# Shooting a spaceship with a photon

• E92M3
In summary, the observer must send the photon in the +y-direction when the spaceship is at x=-vy0/c. In the spaceship's frame, the angle between the spaceship's nose and the photon's velocity is undefined as the spaceship has no velocity in its own rest frame. However, in any other frame, the angle can be calculated using relativistic velocity addition.
E92M3

## Homework Statement

Relative to the rest frame, the trajectory of a spaceship is:
$$x=vt$$
$$y=y_0$$

An observer at:
$$(x,y)=(0,0)$$
wants to send a photon to hit the spaceship at:
$$(x,y)=(0,y_0)$$

a) When and in what direction must the observer send the photon?
b) In the frame of the spaceship, what is the angle between the spaceship and the photon's velocity?

## Homework Equations

Basic velocity to distance relations. Possibly Lorentz transformation?

## The Attempt at a Solution

\
a) Well, the observer is trying to send a photon from (x,y)=(0,0) to (x,y)=(0,y0); therefore he muse send it in the +y-direction. The time it takes the photon to reach (x,y)=(0,y0) is:
$$t=\frac{y_o}{c}$$
Since the spaceship is moving in the +x-direction at speed v, the observer must send the photon when the spaceship is at:
$$x=vt=\frac{-vy_o}{c}$$

b)This part is hard and I have made a few arguments that lead to different paths:
1. The speed of the spaceship in the spaceship's frame is zero, then how could there be an angle?
2. When the photon strikes the spaceship, the photon only has a y velocity while the spacecraft has only a x velocity. Therefore, the angle is 90 degrees.
Which one of my argument is valid?

I don't think I'm understanding the question. So the spaceship starts at x=0, y=y0, and you want to send a photon there from (0,0)? In order for it to arrive at y=y0 when the spaceship still hasn't moved, the photon will have to travel at infinite speed.

ideasrule said:
I don't think I'm understanding the question. So the spaceship starts at x=0, y=y0, and you want to send a photon there from (0,0)? In order for it to arrive at y=y0 when the spaceship still hasn't moved, the photon will have to travel at infinite speed.
My understanding is that the spaceship can be considered to have been moving at constant speed for all time, and we choose a coordinate system so that the point t=0,x=0,y=y0 is on the spaceship's world line. The photon would have to be emitted at some negative time, as E92M3 found.

E92M3, for part b, first look at argument 2: that holds in "the rest frame," but not in the spaceship's frame. Remember that just because an object has $v_x = 0$ in one frame, does not mean that it has $v_x = 0$ in all frames. So argument 2 is not valid.

In argument 1, you are correct that the spaceship has no velocity in its own rest frame, so you're right that there cannot be an angle between the spaceship's velocity and the photon's velocity in the spaceship's rest frame. However, the problem asks for the angle between the spaceship and the photon's velocity... this is not particularly clear wording, I'll admit, but think about it this way: let's say that the nose of the spaceship is aligned along its velocity in "the rest frame." The spaceship's nose then defines a direction in any frame, whether the spaceship is moving in that frame or not. The problem wants you to find the angle between the spaceship's nose and the photon's velocity, in the spaceship's rest frame.

ideasrule said:
I don't think I'm understanding the question. So the spaceship starts at x=0, y=y0, and you want to send a photon there from (0,0)? In order for it to arrive at y=y0 when the spaceship still hasn't moved, the photon will have to travel at infinite speed.

That was not specified in the question.

So should I try relativistic velocity addition?

Last edited:

## What is a photon?

A photon is a fundamental particle that carries electromagnetic energy and has zero mass. It is the basic unit of light and all other forms of electromagnetic radiation.

## How do photons interact with matter?

Photons interact with matter through a process called absorption, where they transfer their energy to the atoms or molecules they encounter. This can cause the atoms to become excited and emit light, or it can be converted into other forms of energy such as heat.

## Why would someone want to shoot a spaceship with a photon?

Shooting a spaceship with a photon can be used as a means of propulsion. By firing a concentrated beam of photons at the back of a spaceship, the photons will transfer their momentum to the ship, propelling it forward. This is known as photon thrust.

## What challenges are involved in shooting a spaceship with a photon?

One of the main challenges is creating a high-powered photon beam that can effectively transfer its momentum to the spaceship. Additionally, the spaceship must be designed to withstand the intense heat and pressure from the photon beam. Precise aiming and targeting is also crucial for successful propulsion.

## Are there any real-world examples of shooting a spaceship with a photon?

Yes, there have been several proposals and experiments involving photon propulsion for spacecraft. For example, NASA's Solar Sail project uses photons from the sun to propel the spacecraft forward. The Breakthrough Starshot initiative also plans to use a powerful laser to shoot a tiny spaceship to a nearby star system.

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