How Does Time Dilation Affect Spacecrafts Traveling at High Speeds?

AI Thread Summary
Time dilation significantly impacts spacecraft traveling at high speeds, such as .99c, especially over vast distances like 60,000 light years. The time dilation equation is crucial for understanding the relationship between the time experienced by the spacecraft and the time observed externally. A user seeks clarification on how to derive the related rate of time dilation to distance traveled after both spacecraft have experienced 40 years of travel. The discussion highlights confusion over the terminology used to describe the positions of the spacecraft and the mathematical approach to the problem. Overall, the conversation emphasizes the complexities of calculating time dilation in relativistic travel scenarios.
Teslanumber1
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1. A spacecraft going at .99c is heading straight towards a star that's at a distance of 60,000 light years. Another ship 25,000 light years below the first one also is heading towards the star also at .99c. What what is the related rate between the time dilation of the first spacecraft to distance traveled at a time when both craft have traveled for 40 years in the time they experience.2. The time dilation equation of To*((1-(v^2/c^2))^-.5)-To=TD
Where To is the time observed inside the space craft, v the velocity of the craft in terms of c(like .3c), c is the speed of light, and TD is time dilated, and or extra time outside of the space craft.

3. I assume you'd take the derivative of the time dilated with respect time so it would be To*((1-(v^2/c^2))^-.5*(c^2*2v*dv/dt))+1*dt/dt*(1-(v^2/c^2))^-.5+-dt/dt. This however I know is completely wrong since time To is already in terms of time, that doesn't make anysense, and then how could you relate this to the distance traveled of the other craft? I really do need help.
This belongs more in cal than in physics so I switched it.
 
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There is no acceleration, the derivative with respect to velocity does not matter.
Teslanumber1 said:
What what is the related rate between the time dilation of the first spacecraft to distance traveled at a time when both craft have traveled for 40 years in the time they experience.
I don't understand the grammar here, is that a translation?
Also, what does "below" mean in space?

Did you draw a sketch?
 
Teslanumber1 said:
1. A spacecraft going at .99c is heading straight towards a star that's at a distance of 60,000 light years. Another ship 25,000 light years below the first one also is heading towards the star also at .99c. What what is the related rate between the time dilation of the first spacecraft to distance traveled at a time when both craft have traveled for 40 years in the time they experience.

Please check what you've typed against what you intended to type. They can't match.
 
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