Time Dilation :- Planet near Black-hole

 

   With general relativity we learned that the gravitational force is best described in terms of warps and curves in space and time. That's most directly evident at the edge of a black hole where gravity is strong. The war-page of space and time is strong and the way we see that is if you were to go to the edge of a black hole but have say strong rocket engines so you don't fall over the event horizon so that you can actually say stay in orbit around the edge of a black hole. The time for us would slow down compared to the rate of passage of time of somebody far away. So for instance we might stay around the edge of a black hole for a week but when we come back say to earth we might find that ten years have gone by because our week was in slow motion. Time is running slow compared to the rate at which time is elapsing on earth. In fact if it was a strong and big enough black hole and if you got close enough to the event horizon to the edge be careful don't fall over but stay just outside. If we might spend a week at that black hole and we come back to earth it might be a million years or billion years have gone by that's the way in which black holes warp the passage of time.

 Explanation form movie Interstellar:-

    As the Cooper and his crew reaches Miller's planet which is near the black hole “Gargantua”. Due to Gargantua's proximity time is highly dilated. Every hour on the planet equals seven Earth years. Just after the touch down on the planet. Cooper says “what he means that – if they spend one hour on that planet, time will pass 7 years on earth.

     1 hour = 7 years

     1 hour = 3600 seconds

     1 day = 24 hours

 

      7 years = (3600 x 24) x 365 x 7 = 221000000 sec

        Time dilation factor = 221000000 /3600

                                                 = 61400

From tick- tick sound in 1 minute in the movie is 48 times then ratio is 60/48 = 1.25

                                         1.25 x 61400 = 77000 Earth second

So 1 tick in Miller’s planet = 77000/3600 = ~21 hours

The time on the Miller’ planet is so high due to “Gargantua” for which 1 hour is 7 years of earth time. Imagine what will be the gravitational force of the plant. Landing of a spacecraft will be impossible on the planet.   

                      Earth gravity = 9.8 m/s

                      Miller’ gravity = (21 x 9.8) m/s

                                             = 205.8 m/s (assumption)