Supernova Explosion: 720 Light-Years Away from Earth

[kvan]

Homework Statement

A space craft, traveling at 0.77c, is just passing the Earth when the light from a Supernova which is traveling in exactly the opposite direction to the ship, reaches it. According to an observer on the Earth the star which caused the explosion was 720 light years away (1 light year = distance traveled by light in one year). According to an observer on the spaceship how long ago did the star explode?

Homework Equations

I tried using:

$$\Delta tsingle-quote=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$$

The Attempt at a Solution

As there is a distance of 720 light years between the supernova and the Earth, it takes light 720 years for light to reach Earth, so I used that value for t. I then used the value of 0.77c for velocity and left c as is. With these numbers I get the equation

$$\Delta tsingle-quote=\frac{720 years}{\sqrt{1-\frac{0.77c^2}{c^2}}}$$

I tried putting in the Latex equation for it but still not really that great at it sorry. But I'm trying to use the lorentz transformation for time dilation of

Delta t' = delta t/ sqrt(1 - v^2/c^2)
But the answer is incorrect, any hints or ideas?

 

[vela]

Fixed your LaTeX.

Homework Statement

A space craft, traveling at 0.77c, is just passing the Earth when the light from a Supernova which is traveling in exactly the opposite direction to the ship, reaches it. According to an observer on the Earth the star which caused the explosion was 720 light years away (1 light year = distance traveled by light in one year). According to an observer on the spaceship how long ago did the star explode?

Homework Equations

I tried using:

$$\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$$

The Attempt at a Solution

As there is a distance of 720 light years between the supernova and the Earth, it takes light 720 years for light to reach Earth, so I used that value for t. I then used the value of 0.77c for velocity and left c as is. With these numbers I get the equation

$$\Delta t'=\frac{720 years}{\sqrt{1-\frac{0.77c^2}{c^2}}}$$

I tried putting in the Latex equation for it but still not really that great at it sorry. But I'm trying to use the lorentz transformation for time dilation of

Delta t' = delta t/ sqrt(1 - v^2/c^2)
But the answer is incorrect, any hints or ideas?

 

[vela]

You need to use the Lorentz transformations because the events are separated by both time and space in both frames.

Find the spacetime coordinates of the explosion in the Earth's frame, and then transform them to coordinates in the spaceship's frame.