within about 18 minutes from launch. It was then moved into a highly elliptical orbit with distance from the Earth being 22,858 km and 247 km at its farthest (apogee) and nearest (perigee) points.
Intermittently, the spacecraft's motors would be fired, leading to a "sling-shot" effect that would lift the craft to higher and more extremely elliptical orbits. The last one had an apogee at 3,86,194 km which brought it almost to the moon. This way, least amount of energy would be used, instead of directly trying to put the space-craft into such a large elliptical orbit.
At around 2,00,000 km from Earth, the satellite begins to feel the moon's gravity as well as that of the Earth. As it goes even closer, this pull becomes larger. It is now well into the lunar transfer trajectory, as seen in the figure.
The space-craft is now in the dual-gravity zone of both moon and the Earth. Since the moon and Earth are pulling it in different directions, there are certain places where the gravitational pull of the Earth and moon exactly cancel each other.
These are called Lagrange points. There are 5 of them, as seen in the figure, with only L4 and L5 being stable points. When the space-craft is at L1 point, there is very little force acting on it from either Earth or moon. L1 is about 60,000 km away from the moon. Since it is an unstable point, it is very easy to move it out of this point. At this point, the rockets are fired to decrease the speed of the space-craft.
This is a very critical stage of the operation. Since the space-craft is now moving towards the moon, there are two things to note.
1. If the rockets are not fired in the correct direction, the space-craft could either hit the moon or else go off in a completely wrong direction.
2. If the space-craft is not sufficiently slowed down, its velocity is so high that it may just fly past the moon without being captured into an orbit around it.
This critical phase was correctly negotiated and the space-craft was captured into an elliptical orbit around the moon. Its orbit is then further lowered to its ultimate intended 100 km circular orbit around the Moon (on November 15), where it will stay for 2 years.
Once the orbit is achieved, the Moon Impact Probe (MIP) will be dropped from Chandrayaan to crash onto the Moon's surface. It will take data both during and after the landing.
Scientists are eagerly looking forward to the near future, when the results of the studies become visible. In the meanwhile, scientists at ISRO are already planning Chandrayaan-2.

BOX: Don't Aim and Shoot!
An amusing point to note in the figure is the position of the moon at the time of the launch. The trajectory of Chandrayaan is carefully calculated, so that it is aimed at the moon as it will be 3 weeks later, since it takes so long to reach there! If Chandrayaan had simply been aimed at the visible moon in the sky on October 22, there would have been a clean miss!