Interstellar (2014) - Calculations and Analysis

                                             Interstellar (2014)
                                              Welcome to the Fountain
                                           Quench Increase your Thirst

Fact : 1
Miller's Planet to outside observers orbits Gargantua every 1.7 hours. On Miller's Planet, that means the planet orbits ten times a second around Gargantua , which is normally faster than the speed of light. But since the spin from Gargantua caused space to whirl around it similar to wind, Miller's Planet does not travel faster than light relative to its space as the laws of physics say you cannot travel faster than light relative to space, but space itself is not bound by the speed limit. As such, faster than light travel is possible by bending and twisting space. However, Gargantua would have to fill half the sky in order for it to be so close.

Fact : 2
The time dilation on Miller due to the gravitational forces of Gargantua would be tantamount to the planet moving through empty space at roughly 99.99999998% the speed of light. 

Fact : 3
Gargantua’s mass must be at least 100 million times bigger than the Sun’s mass. If Gargantua were less massive than that, it would tear Miller’s planet apart. The circumference of a black hole’s event horizon is proportional to the hole’s mass. For Gargantua’s 100 million solar masses, the horizon circumference works out to be approximately the same as the Earth’s orbit around the Sun: about 1 billion kilometers.

Fact : 4
Miller’s planet is about as near Gargantua as it can get without falling in and if Gargantua is spinning fast enough, then one-hour-in-seven-years time slowing is possible. But Gargantua has to spin awfully fast. There is a maximum spin rate that any black hole can have. If it spins faster than that maximum, its horizon disappears, leaving the singularity inside it wide open for all the universe to see; that is, making it naked—which is probably forbidden by the laws of physics

Fact : 5
Einstein’s laws dictate that, as seen from afar, for example, from Mann’s planet, Miller’s planet travels around Gargantua’s billion-kilometer-circumference orbit once each 1.7 hours. This is roughly half the speed of light! Because of time’s slowing, the Ranger’s crew measure an orbital period sixty thousand times smaller than this: a tenth of a second. Ten trips around Gargantua per second. That’s really fast! Isn’t it far faster than light? No, because of the space whirl induced by Gargantua’s fast spin. Relative to the whirling space at the planet’s location, and using time as measured there, the planet is moving slower than light, and that’s what counts. That’s the sense in which the speed limit is enforced.


QUERIES 
1. How old is Miller’s planet? If, as an extreme hypothesis, it was born in its present orbit when its galaxy was very young (about 12 billion years ago), and Gargantua has had its same ultrafast spin ever since, then the planet’s age is about 12 billion years divided by 60,000 (the slowing of time on the planet): 200,000 years. This is awfully young compared to most geological processes on Earth. Could Miller’s planet be that young and look like it looks? Could the planet develop its oceans and oxygen-rich atmosphere that quickly? If not, how could the planet have formed elsewhere and gotten moved to this orbit, so close to Gargantua?

2. What is the gravitational time dilation equation for Miller's planet? As there is 60000 ratio between time on earth and time on Miller's planet , to balance the equation what should be the distance of planet from Gargantua, angular momentum as it is revolving around very fast spinning object and Mass of Gargantua ?

3. We all know Gravitational Time Dilation does not affect Mann's planet as it is far from Gargantua’s vicinity. But we also know, almost immediately after the Endurance’s explosive accident in orbit around Mann’s planet, the crew find the Endurance being pulled toward Gargantua’s horizon. From this it appears when crew leaves Mann’s planet, the planet must be near Gargantua. Following diagram is the orbit of Mann's Planet.

According to this, what should be the orbital period and orbital velocity of Mann's planet for a person on Earth and a person on Mann's planet.

4. How long Dr. Mann spent time on Mann's planet according to him and according to an observer on Earth(Keep its orbital path in mind)? How long did he spend in hibernation for both observers?

5. Why was Endurance able to receive signal from Earth but Earth was not able to receive signal sent by Endurance.

6. When Cooper left Earth, he was 35 Years old and when he returned, He was 124 years old for Murph. 35 + 2 years for Saturn Journey + 23 years for Miller's Planet Journey + 51 years for Black Hole Journey = 111, Where are 13 Years Missing? How Long was Cooper out for himself?

8. What is the Orbital velocity of Miller's planet for a person on Earth and a person on Miller's planet?

9. What is the age of Brand when Cooper arrives at Edmund's Planet?

10. How long Dr. Laura Miller spent time on Miller's planet according to her and according to an observer on Earth? Lets keep in mind that she died minutes ago before Cooper and Brand reached there.

11. Miller’s planet travels around Gargantua’s billion-kilometer-circumference orbit once each 1.7 hours. Could Rom see it moving very fast from Mothership?

12. If Coop and team would try to communicate with Rom from Miller's planet, how would their communication appear? According to Coop how fast would they get response from Rom and similarly how long would Rom get response from Coop & team?

Gabbar Probability

Gabbar Gunshots Probability Analysis

Everyone must have watched movie Sholay(1975). Do you remember the entry scene of Gabbar Singh (Amzad Khan)?

"Kitne Aadmi The"

Exactly That was the scene. In this scene Gabbar kills three of his henchmen. Lets skip the middle conversation and jump to this part.
Gabbar drags a revolver from one of his man and asks the number of bullets in it.
He replies "six". Generally a revolver has 6 bullets compact in a round structure.
 

Here the game begins.

He already made up his mind to kill all three men because he doesn't like coward people but he does not want to shoot them just like that. He wants some entertainment here.

This is the game of probability. He fires three bullets in the air to make remaining count three because he needs to kill only three people and one bullet is enough for each.

Now he revolves the cylinder of revolver in a speedy way so even he doesn't know where are the remaining three bullets.

Then he takes a shot towards each man. 3 chambers are with bullets and 3 are empty, he thinks there are 50-50 chances here.

Now lets analyze the situation here.

What we know
Three bullets are in a consecutive order and three empty chambers are also in consecutive order but it is a circle so any chamber can be its firing position. Only we can say confidently that there is no single empty chamber between two bullets. There is only one gap between two bullets and it is of three empty chambers.

Lets give names to each chamber. Suppose Chamber 1, Chamber 2 and Chamber 3 are empty chambers and Chamber 4, Chamber 5 and Chamber 6 are with bullets. We gave these names anti clock-wise because cylinder moves in clock wise direction so 2 will be fired after first and third will be fired after second and so on.

First shot can be empty or it can be with bullet. Nobody knows. Suppose if first shot is empty. It means either Chamber 1 or Chamber 2 or Chamber 3 in its firing position.

Suppose Chamber 1 is in its firing position during first shot then other two men will be saved because next number is of 2 and then 3 and both are empty chambers so all are saved (That's what happens in the movie)

Suppose Chamber 2 is in its firing position during first shot then second man will be saved because 3 is an empty chamber but 4 is filled with bullet it means last man (Kalia) will be killed. Even he ate salt of his master but no mercy would be here in first place.

 

Suppose Chamber 3 is in its firing position during first shot then second and third both men will be killed because 4 and 5 the chambers are with bullets.

 

Suppose Chamber 4 is in its firing position during first shot then all three will be killed because 4, 5 and 6 are with bullets.

 

Suppose Chamber 5 is in firing position during first shot then second will be killed and third man will be saved because 1 is empty.

 

Suppose Chamber 6 is in firing position during first shot then first and second both will be saved because 1 and 2 both are empty.

 

In this analysis, there are chances, each man can be killed and each can be saved. But can you predict what may happen with next?

You can't predict the future of first two men in any condition. You can predict the future of only last man and that's in two conditions only.
1) If First man is killed and second is saved
2) If first man is saved and second is killed

In first situation, you can easily find that chamber 6 was in firing position during first shot that's why first is killed and second is saved because second got chamber 1 which is empty. Now third man will get chamber 2 which is also empty and he will be saved too. There is no other condition for this situation.

In second situation, still you can find that chamber 3 was in firing position that's why first is saved and second is killed because second got chamber 4 which is with bullet. Now third man will get chamber 5 which is also with bullet and he will be killed too. There is no other condition for this situation too.

Both are unique situations.

Except these two conditions you can't predict future of third man.

Suppose first two are saved then you can't predict the fate of third.
He can be killed if chamber 2 was in firing position during first shot.
He can be saved if chamber 1 was in firing position during first shot.

Suppose first two are killed even then you can't predict the fate of third.
He can be killed too if chamber 4 was in firing position during first shot.
He can be saved if chamber 5 was in firing position during first shot.

Conclusion :
If second shot is different than first shot only then you can predict the behaviour of third shot.

Moral :
But after all none of this matters because eventually Gabbar would kill all three.

Fascinating Facts About Tigers

There is little doubt that tigers are some of the most beautiful, royal and scary animals nature has ever produced. They are incredible hunters, the biggest of all cat species (excluding the liger, which is a combination of lion and tiger) and can hunt in the water or land in equal measure.But if you think you know all there is to know about this magnificent animal, think again as you read this list of 22 fascinating tiger facts.