Physics 9702 · AS & A Level · Gravitational force between point masses
Gravitational force between point masses — practice question
A binary star is formed by star A, with mass $4.0 \times 10^{30}\,\text{kg}$, and star B, with mass $2.0 \times 10^{30}\,\text{kg}$; the two stars are separated by a distance of $3.3 \times 10^{12}\,\text{m}$. As shown in Fig. 1.1, both stars travel in circular orbits about their shared centre of gravity X. The orbital radius $R_B$ of star B is twice the orbital radius $R_A$ of star A.
(a)[2]
State Newton’s law of gravitation.
(b(i))[2]
Use Newton’s law of gravitation to calculate the magnitude of the gravitational force that each star exerts on the other.
(b(ii))[1]
Calculate the centripetal acceleration of star A.
(b(iii))[3]
Use your answer in (b)(ii) to determine the period of star A’s orbit.
(b(iv))[3]
By inserting a tick (✓) in each row, complete Table 1.1 to show how the quantities listed for star B compare with the same quantities for star A.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “(gravitational) force is (directly) proportional to the product of the masses” …