How much did Scott Carpenter age less when he orbited the earth 22 times?

  • Thread starter Thread starter genesis1
  • Start date Start date
  • Tags Tags
    Age Earth
Click For Summary
SUMMARY

Scott Carpenter orbited the Earth 22 times in 1962 at an altitude of 160 km, which necessitates the application of special relativity to calculate the time dilation experienced. The relevant equations include L = Lp(1 - v^2/c^2)^0.5 and delta t = t /(1 - v^2/c^2)^0.5, where 't' represents proper time. The challenge lies in determining Carpenter's velocity and the duration of each orbit, as these variables are not provided. Understanding the relationship between orbital radius and velocity is crucial for solving the problem accurately.

PREREQUISITES
  • Understanding of special relativity concepts, specifically time dilation.
  • Familiarity with orbital mechanics and gravitational acceleration.
  • Knowledge of the equations governing relativistic effects, particularly L = Lp(1 - v^2/c^2)^0.5.
  • Ability to perform calculations involving circular orbits and velocities.
NEXT STEPS
  • Research the calculation of orbital velocity using the formula v = √(GM/r) for circular orbits.
  • Study the implications of time dilation in special relativity with practical examples.
  • Explore the concept of proper time versus coordinate time in relativistic physics.
  • Investigate the effects of altitude on gravitational acceleration and its impact on orbital mechanics.
USEFUL FOR

Students studying physics, particularly those focusing on relativity and orbital mechanics, as well as educators looking for practical examples of time dilation in real-world scenarios.

genesis1
Messages
2
Reaction score
0

Homework Statement



Scott Carpenter orbited the Earth 22 times in 1962. Assuming he was 160 km above Earth in a circular orbit, determine the time difference between someone on the Earth and Carpenter for the 22 orbits.

Homework Equations


L = Lp(1 - v^2/c^2)^.5 delta t = t /(1 -v^2/c^2)^.5 Note the t on right hand side of equation is the proper time.


The Attempt at a Solution


All that is given in the problem is the proper length 160,000m. The problem does not specify how fast Carpenter is moving or how long it took to complete one orbit. Obviously Carpenter is going to be measuring proper time and delta t is the time someone measures on the Earth. I have tried solving for v in the first equation and substitute in the second equation. Still leaves you with three unknown variables.
 
Physics news on Phys.org
If you know the radius of the orbit, you can determine how fast he is moving and how long it took. He is in orbit so the acceleraton must be the acceleration due to gravity at that height.
 

Similar threads

Proper time in moving frame of reference
  • · Replies 5 ·
Replies
5
Views
3K
How Does Time Dilation Affect Aging in Orbit?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Does Special and General Relativity Affect Aging of Apollo Astronauts?
  • · Replies 10 ·
Replies
10
Views
4K
How Does Energy Transformation Occur in Quantum Orbital Mechanics?
  • · Replies 6 ·
Replies
6
Views
4K
High School How long it takes the Earth to fall halfway to the Sun--ellipse method
  • · Replies 3 ·
Replies
3
Views
2K
Understanding how to "tack on" the time wiggle factor
  • · Replies 8 ·
Replies
8
Views
2K
Relativistic frequency shift of satellite signal
  • · Replies 2 ·
Replies
2
Views
3K
General Relativity - Circular Orbit around Earth
  • · Replies 32 ·
2
Replies
32
Views
4K
Time that a comet spends inside Earth's orbit
  • · Replies 2 ·
Replies
2
Views
2K
What is the Accretion Rate of Earth?
  • · Replies 9 ·
Replies
9
Views
4K