# How do they calculate light-years?

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For example, how do they know that the Eistein Ring is “12 billion light-years” away? Why not 10 or 20? How do they arrive at that number?

In: 2

The speed of light = c

Distance = d

Time = t

Equation: d = c * t

Light in a vacuum travels at a velocity of about 300000 kilometers per second.

So C = 300000km

There are 31556952 seconds in a year.
So T = 31556952

Now all that needs to be done is apply our formula to find out the Distance.

300000 × 31556952 = 946708560000 kilometers

2 different techniques are used.

1. Trigonometry.
The Earth’s orbit around the sun has a diameter of about 186 million miles (300 million kilometers). By looking at a star one day and then looking at it again 6 months later, an astronomer can see a difference in the viewing angle for the star. With a little trigonometry, the different angles yield a distance.

2. brightness of the star. There is no direct method currently available to measure the distance to stars farther than 400 light years from Earth, so astronomers instead use brightness measurements. It turns out that a star’s color spectrum is a good indication of its actual brightness. The relationship between color and brightness was proven using the several thousand stars close enough to earth to have their distances measured directly. Astronomers can therefore look at a distant star and determine its color spectrum. From the color, they can determine the star’s actual brightness. By knowing the actual brightness and comparing it to the apparent brightness seen from Earth (that is, by looking at how dim the star has become once its light reaches Earth), they can determine the distance to the star.

Very long astronomical distances are approximated using the “Cosmic distance ladder.”

It’s called a “ladder” because we slowly built it up rung by rung. For objects that are close enough that the movement of the earth itself can cause a perceptible change in their relative location, we can use trigonometry.

We can then learn a lot about those nearby objects (such as how bright they are), and when we see similar objects farther away, we can calculate their distance using observations of how they have relatively dimmed. This works particularly well for certain kinds of supernovae, which are known to have a particular peak brightness.

This lets us measure the distance of many more exotic things that are even farther away, which scientists have put on the distance ladder using a variety of physical properties. These include gravitational waves, light spectra, and even theories about the typical width of a galaxy.

None of these methods are airtight, and you could probably find serious scientists who disagree with a given distance measurement, especially for things outside our own galaxy.

The Earth goes around the Sun, so, at different times of year, the Earth is in a different place.

An astronomer can measure the position of an object in the sky and record the angle. If the astronomer does this when the Earth is at two different positions, the astronomer gets two slightly different angles.

You can then draw a triangle, using the imaginary line between the Earth’s positions on the two days measurements were taken as the bottom, and angles measured on the two dates to be the angles that the sides meet the bottom. Where the sides of the triangle meet is where the thing you are measuring is.

Now you have a triangle where you know the length of 1 side and all the angles inside, you can use geometry to figure out the length of the other sides of the triangle (distance to the thing from Earth).

A light year is just a distance. It’s about 5.9 trillion miles.

1) Parallax. Put your thumb in front of you and look at the screen. Close one eye and see where your thumb is compared to a point on your screen. Then do the same thing with the other eyes. You will see that your thumb move right and left as you switch eye. That’s because the angle between you eye, thumb and the screen change depending on which eye you use. You could calculate the distance to your thumb with some trigonometry by measuring the difference in angle and the distance between your two eyes. Well we can do the same thing with stars, but instead of your two eyes we use the position of the Earth on it’s orbit 6 month apart. Since we know this distance we just need to measure the difference of angle of a particular star at those two moment in time. This method only work for stats within 400 light years of Earth, because after that the difference in angle is so small that we can’t measure it with enough precision.

2) Brightness. When light propagate according to the inverse square law, which is just a fancy way to say that if the light travel twice as far, it will be 4 times less bright. So if we know the real brightness (called absolute magnitude) and we measure the brightness we see (called apparent magnitude) we can calculate the distance that light had to travel to look that way. The question is now, how do we know what is the real brightness of something. The answer is we don’t always know, but we do know for specific things and we call those standard candle. There is a lot of different Standard Candle and some are complicated, so I won’t talk about all of them.

Cepheid Variables are star that change in luminosity over some period of time (days to months) and some people really smarter than me in the early 20th century discovered that there is a link between that period and the real brightness of a star. So by identifying the right type of variable abd measuring their period, we would be able to calculate their real brightness and compared that to what we actually see to calculate the distance.

Type 1a Supernovae are created when two stars are orbiting each other. If one of them is a white dwarf and they orbit close enough to each other, the gravity of the white dwarf might start to attract the hydrogen off the other star. The mass of the white dwarf will start to go up until it reach 1.44 Solar Mass. At this exact moment, the mass of the white dwarf will reach a critical mass for fusion and create a supernovae. These supernovae all have the same energy and the same brightness. So as long as you can identify that type of supernovae, we can calculate the distance.

Like I said, there is others type of Standard Candle that exist.