Question

Suppose you observe a star orbiting the galactic center at a speed of 1300 km/skm/s in a circular orbit with a radius of 18 light-days. Calculate the mass of the object that the star is orbiting.

Answer 1

Answer: 1.1818^37 kg

Step-by-step explanation:

Given that:

Orbit speed = 1300 km/s

Radius (r) = 18 light days

Mass of object the star is orbiting :

Using the relation :

M = rv² / G

Where ; r = Radius in m ; v = velocity in m/s

G = 6.67 * 10^-11 = gravitational constant

18 light days in meters = 4.662 * 10^14 m

v = 1300km/s to m/s

v = (1300 * 1000)m /s = 1300000 m/s = 1.3 * 10^6 m/s

Hence ;

M = (4.662 * 10^14 * (1.3 * 10^6)^2 / (2/3) * 10^-10

M = (4.662 * 10^14) * (1.69 * 10^12) / (2/3) *10^-10

M = (7.87878 * 10^26) / 6.67 * 10^-11

= 1.1818^37 kg