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

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The discussion centers on calculating the time it takes for Rocket Orion, traveling at 0.900c, to completely pass Rocket Sirius, which moves at 0.700c. The key points involve determining the observed velocity of Orion from Sirius's frame of reference and the relativistic effects on length contraction. The participant initially considers using simple subtraction for velocities but realizes the need for the relativistic addition of velocity formula. After some confusion, they clarify their understanding of the frames of reference involved. The conversation highlights the complexities of relativity in practical scenarios.
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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?
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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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