2 (a) The Event Horizon Telescope (EHT) project utilizes several radio telescopes so as to have a large effective area. Assume that the effective diameter of EHT is about 104 km and that its operating wavelength is ~ 1.3 millimetre. (i) Estimate the angular resolution of EHT in units of arc-second. (ii) The supermassive black hole (SMBH) lying at the centre of the An- dromeda galaxy, which is at a distance ~ 2.5 106 light-years from Earth, weighs about 2 108 M. Verify through calculations whether the EHT would be able to resolve the region at a distance 2 5 Rs from the centre of the SMBH. Here Rs is the Schwarzschild radius of a black hole. (iii) A star is going around this SMBH in a circular orbit of radius 107 cm. Estimate the speed of the star. (iv) In a supernova explosion that occurs at a distance 7 x 1016 cm from the SMBH, the resulting neutron star that is formed is ejected with a speed 75 km/s relative to the SMBH. Will the neutron star be able to escape from the gravity of the SMBH? (b) A hymn in a Vedic text prescribes that a vedic ritual of carrying out Yajna by lighting up the sacred fire be conducted when Kritika Nakshatra (i.e. Pleiades constellation) rises on the horizon during the Vernal Equinox (i.e. Spring Equinox). Explain qualitatively how one may infer that this Vedic hymn was composed around 2334 years BCE. 3 (a) Using Virial Theorem, obtain a relation between average temper- ature, mass and radius of a self-gravitating gas cloud. Show that when such a gas cloud loses energy to the environment, its average temperature increases. What happens if energy from outside is added to such a self-gravitating gas cloud and why? (b) Giving reasons, explain why during the Spring Equinox as well as