# Special relativity and simultaneity: Spacecraft and Target

• LCSphysicist
In summary: In this time, the spacecraft would have already passed the first target. If we consider the time between the spacecraft shoot and the hit of the second target, we would have ##\tau+\tau=2##, and, consequently, the spacecraft would have already passed the second target when it hit the first target.
LCSphysicist
Homework Statement
.
Relevant Equations
.
I made an exercise whose question is like that:

A spacecraft moves with speed v at the axis x. There are two target at the axis x, in which the distance between them is L at the ground frame. Suppose that the spacecraft shoot the target simultaneously when it passes by the target. A|so, neglect the time between the spacecraft shoot and the hit of the target. Is there a frame in which both targets are hitted simultaneously? If yes, what is the velocity of the frame?

Now, i have found an answer that i am 99% sure is wrong, but just want to make sure and, also, would like to know the speed of this frame for both hits simultaneously:

I have decided to name two events:
Event A: Spacecraft passes the first target/hit the first target.
Event B: Spacecraft passes the second target/hit the second target.

Using lorentz transformation, $$\Delta t' = \gamma ' (\Delta t - \beta' \Delta x) = \gamma ' (\Delta t - \beta' v \Delta t) = 0$$
$$\implies$$
$$1 - v'v = 0, v<1 \implies v'>1$$

So there are no frame in which the target are hitted simultaneously.

I am aware of the lost of simultaneously, so i am sure i am wrong because probably in the frame S' the missle is not fired and wouldn't hit the target at the same time the spacecraft passes the target.

But the problem i am having is to understand how could i find the velocity of S' without i know the missle speed? Someone can help me?

Delta2
Herculi said:
Homework Statement:: .
Relevant Equations:: .

So there are no frame in which the target are hitted simultaneously.
Surely. If there were such a frame, there must be two same rockets in that frame.

Last edited:
Herculi said:
Homework Statement:: .
Relevant Equations:: .

Suppose that the spacecraft shoot the target simultaneously when it passes by the target. A|so, neglect the time between the spacecraft shoot and the hit of the target. Is there a frame in which both targets are hitted simultaneously?
This supposition is wrong. The proper distance between the targets is L; the contracted distance, wrt the spacecraft , is## L_c=L/\gamma##, thus it takes the proper time ##\tau={L_c/v}## for the spacecraft to go from the first to the second target.

## 1. What is special relativity and how does it affect spacecraft and their targets?

Special relativity is a theory in physics that explains how objects move and interact in space and time. It states that the laws of physics are the same for all observers in uniform motion and that the speed of light is constant in all inertial frames of reference. This theory has significant implications for spacecraft and their targets, as it affects how time and distance are perceived and measured in different reference frames.

## 2. How does special relativity impact the concept of simultaneity in space?

Special relativity states that the concept of simultaneity is relative and depends on the observer's frame of reference. This means that events that appear to occur simultaneously for one observer may not be simultaneous for another observer in a different reference frame. This is because the relative motion of the observers affects the perception of time and distance between events.

## 3. Can special relativity explain the phenomenon of time dilation in space travel?

Yes, special relativity predicts that time will pass slower for objects that are moving at high speeds relative to an observer. This is known as time dilation and has been observed in experiments and in the behavior of high-speed particles. This phenomenon has significant implications for space travel, as astronauts on a spacecraft traveling at high speeds will experience time passing slower compared to those on Earth.

## 4. How does the speed of light play a role in special relativity and spacecraft travel?

The speed of light is a fundamental constant in special relativity and plays a crucial role in understanding the behavior of objects in motion. It is the fastest speed at which any object can travel, and according to special relativity, it is the same for all observers in any inertial frame of reference. This means that no object can travel faster than the speed of light, and as an object approaches the speed of light, its mass and energy increase.

## 5. Is there any evidence to support the principles of special relativity in space?

Yes, there is a considerable amount of evidence that supports the principles of special relativity in space. This includes experiments such as the Michelson-Morley experiment, which demonstrated the constancy of the speed of light, and observations of time dilation in high-speed particles. Additionally, the GPS system, which relies on special relativity to make accurate calculations, is another example of the theory's successful application in space technology.

Replies
4
Views
1K
Replies
2
Views
1K
Replies
10
Views
1K
Replies
6
Views
3K
Replies
2
Views
1K
Replies
3
Views
1K
Replies
11
Views
2K
Replies
10
Views
2K
Replies
3
Views
965
Replies
3
Views
1K