Plaskett's binary system consists of two stars that revolve In a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is |v | = 240 km/s and the orbital period of each is 12.5 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 times 1030 kg Your answer cannot be understood or graded. More Information solar masses

The simplest types of orbits in celestial mechanics are circular orbits, in which an orbiting body moves around a gravitational mass while maintaining a constant radius.

Calculation:

We learn from the question that the stars'

masses are m1 = m2 = M.

Each star orbits at a speed of Vs = 240 km/s or 240000 m/s.

T = 12.5 days, often known as 12.5246060, or 1080000sec, is the orbital period.

The mathematical formula for the centripetal force exerted on these stars is

Fc = Mv²/r

The mathematical formula for the gravitational force exerted on these stars is

Fg = GM²/d²

so Fc = Fg

Mv²/r = Gm₁ₓm₂/d²

v²/r = GM/(2r)²

v²/r = GM/4r²

M = v² × 4r /G

Each sun travels a certain distance during one cycle, which is mathematically expressed as

D = V × T

D = 240000 × 1080000

D = 2.592×10¹¹ m

Now this can also be represented as

D = 2πr

Therefore

2πr = 2.592×10¹¹ m

r = 2.592×10¹¹ / 2π

r = 4.124 × 10¹⁰ m

So,

M = v² × 4r/ G

M = (240000)² × 4 × 4.124 × 10¹⁰/ 6.67 × 10 ⁻¹¹

M = 1.43 × 10³²kg.

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