Plan your route before writing. Use equations, diagrams, units, and a clear final justification where needed.
Two identical stars, each of mass m, orbit their common centre of mass in circular orbits of radius r. The stars are separated by a distance 2r. Their orbital period is T.
(a)
1 mark
Write down an expression for the gravitational force between the two stars.
(b)
3 marks
Show that the orbital speed v of each star is given by v = √(Gm/4r).
(c)
5 marks
The stars are separated by 4.0 × 10¹¹ m and have an orbital period of 2.0 years. Calculate the mass of each star. The gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(d)
2 marks
Explain why the gravitational force on each star is directed towards the common centre of mass, even though the other star is at a distance 2r away.
(e)
1 mark
State one assumption made in this model.
