a) During the 18 years that the galactic centre has been observed, the star SO-2
ID: 304938 • Letter: A
Question
a) During the 18 years that the galactic centre has been observed, the star SO-2 completed a full orbi having a period of 16.17 years. Convert this period into seconds (1 yT 3.16x10' seconds) (seconds) b) Finding the semi-major axis, a. The angular size of the orbit of the star SO-2 is 0.165 Convert the angular size of the orbit in arcsecinto radians: 0.165 arcsec 206,265 arcsec/rad The distance to the centre of the galaxy is given as 7 940 pc Convert this distance into meters: · 7940 pc × (3.09×10162) = .Find the major axis of the orbit using the formula: (1 mark) major-axis (m) = (angular size (rad))xdi stance(m) .Find the size of the semi-major axis by dividing major- axis +2 From Newton's Universal Gravitation Law, the mass of the supermassive black hole at the centre of our galaxy can be calculated with the formula: 4n2 a G T2 where G = 6.67x10-11 ? kg-s (kg) The mass of the Sun is approximately Me = 1.99×1030 kg. Express the mass of the balck-hole in solar masses. (Hint: calculate the ratio of the two masses) c) Compare the size of the semi-major axis a, of the SO-2 star to the size of the Solar System using the distance to the outer edge of the Kuiper Belt of about 55 AU. (1 AU-1.496x1011 m) d) e) Anumber of recent publications give the mass of the central object of the Milky Way Galaxy as approximately 4 million times the mass of the Sun. How do your results compare?lExplanation / Answer
a. Given 1 yr = 3.16 * 10 7 sec
thus 16.17 yr = 16.17 * 3.16 * 107 = 51.09 * 10 7 sec
b. 1. The angular size of orbit of the star = 0.165 arcsec
converting angular size of the orbit in arcseconds in radian
we know that 1 radian = 206265 arc second
Thus angular size of the orbit in radian = 0.165/206265 = 7.9994 * 10-7 radian
2. to convert distance in meters.
we know that 1 pc = 3.09 * 1016 metres
Thus 7940 pc = 7940 * 3.09*1016 = 2.453 * 1020 metres
3. major axis = angular size * distance = 7.9994 * 10-7 * 2.453 * 1020 = 1.9622 * 1014 m
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.