# In the center of the Galaxy there is a supermassive black hole with a radius of about 10 million kilometers. Is it possible to study

In the center of the Galaxy there is a supermassive black hole with a radius of about 10 million kilometers. Is it possible to study the structure of its surroundings using a radio interferometer with the Radioastron space telescope? With one optical telescope with a lens diameter of 1 m?

the project allowed to obtain a resolution of 7 microseconds of an arc = 0.000007 ″.
Now, using the empirical criterion of Rayleigh resolution (see here), we determine the resolution of the optical telescope
θ = 1.22 * λ / D = 1.22 * 0.5μm / 10 ^ 6μm = 0.00000061 rad = 0.13 ″
The resolution of interest to us is equal to the angular size of the black hole:
10 million km / (25 thousand light years) = 10 ^ 7 km / (25000 km * 300000 * 86400 * 365) = 4.2 * 10 ^ -11 = 0.000009 ″
As you can see, “Radioastron” is quite capable of exploring the vicinity of this black hole with a resolution of the order of its size, while an optical telescope with a 1-meter lens falls short of 0.13 / 0.000009 = 14 thousand times in resolution.

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