“Twenty years from now, when space travel is likely to become mundane like airline travel today, we don’t to be buying tickets on other people’s space vehicles” – G Madhavan Nair, Former chairperson ISRO

The 24th of September 2014, was a proud moment for every Indian. ISRO under the successfully placed the satellite (Mangalyaan) into mars orbit.

About Mangalyaan

The Mars Orbiter Mission (MOM), also called Mangalyaan is a space probe orbiting Mars since 24 September 2014. It was launched on 5 November 2013 by the Indian Space Research Organisation (ISRO). It is India’s first interplanetary mission and it made it the fourth space agency to achieve Mars orbit, after Roscosmos, NASA, and the European Space Agency. It made India the first Asian nation to reach Martian orbit and the first nation in the world to do so on its maiden attempt. ISRO spent $75 million to launch the mission, making it the least-expensive Mars mission to date.

The spectacular journey

The following diagram shows how the satellite’s journey of approximately 325 days took place.

For many people it looks like a “magic” the way the orbit of the satellite changes from the one around earth to the one that is around mars. A knowledge of Physics shows that in principle it is quite simple. So let us start.

What Physics is involved?

Sir Isaac Newton showed that the gravitational force on the satellite by earth is inversely proportional to the square of the distance between the two i.e. . He also showed that for every force on body A by body B, there is a reaction force on body B by body A (This is the famous Newton’s 3rd Law).

Now, we put the satellite inside a rocket (near the nose of the rocket). From the nozzle (at the bottom of the rocket), a fast burning gas will eject downwards. This will push the rocket vertically upward. This is similar to allowing air to come out from a blown up balloon and seeing the balloon to fly in the opposite direction (Newton’s 3rd Law). Once we cross the atmosphere of earth, the rocket will open up and the satellite is given the required orbital velocity (again by ejecting burning gases in the opposite direction). This will make the satellite revolve around a circular orbit.
Note: 1PU students even derive the formula for the orbital speed.

The remaining part of the rocket will fall down (after the fuel is used up), and will burn as it re-enters the atmosphere (so don’t worry about it hit your head some day).

But how to actually change the orbit?

The satellite is now revolving earth in a circular orbit. Now we want to manoeuvre the satellite. This means we want to change its orbit. For this you have to remember that the orbital velocity of the satellite is given by . So its kinetic energy is and its potential energy is . Thus total energy of the satellite is .
If we want the satellite to revolve in a bigger orbit, should increase. As increases, the above equation says the total energy also increases (Remember minus 2 is greater than minus 3). This requires that we should apply force (by burning gases in the propulsion system) in the same direction as the motion (velocity) of the satellite. This way the force does positive work. This force applied is what they call “kick”.

Suppose a kick is given to the satellite at some point in the circular, the satellite will now revolve in an elliptical orbit as shown in the diagram below.

The perigee of the new orbit (where the satellite is closest to Earth) lies at the point where the kick was applied. By repeating this (seven times for Mangalyaan) , the satellite can be made to revolve in bigger and bigger elliptical orbit. Now remember, as the distance of the satellite from the earth increases, the gravitational influence of the earth on the satellite decreases.

The final Kick

After around 325 days, Mars is in position 3 (shown in the first diagram). During this moment the earth is at the shown position. And the satellite’s highly elliptical orbit will make the satellite reach near mars. Now the satellite will feel a greater force of attraction from mars than compared to earth. With the help of another “kick”, the satellite is given the correct orbital velocity so that it will now revolve around the mars at a distance of around 515 km.

Final words

So, you see the principle is quite simple. Of course the details of the path, orientation of the orbit, the actual forces required, etc. are intricate and require a more elaborate discussion.

I sincerely hope the young minds will be part of such missions in future!

Best wishes,
Pankaj Tamang, HOD Edushrine.