### How do astronomer measures the size of any celestial objects?

• What techniques and tools are available to the astronomers to measure the size of any celestial objects such as, stars or perhaps black holes that doesn't emit light nor reflects starlight?

• pela Correct answer

7 years ago

If a celestial body is larger than the resolving power of a telescope, its size can be measured directly. This is the case for most galaxies, molecular clouds in the Milky Way and nearby galaxies, and even for a few nearby stars. EDIT: See discussion by Rob Jeffries on how these measurements are carried out for stars using interferometry.

For more distant stars, we can rely on our understanding of stellar evolution, which tells us pretty accurately the radius, once we know its spectrum (EDIT: or just a assume blackbody radiation and use the formula given by Rob). If the star is a member of a binary system whose orbit we observe roughy edge-on, we can measure how the luminosity declines as one star occults the other, and calculate the radius. This can also be used to measure the sizes of exoplanet. And for stars, the same technique is even possible using our own Moon as occulter. See a description here.

Black holes (BH) that don't emit light, cannot be measured (at least not until we are able to detect gravitational waves), but often BHs are surrounded by a disk of accreting gas, which is heated to million of degrees by friction as it spirals down the drain. Measuring the temperature of this gas tells us the mass of the BH, which is directly proportional to its radius ($R_{\mathrm{BH}} \simeq 3 M/M_\odot$ km).

A nice technique for measuring the size of the quite small region of gas clouds around a supermassive BHs, even though they are billions of lightyears away, is called reverberation mapping. Here, some of the light emitted from the BH's accretion disk travels directly in our direction, while some of if travels in other directions, illuminating the clouds around it. When we measure the light from those clouds, the signal looks like the directly observed signal, but with a delay $t$ corresponding to extra length of the path that the light has taken. Since we know the speed of light $c$, we can calculate the extra distance as $d = ct$, i.e. the size of the system.

+1 for remembering eclipsing binary systems. Apart from interferometry this *is* the only direct technique.

I wrote "a few" stars have had their radii measured by interferometry, but actually I don't know how many, and I wasn't able to find out before lunch time. Do you know, @Rob?

Only of order 100. I only look at low-mass stars, where the number is like ~20. There are also of order 100 eclipsing binaries with well-measured radii.