The two stars in a binary star system have masses 2.0×1030 kg and 6.4×1030 kg .

ID: 1506006 • Letter: T

Question

The two stars in a binary star system have masses 2.0×1030 kg and 6.4×1030 kg . They are separated by 2.1×1012 m .

Part A

What is the system's rotation period, in years?

Express your answer to two significant figures and include the appropriate units.

Part B

What is the speed of the lightest star?

Express your answer to two significant figures and include the appropriate units.

Part C

What is the speed of the heaviest star?

Express your answer to two significant figures and include the appropriate units.

here,

m1 = 2 * 10^30 kg

m2 = 6.4 * 10^30 kg

d = 2.1 * 10^12 m

centre of mass , x = ( 2 * 10^30 * 0 + 2.1 * 10^12 * 6.4 * 10^30) /( 2 * 10^30 + 6.4 * 10^30)

x = 1.6 * 10^12 m

let the angular speed be w

gravitational force = centripital force

G * m1 * m2 /( d^2) = m1 * x * w^2

6.67 * 10^-11 * 2 * 6.4 * 10^60 /( 2.1 * 10^12)^2 = 2 * 10^30 * 1.6 * 10^12 * w^2

w = 7.78 * 10^-9 rad/s

time period , T = 2 * pi /w

T = 2 * pi /( 7.78 * 10^-9)

T = 8.07 * 10^8 s

the system's rotation period is 8.07 * 10^8 s

the speed of the lightest star , v = x * w

v = 1.24 * 10^4 m/s

the speed of the heaviest star , v' = ( d - x) * w

v' = ( 2.1 * 10^12 - 1.6 * 10^12) * 7.78 * 10^-9

v' = 3.89 * 10^2 m/s

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