Length contraction of two spaceships

In summary, the conversation discusses the problem of finding the relative velocity of two space ships, each measuring 100 meters in length, as they travel towards each other at a speed of 0.85c relative to the Earth. The equations involved include λ = 1 / √1 - (v2/c2), x' = λ(x - vt), and L' = L / λ. The question arises of how to find the relative velocity according to Einstein's theory, as the Newtonian approach of 1.5c does not seem to work. The solution involves using the equation v_{BA}=\frac{v_B-v_A}{1-\frac{v_Av_B}{c^2}} to calculate the
  • #1
Saxby
45
0

Homework Statement


Two space ships, each a hundred metres long when measured at rest, travel toward each other with a speed of 0.85c relative to the Earth.


Homework Equations


λ = 1 / √1 - (v2/c2)
x' = λ(x - vt)
L' = L / λ

The Attempt at a Solution


Well to be honest i may be missing an equation or something but that's what i was given.

I find that the relative velocity of one spaceship to another (according to Newton) would be 1.5c. This doesn't work using the equations above. I know i have to find the relative velocity according to Einstein's theory but i don't know how.
 
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  • #2
Saxby said:

Homework Statement


Two space ships, each a hundred metres long when measured at rest, travel toward each other with a speed of 0.85c relative to the Earth.


Homework Equations


λ = 1 / √1 - (v2/c2)
x' = λ(x - vt)
L' = L / λ

The Attempt at a Solution


Well to be honest i may be missing an equation or something but that's what i was given.

I find that the relative velocity of one spaceship to another (according to Newton) would be 1.5c. This doesn't work using the equations above. I know i have to find the relative velocity according to Einstein's theory but i don't know how.
So, you are trying to find the relative velocity of one to the other?

Let the first spaceship be spaceship A and the second be spaceship B.

Consider ##v_{BA}=\frac{v_B-v_A}{1-\frac{v_Av_B}{c^2}}##.
 

FAQ: Length contraction of two spaceships

How does length contraction occur between two spaceships?

Length contraction is a phenomenon predicted by Einstein's theory of relativity. It occurs when two objects are moving relative to each other at high speeds. As the speed of an object increases, its length in the direction of motion appears to decrease from the perspective of an observer. This is due to the distortion of space and time caused by high velocities.

What is the formula for calculating length contraction between two spaceships?

The formula for calculating length contraction is L = L₀/γ, where L₀ is the rest length of an object and γ (gamma) is the Lorentz factor. The Lorentz factor is given by γ = 1/√(1 - v²/c²), where v is the velocity of the object and c is the speed of light. This formula shows that as the velocity of an object approaches the speed of light, its length approaches zero from the perspective of an observer.

How does length contraction affect the appearance of two spaceships?

From an observer's perspective, length contraction causes the two spaceships to appear shorter in the direction of motion. This means that the distance between the front and back of the spaceships will be shorter than their actual lengths. This effect is only noticeable at extremely high speeds, close to the speed of light.

Can the length contraction of two spaceships be observed from within the spaceships?

No, the length contraction of two spaceships can only be observed from an external perspective. This is because length contraction is a result of the distortion of space and time, which is only noticeable to an external observer. From within the spaceships, the objects and their surroundings will appear normal.

Is length contraction a real phenomenon or just an illusion?

Length contraction is a real phenomenon that has been confirmed by numerous experiments and is an essential aspect of Einstein's theory of relativity. While it may seem counterintuitive, the effects of length contraction have been observed and validated through scientific research. It is a fundamental concept in understanding the behavior of objects at high speeds.

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