# How Far Are Stars? Calculating Distance to Earth

• ElectroBurger
In summary, there are various techniques used to calculate the distance between Earth and a star. The most accurate method is stellar parallax, which involves measuring the angle between a star and a background mark at different times of the year to account for Earth's movement around the sun. This method is effective for stars within 20 light years of Earth. For more distant stars, other methods such as comparing the brightness of stars or using redshift can be used. Astronomers also use units such as parsec, which is equal to 3.262 light years, to measure these distances. However, these methods are not as accurate for larger distances due to the expansion of the universe.
ElectroBurger
How do people calculate the distnce between Earth and a star?

Hold out your finger at arms length
Now close one eye
Open it and close the other eye instead
You can see the finger appear to move against what's behind it.
If you measure the angle between the finger and some background mark and know the distance between your eyes you can work out the distance to your finger

In the case of stars you make measurements 6 months apart and use the Earth's movement around the sun for the baseline. This let's you measure the nearest stars very accurately. It's called stellar parallax.

Then for more distant stars we use the fact that 2 stars with the same real (absolute) brightness will appear different (apparent) brightnesses if they are at different distances. We use this to find the distances to more distant stars by comparing their brightness to the ones we measured close to us.

Hi Mgb-phys, can we use redshift index to estimate the distance of far away galaxies?

There are a whole series of techniques as you get further away.
So beyond the techniques above for stars you can use Cepheid variables to give you the distance to nearby galaxies, then type I supernova, and then finally cosmological redshift for the most distant objects.

Expanding on what mgb_phys said, the method of stellar parallax currently works out to a distance of approximately 1,500ly. This, however, will be expanded within several years to around 10,000ly. Stellar parallax is really the only "direct" method that we have of measuring distances to star in so far as it relies solely on the assumptions of geometry. Everything else is based on inference.

As mgb_phys said anything else relies on the principle that there are objects in our universe which are esentially the same (put out the same amount of light), so by measuring how much we receive, we can compute the distance to the object.

Thank you all for the help,

I've never thought of using parallax to find distant stars. I suppose that it's quite easy to calculate distance once we know the way we travel through space.

But wouldn't these distances between us and the stars change since the universe is expanding?

Making several measurements to the same star over time would tell us the rate of accelerated expansion of the universe, correct?

ElectroBurger said:
But wouldn't these distances between us and the stars change since the universe is expanding?
No the galaxy (and the local cluster of galaxies) is held together by gravity.
The distance to nearby stars does change slightly as the galaxy rotates, each star is moving in a slightly different orbit and affected by the motion of other nearby stars.

Making several measurements to the same star over time would tell us the rate of accelerated expansion of the universe, correct?
Not on the timescales we live for!
You can measure the expansion rate from measuring the speed and distance to very distant objects. It's possible to measure the speed directly from the redshift of the spectral lines.

Nearby stars can be distanced based on parallax - the measured difference between their position relative to distant stars and the position of Earth at six month intervals. This kind of measurement is accurate for any star within about 20 light years of earth. Indirect methods must be used at greater distances.

Chronos said:
This kind of measurement is accurate for any star within about 20 light years of earth.
The Hipparchos mission pushed that out to around 200pc ( 650ly) for high accuracy results and further for the 10-20% accuracy measurements.

you used the measurment of a parsec, exactly how is that defined? I know that a light year is not an SI unit, and the au is, but is the pc?

ElectroBurger said:
you used the measurment of a parsec, exactly how is that defined? I know that a light year is not an SI unit, and the au is, but is the pc?

Parsec is short for "parallax second" it is the distance at which the stellar parallax would be 1 arc-second (an arc second is 1/3600 of a degree). It is equal to 3.262 light years.

Astronomers don't like writing down long number so make up their own units.

If the base of the triangle is one au (the Earth sun distance) and the angle of the star is one arc-sec (about the smallest angle you can see through a blurry atmosphere) then the distance is one parsec. The nearest star is around 1.2parsec

## 1. How do scientists calculate the distance to stars?

Scientists use a method called parallax to calculate the distance to stars. This involves measuring the apparent shift in the position of a star when viewed from two different locations on Earth, and using trigonometry to determine the distance based on the angle of the shift.

## 2. How accurate are the distance measurements to stars?

The accuracy of distance measurements to stars depends on several factors, such as the precision of the instruments used and the distance of the star. Generally, distances to nearby stars can be measured with high accuracy, while distances to more distant stars may have a larger margin of error.

## 3. What units are used to measure the distance to stars?

The distance to stars is typically measured in light years (ly) or parsecs (pc). A light year is the distance that light travels in one year, which is equivalent to about 9.46 trillion kilometers. A parsec is a unit of measurement based on parallax and is equivalent to about 3.26 light years.

## 4. How do scientists determine the distance to stars that are too far for parallax measurements?

For stars that are too far for parallax measurements, scientists use other methods such as spectroscopic parallax, which involves analyzing the light spectrum of a star to determine its luminosity and then calculating its distance based on its apparent brightness. Other methods include using standard candles, such as supernovae, which have a known brightness and can be used to calculate distances to other stars.

## 5. Can the distance to stars change over time?

Yes, the distance to stars can change over time due to their relative movement in the universe. Stars may move closer or farther away from Earth, which can affect their measured distance. Additionally, as our technology and methods for measuring distance improve, the estimated distances to stars may also change.

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