A planet makes a circular orbit with period ?T around a star. If it were to orbit, at the same distance, a star with three times the mass of the original star, would the new period (in terms of T ? ?) be (a)? ?, (b) (c) ?T,? (d) , or (e) ?T?/3?

Solution 2DQ The time period of orbital revolution of the planet around the star is given by the expression, 2r T = v , where r is the radius of the orbit and v is the orbital speed. GM Orbital speed has the expression, v r , M is the mass of the star. Now, substituting this value in the equation for T, T = 2r Gr 2r3/2 T = GM …..(1) Now, if the new star has three times the mass of the original star,= 3M , then from equation (1), new period is, 2r3/2 T = 3GM 1 2r3/2 T = 3 GM T = T/ 3 (from equation (1)) Therefore, the new time period will be T/3, which is option (d).