How Does Time Dilation Affect Spacecrafts Traveling at High Speeds?

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SUMMARY

This discussion focuses on the effects of time dilation on two spacecraft traveling at 0.99c towards a star located 60,000 light years away. The time dilation equation used is TD = To * ((1 - (v^2/c^2))^-0.5) - To, where To represents the proper time experienced by the spacecraft. The participants explore the mathematical relationship between time dilation and distance traveled, specifically after both spacecraft have traveled for 40 years in their respective frames. The conversation highlights the complexities of relating time dilation to distance in a relativistic context.

PREREQUISITES
  • Understanding of special relativity and time dilation
  • Familiarity with the time dilation equation TD = To * ((1 - (v^2/c^2))^-0.5)
  • Basic calculus, particularly derivatives
  • Knowledge of relativistic speeds, specifically velocities approaching the speed of light
NEXT STEPS
  • Study the implications of time dilation in special relativity
  • Learn how to apply the time dilation equation in practical scenarios
  • Explore the concept of proper time versus coordinate time in relativistic physics
  • Investigate the effects of relativistic speeds on distance measurement in space travel
USEFUL FOR

Students of physics, aerospace engineers, and anyone interested in the implications of relativistic travel on time and distance in space exploration.

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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