Solving the Relativity Question: When Does Mission Control Receive Confirmation?

[andytran]

hey


here is the question,

suppose an explorer set out on a ship traveling to some stars at a constant velocity of 0.9c. every week mission controller and explorer each transmit status report to each other and acknowledge receipt by transmitting a confirmation signal back

when does mission control receive the first confirmation signal?

when does the explorer receive the first status report?

any suggestions are welcomed!.
thx

 

[Source]

Using your relativity formulas, figure out how far the explorer has gone after one week. Then divide that distance by 186,000 and you'll get how many seconds it takes the message to reach the planet. The reverse trip... I'm not so sure on. If I weren't so focused on other areas of physics atm, I'd be able to help more. Hope I helped some though?

 

[Andrew Mason]

hey


here is the question,

suppose an explorer set out on a ship traveling to some stars at a constant velocity of 0.9c. every week mission controller and explorer each transmit status report to each other and acknowledge receipt by transmitting a confirmation signal back

when does mission control receive the first confirmation signal?

when does the explorer receive the first status report?

any suggestions are welcomed!.
thx

You have to use the Lorentz transformation to determine the time (t) and location (x) in the mission controller (rest) frame when the confirmation signal is sent. Then, using t = x/c determine when in the rest frame the signal is received and confirmation sent. You then use the reverse Lorentz transformation to determine that time as measured in the explorer's (moving) frame and the explorer's position at that time (relative to the controller but measured in the moving frame). Then, using t'=x'/c you can determine what time it will be received by the explorer.

AM