### How big is one arcsecond at various distances?

• I've been reading this article
https://en.wikipedia.org/wiki/Celestial_coordinate_system
and a question came to my mind.

The minimum units are seconds ( ″ ). I picture an angle of 1 second as being like a "cone" going out from Earth. It's really small at the beginning but as you go further its width increases.

How wide does this cone get as you get further into the universe? How big is an arcsecond on different astronomical bodies?

The coordinate system is as precise as you want to make it. It's like any other coordinate system: add more decimal places and you have a more precise location.

What @Asher says is not exactly true. The precision of your coordinate system is limited by how precisely you can define its zero-point. However the positions of things in this coordinate system can have finite precision, which is determined by your telescope/measurment method.

so it depends on the telescope you are using? how can that be the rule?

Edited to reflect the comment below my answer.

• James K Correct answer

5 years ago

How big is one arcsecond at various distances?

An arcsecond is a small angle, 1/3600 of a degree or about 5 millionths of a radian ($4.85\times10^{-6}$). To estimate the size of something that appears 1 arcsecond across you can use the small angle approximation to trigonometry: Multiply the distance to the object by $4.85\times10^{-6}$

Examples:

• One arcsecond on the moon is 1.87km

• One arcsecond on the sun is 727km

• One arcsecond on Mars (when it is closest to Earth) is 237km

• One arcsecond at distance of one parsec is one astronomical unit (AU), by definition

• One arcsecond on Alpha Centauri is 200 million km

• One arcsecond on the Andromeda galaxy is 100 trillion km

The atmosphere limits how much detail you can see. Typically the smallest detail you can see is about 3 or 4 arcseconds, though professional telescopes do better by being built on the top of mountains and using various tricks, like adaptive optics.

Ys this is exactly what i was looking for thanks! Now i feel we are really short-sighted... I will edit my question to your bold

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Content dated before 7/24/2021 11:53 AM

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