Question

5. Once the Veracious is clear of the Earth's gravity, NASA operating procedure calls for the firing of the quark fusion quantum accelerator to boost velocity to 90 percent of the speed of light. After that, no acceleration by either fusion reactor will operate except for of course corrections and the return trip to Earth. At the rate of 0.9c then, how many years will it take for you to reach your destination? (Ignore the month it takes to safely bring the ship up to speed.)

Answer: For the number of years it takes to reach the destination aboard the Veracious, one can use the equation t=d/v, so t=10,000/0.9=11,111.11 years.

6. Einstein determined that according to his Special Theory of Relativity, time actually slows for those traveling at speeds near the speed of light. Using the formula for time dilation and the time calculated as seen from Earth in the previous calculation, determine how many years will pass as observed by the occupants of the Veracious. Are you determining dilated or proper time?

Answer: This seems to be dilated time, as seen from the point of view of the occupants of the Veracious, using the previous calculation. So deltato=deltat*sqrt(1-(v/c^2)=10000/sqrt(0.19)=22,941.571 years.

I need help checking question 6, I know that closer to a black hole time slows, so it doesn't make sense to me that the answer for the people on the Veracious would be double that of observers on Earth! Did I do something wrong with the calculations? Is this, indeed, dilated time? Would it actually be 4843.22 years?

Answer 1

6] Time taken in the Earth frame (actual time, not proper time) is:

t = 11111.11 years

this time will be the 'Dilated time' since the Earth frame is the ground frame.

the Lorentz factor for v = 0.9c is:

so, the proper time (time as measured in the moving frame of Veracious) will be:

.

Time slowing down closer to a blackhole is a concept from General Relativity where gravity affects the time passage. It should not be confused with Special Relativity (which is the subject of this question).