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Paracelsus19 t1_j5hu5ak wrote

Basically, by careful observation and then doing math calculations. You measure the object's angular size as you see it in the sky and then you work out its distance based on its orbit. When you combine these two measurements, you should then be able to find the real size of an object. I hope I am explaining both correctly and clearly. There are some links below to help beak down the answer and go into further detail.

https://www.astronomynotes.com/solarsys/s2.htm

https://lonewolfonline.net/angular-size/#:~:text=Angular%20size%20refers%20to%20the,size%20of%20approximately%2030%20arcminutes.&text=The%20angular%20size%20of%20an,its%20distance%20from%20the%20observer.

https://youtu.be/Cn8Yuf0Pnsw

https://youtu.be/XF9stDi8XkM

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mfb- t1_j5ild6m wrote

There are only a handful of stars where we can measure the angular size directly. It's far more common to measure the distance, the temperature (-> surface brightness) and apparent brightness of stars. Combined they tell us the radius of the object. That knowledge then be applied to stars too far away to measure the distance directly.

For exoplanets the brightness in images can still be useful, but the most accurate radius measurements come from transits: We measure which fraction of the starlight is blocked, so we can use the radius of the star to measure the radius of the planet.

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