Solving the Expansion of the Crab Nebula

[Fizzicist]

Homework Statement

The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. The explosion was seen on the Earth on July 4, 1054 a.d. The streamers glow with the characteristic red color of heated hydrogen gas. In a laboratory on the earth, heated hydrogen produces red light with frequency 4.568 * 10^14 Hz ; the red light received from streamers in the Crab Nebula pointed toward the Earth has frequency 4.586*10^14 Hz.

Find velocity of expansion (solved)

Assuming that the expansion speed has been constant since the supernova explosion, estimate the diameter of the Crab Nebula in 2004 a.d. Give your answer in light years.

Homework Equations

The equation for the doppler effect for light is fR = sqrt((c-v)/(c+v))fs with fR= frequency of waves heard by receiver, and fs = frequency of waves emitted by source.

The Attempt at a Solution

I don't know what the frequency of the waves emitted by the supernova is, only the frequency received. It looks like this equation has two unknowns (v and fs), so I don't know how to solve for v. Is there something I'm missing here?

Edit: I solved for the velocity. Apparently I had some numbers mixed up. Now I am having problems solving for the diameter. How do you find the diameter when you don't know how long it's been expanding?

 

[Shooting Star]

How do you find the diameter when you don't know how long it's been expanding?

The diameter you are asked to find is the diameter as seen from the Earth now. The time it exploded as seen from Earth is given.

 

[Moetasim]

Dear student,

First of all, great job on solving for the velocity of expansion! Now, let's focus on finding the diameter of the Crab Nebula in 2004 a.d. As you correctly pointed out, we do not have the exact time of when the supernova explosion occurred. However, we do know that it was seen on Earth in 1054 a.d. and we have the frequency of the red light received from the streamers in 2004 a.d. So, we can use the time difference between these two events to estimate the diameter.

We can use the equation d = vt, where d is the diameter, v is the velocity of expansion, and t is the time difference between the two events. In this case, t would be 950 years (2004 a.d. - 1054 a.d.). So, we can plug in the values we have and solve for the diameter.

Another way to approach this problem is to use the fact that the Crab Nebula is expanding at a constant speed. This means that the distance between any two points in the nebula is increasing at a constant rate. So, we can use the formula v = d/t, where v is the velocity of expansion, d is the diameter, and t is the time difference between the two events. Again, we can plug in the values we have and solve for the diameter.

I hope this helps! Keep up the good work in your scientific endeavors.