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Its actually kind of tricky. Most of what astronomers can see are stars because give off light (duh). but to figure out the mass of on object cant be determined by looking through a telescope. what has to happen is astronomers will find stars that are in a 'binary star system' which means there is one star that orbits another star. However, this isnt COMPLETELY true, actually both stars will orbit around a central point, but usually it just appears that the star with the more mass remains stationary while the smaller object does all the moving. this actually happens with our sun too, it is not completely at the center of the solar system, but actually orbits around a central point. now back to these binary star systems, if astronomers can figure out the mass of one of the stars (lets say it is comparable to the mass of our sun) then they determine how much the second star in the system moves and through a series of calculations can determine the mass of the second star. they then use data they collect and apply it to other stars...perhaps stars that are not in a binary star system. im not sure about the exact formulas that they use, but this is just a general idea of how it works. if you are wondering how big something is like a nebula or galaxy, im not exactly sure on that. astronomers measure how far stars are by observing a star, and then 6 months later they observe the star again (usually taking pictures). they track how far the star has moved against stars that are much further away. this is really tricky because stars BARELY change their position against other stars. its sort of a hard concept to explain without a visual aide. in short, they see how much a star appears to move againt starts that dont appear to move. then they do calculations (using angles and what not) to determine the distance...but i think they can only do this up to a distance of about 1000 light years away. its really crazy what astronomers can figure out by using science! i would suggest taking an astronomy class if you have any interest at all...i did at it is my favorite class...sorry this was so long, but hope it helped a little with some concepts..
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