Vikram Lander Soft Landing Experiment − Event Analysis

We all have been anxiously waiting to know what has happened to Vikram Lander during the last few minutes before its touch down on Moon's surface. Here I'm going to take up a small exercise to deduce whether or not Vikram Lander will ever be communicable. This attempt is to decode the event to study possibilities from the perspective of a curious student of science. It's not a failure analysis or root cause analysis as such analyses need a more detailed event data that has been obtained till loss of communication.

The experiment by ISRO is an extremely challenging one. Great missions bring greater challenges. Naturally, at each stage, there involved the risk of falling short somewhere. Despite that what ISRO's team has been able to achieve is truly incredible. They have taken a leap of faith. The interest that this experiment has kindled in young minds is invaluable and its intangible benefits will remain unparalleled in near future.

In true sense, the exercise at hands today is more about dispassionately appreciating the basic physics of the event based on limited data available through live telecast and of course wikipedia.

Mass 1471 kg (source: wiki)
Last velocities reported
Horizontal velocity Vh 48.1 mps,
Vertical velocity Vv -59 mps,
Altitude 0.335 km, 1.09 km left before touch down. (Source: recording of live telecast of the event from mission control room by DD National)

Absolute velocity V 78.84 mps, 276.6 kmph
Lander moving at an angle of 51° with moon surface.

Kinetic energy KE possesser by lander = 0.5mV2
= 4,342,392 J = 4242.392 kJ

Moon's gravity 1.62 m/s2 (mostly not used in calculations being a small value)

Approximate time to descend to surface at constant vertical velocity
= 335 m/59 mps = 5.68 s

Required time with available thrusters is way higher than available time if no resistive force is present to reduce velocity of the descending lander.

Required magnitude of constant force opposing the motion of lander in bringing the lander to rest in 5.68 seconds
= 4242.392 kJ ÷ 335 m = 12.66 kN
Force needed at each thruster
= 12.66 kN ÷ 4 = 3.17 kN

Required acceleration (negative)
= −12.66 kN ÷ 1471 kg
= − 8.61 m/s2, which is plausible if orientation of lander is proper.

Considering the information that is coming in recently, the lander lost the orientation and leading to less effective braking. Also the horizontal velocity was seen to have diminished fast and vertical velocity had seen a significant rise. This was evident from the trajectory deviation. They probably assisted descent also. The last visual of the graph of trajectory showed the descent was fast going close to vertical. This reinforces the suspicion that the lander had lost orientation and thrusters were becoming less effective. This means the lander dived into moon surface at a velocity of around 280 kilometres per hour (approximately adding effect of moon's gravity) thus leaving hardly any hope for its equipment to remain undeformed and functional - communication antennas included. Imagine a formula one car crashing into a large concrete block at 280 kilometers per hour. Will we consider repairing the remains, that once made the car seen before impact? More likely than not, the answer will be No. After eliminating least probable scenario, the only scenario is left with us according to which the lander dug into moon's surface to some extent if the surface at point of first contact was soft enough. Also it's likely that it would have tumbled along surface several times before coming to halt.

It's a sure thing that ISRO's team, which is in possession of telemetry data till 335 meter, in my opinion, doesn't expect to establish communication with lander. It'll be a miracle if they do!

...

The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.
- Rober Frost (1874-1963)