State what is meant by the event horizon of a black hole.
In a recent study, astronomers utilized an international network of radio telescopes, named EHA (Event Horizon Array), and an orbiting optical telescope, named Gaia-X, to study stellar activities near a supermassive black hole at the center of the distant galaxy M104-Z.
Table 2 shows data for both telescopes.
Table 2
| Aperture | Operating wavelength | |
|---|---|---|
| EHA | 8.5×106 m8.5 \times 10^6 \text{ m}8.5×106 m | 0.85 mm0.85 \text{ mm}0.85 mm |
| Gaia-X | 4.2 m4.2 \text{ m}4.2 m | 450 nm450 \text{ nm}450 nm |
The supermassive black hole is located 5.5×107 light years5.5 \times 10^7 \text{ light years}5.5×107 light years from Earth and has a mass of 6.4×1096.4 \times 10^96.4×109 times the mass of the Sun.
The radius of the event horizon of this black hole is RRR.
Astronomers propose to use either the EHA or the Gaia-X telescope to resolve stellar orbits within a region whose distance from the centre of the black hole is less than 300R300R300R.
Discuss, with calculations, which telescope is more suitable for this observation.
A star is orbiting this supermassive black hole. The star is observed in the plane of its orbit. The wavelength of a spectral line observed in the light emitted from the star varies between a maximum and a minimum value:
Calculate the orbital speed of the star.
