# How Far Is the Crab Nebula from Earth?

• Daniel Luo
In summary, the Crab Nebula is the result of a supernova that was observed by Chinese astronomers in 1054. It can be seen with a small telescope and all parts are moving away from the center at a speed of 1.18*10^6 m/s. The angle that the Crab Nebula forms with the Earth is 0.083 degrees. Using trigonometry and the supernova's expansion rate, one can calculate the distance from Earth to the Crab Nebula, which is approximately 9.1*10^18 m or 960 light years. This method is commonly used in astronomy where angular measurements are more prevalent.
Daniel Luo

## Homework Statement

Hi.

The Crab Nebula which can be seen with even a small telescope, is the result of a supernova. All parts of the nebula are moving away from the centre at 1.18*10^6 m/s. The angle that the Crab Nebula forms with the Earth is 0.083 degrees. This supernova was observed by chinese astronomers in 1054. You can assume that the Crab Nebula has expanded at a uniform rate since then.

- What is the distance from Earth to Crab Nebula?

## Homework Equations

Distance = Speed of light * Time elapsed.

## The Attempt at a Solution

I said that there was 2014-1054=960 years since we first observed it. Hence 960 lightyears which is equal to 9.1*10^18 m. However, this is wrong according to the answers (and wikipedia while we're at it). Btw, what do I need the expansion speed for? It's so small compared to c. And what about the angle? Any help is appreciated. Thank you.

Use a bit of trig to figure this out. It always helps to draw a diagram if the problem lends itself to it. Fill the known quantities in on the diagram. Upload it if you are still having problems.

I did that already... And I get the same answer... What am I doing wrong?

Draw the triangle that the Crab Nebula makes with the earth. Fill in the angle and known distance and upload the image if you can.

I don't think it will be much help to you. It's reversed.

Please can't you just tell me what I'm doing wrong?

#### Attachments

• Photo on 15-10-13 at 15.26.jpg
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You can get the diameter, D, of the CN since it has expanding for 960 years using its expansion rate. Together with the angle that D extends at the Earth you can then calculate R, the distance to the CN. Hint: Work in radians.

I simply do not understand what you just wrote. The diameter is 2 * 1.18*10^6 m/s * 960 years * 31557600 years/s = 7.15 * 10^16 m. What do I do from here?

For an angular measurement, θ, in radians, we have that

θ = s/r

where s is the arc length, D in this case, and r is the radius of the circle, the distance to the CN in this case.

How can the radius be the distance from CN to Earth? Isn't the radius simply the radius of crab nebula? And how is the arc length how much CN has expanded the last 960 years?

The given angle is the angle that the diameter of the nebula subtends at the earth, as you indicated on your diagram. So if we work in radians then the r in the formula above is the distance to the nebula and the arc length, s in the formula, is the diameter of the nebula.

Couldn't you also say that the radius is the opposite side in the right angled triangle. The adjacent side is the distance from CN to Earth, and the 0.083/2=0.0415 degrees is the angle. Since tan(0.0415) = radius/distance we have that the distance is radius/tan(0.0415). This gives the right answer.

The methods are equivalent. The angular approach is more common in astronomy where almost everything is measured in angular terms.

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1 person

## 1. How far away is the Crab Nebula from Earth?

The Crab Nebula is approximately 6,500 light years away from Earth. This means that it would take light 6,500 years to travel from the Nebula to Earth.

## 2. How was the distance to the Crab Nebula determined?

The distance to the Crab Nebula was first estimated in 1921 by astronomer Edwin Hubble using the period-luminosity relation of Cepheid variable stars. This method has since been refined and confirmed by other observational techniques, including parallax measurements and spectroscopic redshifts.

## 3. What is the size of the Crab Nebula?

The Crab Nebula has a diameter of approximately 11 light years. This makes it one of the largest and most well-known supernova remnants in our galaxy.

## 4. Can the Crab Nebula be seen with the naked eye?

Yes, the Crab Nebula is visible to the naked eye as a faint, fuzzy patch in the constellation Taurus. However, it is best viewed with a telescope or binoculars.

## 5. How long will it take for the Crab Nebula to reach Earth?

Due to its distance from Earth and the expansion of the universe, it is unlikely that the Crab Nebula will ever reach Earth. However, its light will continue to reach us for thousands of years to come.

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