Calculating distance using redshift

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In summary, the conversation is about a formula for calculating distance using redshift, the speed of light, and Hubble's constant. The speaker is confused about the units used for Hubble's constant and wonders if their calculation is correct. They eventually find an online calculator that helps them get the correct results.
  • #1
Goldilocks32
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Hi. I have pretty rudimentary math skills, and am hoping someone can explain this formula for me, found online a number of places including:

http://www.astrophysicsspectator.com/topics/overview/DistanceExtragalactic.html

for calculating distance (d) in megaparsecs using redshift (z), the speed of light (c), and Hubble's constant (H).

d = c z/H

It's the (units in) Hubble's constant that have me confused. In the example from the link, "we see that objects with a redshift of 0.1 are about 4.6 gigaparsecs [a]way", assuming an H of 65 km s-1 Mpc-1. So I assumed c here would be in km/s, but:

300000 * (0.1/65) = 461

Which is 0.46 gigaparsecs, not 4.6. What is it about the units/Hubble's constant here that I don't get?

Here's what I guessing: units ^ -1 mean 65 should be multiplied by 0.1, which is different than 65 ^ -1. This would make H 6.5, and the result would be correct. Is that right? If so, why is the notation km/s-1/Mpc-1? How would that be different from km/s/Mpc-1?
 
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  • #2
I think your calculation (as it was) is correct. Your guess about the units is definitely not right---the units are separate from the number attached to them.
Maybe their result is just a typo...
 
  • #3
Yeah, you're right. The next thing I tried this on was the Large Magellanic Cloud, which produced even more bizarre results, but I found a calculator for this online:

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/hubble.html#c3

And eventually got some data to match up (it seems the LMC's redshift is an anomaly, so my first test case was a typo and my second anomalous -_-).
 
Last edited:
  • #4
Haha, just some bad luck I guess!
Way to be thorough---good job
 
  • #5


Hello,

Thank you for your question. Calculating distance using redshift can be a bit confusing, but I will try my best to explain it to you.

First, let's start with the formula: d = c z/H. This formula is derived from the Hubble's law, which states that the recession velocity (z) of a galaxy is proportional to its distance (d) from us. In other words, the farther a galaxy is from us, the faster it appears to be moving away from us.

Now, to understand the units in the Hubble's constant (H), we need to break it down. The Hubble's constant (H) is a measure of the rate at which the universe is expanding. Its units are kilometers per second per megaparsec (km/s/Mpc). This means that for every megaparsec (Mpc) of distance, the speed of recession increases by 65 kilometers per second (km/s). So, in your example, a galaxy with a redshift of 0.1 would be moving away from us at a speed of 6.5 km/s for every megaparsec of distance.

Now, let's take a look at the units in the formula: d = c z/H. The speed of light (c) has units of kilometers per second (km/s), and the redshift (z) is a dimensionless quantity. So, when we divide the speed of light (c) by the Hubble's constant (H), we are essentially canceling out the units of kilometers per second (km/s). This leaves us with just units of distance (megaparsecs) for the final answer.

To address your confusion about the notation of km/s-1/Mpc-1, it is important to note that the negative exponent (-1) indicates division. So, km/s-1/Mpc-1 can be read as km/s divided by Mpc, which is the same as km/s/Mpc-1.

In summary, the formula for calculating distance using redshift can be simplified as follows: d = (c/z) * (1/H). The units of Hubble's constant (H) are km/s/Mpc, and the negative exponent in the notation indicates division. I hope this helps to clarify any confusion you had. Please let me know if you have any further questions.
 

1. How is redshift used to calculate distance in astronomy?

Redshift is a phenomenon in which light from distant objects in the universe appears to shift towards the red end of the electromagnetic spectrum. This is caused by the expansion of the universe and can be measured by comparing the wavelength of light emitted by a distant object to the wavelength of that same light observed on Earth. By using a formula known as Hubble's Law, which relates the redshift to the distance of the object, astronomers can calculate the distance to the object.

2. What is the relationship between redshift and distance?

The relationship between redshift and distance is known as Hubble's Law. This law states that the farther away an object is, the greater the redshift will be. This is because the universe is constantly expanding, causing objects to move away from each other at increasing speeds. As an object moves away, the light it emits is stretched to longer wavelengths, resulting in a higher redshift.

3. Can redshift be used to measure the exact distance to an object?

No, redshift can only give us an approximation of the distance to an object. This is because there are other factors that can affect the redshift of an object, such as its peculiar velocity or the gravitational pull of nearby objects. However, for objects that are far enough away, these effects are negligible and redshift can provide a fairly accurate estimate of the distance.

4. How does the redshift measured from different parts of an object differ?

The redshift measured from different parts of an object can differ due to the Doppler effect. This is the change in wavelength of light due to the relative motion between the observer and the source of light. For example, if one side of an object is moving towards us, the light from that side will appear blueshifted, while the light from the other side will appear redshifted. This can complicate the calculation of distance using redshift and requires careful analysis by astronomers.

5. Are there any limitations to using redshift to calculate distance?

While redshift is a useful tool for estimating distances in astronomy, it does have its limitations. For one, it can only be used for objects that are very far away, as the effects of redshift become negligible at smaller scales. Additionally, it assumes that the universe is expanding at a constant rate, which may not always be the case. Furthermore, redshift does not take into account the effects of dark energy, which is thought to be responsible for the accelerated expansion of the universe. Therefore, redshift can provide a rough estimate of distance, but it should be used in conjunction with other methods for more accurate measurements.

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