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a) Calculate the time required for one pulse to occur, as measured by the astronaut.

b) Calculate the time required for one pulse to occur, as measured by an Earth-based observer.

c) Calculate the astronaut’s pulse, as measured by an Earth-based observer.

d) What effect, if any, would increasing the speed of the spacecraft have on the astronaut’s pulse as measured by the astronaut and by an Earth-based observer? Why?

this is my solution

a. the time for one pulse to occur in the astronauts frame is 1 minute/70 beats per minute or 1/70 minute or 60/70 seconds which in decimal form is 0.857 seconds.

b. the formula for time dilation is part of the Lorentz transformation is:

t = t0/(1 - (v^2/c^2))^1/2

= 60/70/[1 - (.81/1)]^1/2

= 60/70[.19]^1/2

= 60/70(0.435889894354067)

= 0.37 seconds

So they are about .37 seconds apart form the frame of reference of the Earthling

c. Pulse is 1/.37 seconds or 2.677 beats per seconds which is:

2.67651689515656 x 60 = 160.6 beats per minute

d. As the speed of the astronaut increases the astronauts pulse will also increase from the frame of reference of the Earthling. As v approaches c the denominator or the Lorentz transformation approaches 0 so the whole thing goes to infinity.

is that right?