Answer:
M = 9.9 x 10⁶ Solar masses
Explanation:
Here the centripetal force is given by the gravitational force between star and the object:
[tex]Gravitational\ Force = Centripetal\ Force \\\frac{mv^2}{r} = \frac{GmM}{r^2}\\\\M = \frac{v^2r}{G}[/tex]
where,
M = Mass of Object = ?
v = orbital speed of star = 1400 km/s = 1400000 m/s
G = Universal Gravittaional Constant = 6.67 x 10⁻¹¹ N.m²/kg²
r = distance between star and object = (26 light-days)(2.59 x 10¹³ m/1 light-day) = 6.735 x 10¹⁴ m
Therefore,
[tex]M = \frac{(1400000\ m/s)^2(6.735\ x\ 10^{14}\ m)}{6.67\ x \ 10^{-11}\ N.m^2/kg^2}[/tex]
M = (1.97 x 10³⁷ kg)(1 solar mass/ 1.989 x 10³⁰ kg)
M = 9.9 x 10⁶ Solar masses
