Answer:
mass of star = 5035.52 x 10^28 kg
Step-by-step explanation:
We would apply Kepler's third law. The equation is expressed as
T^2 = 4π^2r^3/Gm
By cross multiplying,
mT^2 = 4π^2r^3/G
Dividing both sides by T^2, it becomes
m = 4π^2r^3/GT^2
where
T is the time or period of the planet's motion
r is the radius of the orbiting planet
G is the universal gravitational constant
m is the mass of the star
From the information given,
T = 680 days
We would convert it to seconds. Recall,
1 day = 86400 seconds
680 days = 680 x 86400 = 58752000 seconds
G = 6.67259 × 10^-11 N · m2/kg2
r = 6.65 × 1011 m
π = 3.14
By substituting these values into the formula, we have
m = 4 x 3.14^2 x (6.65 × 10^11)^3/6.67259 × 10−11 x 58752000^2
m = 5035.52 x 10^28 kg
mass of star = 5035.52 x 10^28 kg