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two starts in a binary system orbit around their center of mass. the centers if the two starts are 7.45*10^11m apart. the larger star has a mass of 3.84*10^30 and its center is 1.81*10^11m from the system's center of mass. what is the mass of the smaller star?

User AKIWEB
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1 Answer

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The mass of the smaller star is determined as 1.23 x 10³⁰ kg.

How to calculate the mass of the smaller star?

The mass of the smaller star is calculated by applying the concept of center mass as shown below.

m₁r₁ = m₂r₂

where;

  • m₁ is the mass of the larger star
  • m₂ is the mass of the smaller star
  • r₁ is the radius of the larger star
  • r₂ is the radius of the smaller star

m₁r₁ = m₂(D - r₁)

where;

  • D is the distance between the two center masses

m₁r₁ = m₂(D - r₁)

(3.84 x 10³⁰) x (1.81 x 10¹¹) = m₂(7.45 x 10¹¹ - 1.81 x 10¹¹)

6.95 x 10⁴¹ = m₂(5.64 x 10¹¹)

m₂ = (6.95 x 10⁴¹ ) / ( 5.64 x 10¹¹ )

m₂ = 1.23 x 10³⁰ kg

User Nabn
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