The distance between our solar system and the black hole Gargantua is 10 billion

Question

The distance between our solar system and the black hole Gargantua is 10 billion light-years. (One light-year is approximately 9.5 times 10^15 m). Traveling at 0.75c, this means that it will take: or about 13.4 billion years-a very long time! This is the amount of time for the trip as measured by those who remain on Earth. To the astronauts on the ship, however, time is dilated relative to that measured on Earth. This means that a given time interval is smaller. The trip time measured by the astronauts is: where gamma is a dimensionless factor that accounts for the dilation: This makes the t_shiP = 8.8 billion years-not much of an improvement. So...even though the ship is traveling at very high speed, the trip time is essentially infinite. Calculate t_us and t_ship when v = 0.99c. Is the trip time any better than at v= 0.75c? How fast would they have to travel to make their trip time 1 billion years? Since the speed of light is constant, the distance the ship travels as measured by the astronauts gets contracted. The distance they measure is: d_ship = d/y = 10e9/1.51 - 6.6 billion light years What is the great advantage of sending the spaceship Endurance through the wormhole to Gargantua?

Explanation / Answer

From the given data

tsu =d/v =d/0.99c=(109)(9.5*1015)/(0.99)(3*108) =9.5*1016/2.97=3.198*1016s

now tship =d/rv =3.198*1016s/7.089=4.511*1015s

Then r =1/Sqrt[(1-(v/c)2] =1/Sqrt[(1-(0.99)2] =7.089

It is better than the v =0.75c

b)

it has to move with a speed (v) =0.99c

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.