State what is meant by a gravitational force.

1. (a)State what is meant by a gravitational force.[1]
2. (b)A binary star system consists of two stars S₁ and S2, each in a circular orbit. The orbit of each star in the system has a period of rotation T. Observations of the binary star from Earth are represented in [Figure 1.1]. Observed from Earth, the angular separation of the centres of S₁ and S₂ is 1.2 × 10⁻⁵ rad. The distance of the binary star system from Earth is 1.5 x 10¹⁷ m. Show that the separation d of the centres of S₁ and S₂ is 1.8 × 10¹² m.[1]
3. (c)(i)The stars S₁ and S2 rotate with the same angular velocity ω about a point P, as illustrated in [Figure 1.2]. Point P is at a distance x from the centre of star S₁. The period of rotation of the stars is 44.2 years. Calculate the angular velocity ω.[2]
4. (c)(ii)By considering the forces acting on the two stars, show that the ratio of the masses of the stars is given by mass of S₁ / mass of S₂ = (d− x) / x[2]
5. (c)(iii)The mass M₁ of star S₁ is given by the expression GM₁ = d²(d – x)ω² where G is the gravitational constant. The ratio in (ii) is found to be 1.5. Use data from (b) and your answer in (c)(i) to determine the mass M₁.[3]

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