How Long Does It Take for One Rocket to Pass Another at Relativistic Speeds?

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Homework Help Overview

The discussion revolves around a problem in relativistic physics involving two rockets, Orion and Sirius, traveling at significant fractions of the speed of light. The original poster seeks to understand the time it takes for one rocket to completely pass another from the perspective of the slower rocket's frame of reference.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to determine the observed velocity and length of rocket Orion from the frame of reference of rocket Sirius. They express confusion regarding the correct application of relativistic velocity transformations.

Discussion Status

Some participants have provided guidance on the need to apply the relativistic addition of velocity formula to find the correct relative speed. The original poster indicates they have resolved their confusion after receiving input.

Contextual Notes

There is an indication that the original poster initially considered different frames of reference, including whether to use Earth as a stationary frame. This reflects the complexity of relativistic problems and the assumptions involved.

ZanyCat
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I do have a specific example/problem, but my actual question is more so conceptual (I'm sure that seeing someone confused by relativity is a first around here!).

The problem:

Two rockets are each 1000m long in their rest frame. Rocket Orion, traveling at 0.900c relative to the earth, is overtaking rocket Sirius, which is poking along at a mere 0.700c. According to the crew on Sirius, how long does Orion take to completely pass?
That is, how long is it from the instant the nose of Orion is at the tail of Sirius until the tail of Orion is at the nose of Sirius?
_____________________________________________________________________________________

Okay, so I'm thinking that I'll need to find a) the observed velocity of O in S's FOR and b) the observed length of O in S's FOR, and go from there.

My confusion is coming from the velocities. I'm taking S as my Frame of Reference, so from S's FOR, is O moving past at 0.200c? Or do I need to transform the velocity?
 
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ZanyCat said:
Okay, so I'm thinking that I'll need to find a) the observed velocity of O in S's FOR and b) the observed length of O in S's FOR, and go from there.
Good.

My confusion is coming from the velocities. I'm taking S as my Frame of Reference, so from S's FOR, is O moving past at 0.200c?
No. To find the velocity of O with respect to S, you'll need to use the relativistic addition of velocity formula.
 
I'm struggling with that part. Do I need to consider the Earth as my stationary FOR, then?
 
Never mind, got it sorted, thanks Doc!
 

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