Far, far away, a Red Supergiant (wavelength of 685 nm) star suddenly explodes (known as a

supernova). If the supernova was observed on Earth, 5.83x108 lightyears away, how long ago

did the explosion occur? Determine the frequency of the light emitted from the Red Supergiant

before the explosion. Find the observed frequency if the Red Supergiant and the Earth were

moving apart at a speed of 8,850,000 m/s.

Note: 1 year = 365.25 days

c = 3.00 x 108 m/s

1) the explosion occurs years ago

2)

Explanation:

1)

The light coming from the exploding supernova travels at constant speed, which is the speed of light:

And since it travels with uniform motion, the distance it covers in a time t is given by:

where t is the time taken.

Here, we know that the distance of the supernova from the Earth is

where 1 light-year is the distance covered by light in 1 year. This means that in 1 year, light covers a distance of 1 light-year; in 5 year, light covers a distance of 5 light-years; and so on.

Therefore here, since the distance is

This means that the time taken by light is

years

And therefore, the explosion occurs years ago.

2)

First of all, the real frequency of the light emitted by the supernova is given by

where

c is the speed of light

is the proper wavelength

Substituting,

The frequency observed on Earth is shifted (Doppler effect) due to the relative motion between the supernova and the Earth; the apparent frequency observed on Earth is given by

where

c is the speed of light

is the speed at which the supernova is moving apart

Substituting the values, we find the apparent frequency:

the answer would be c