Q.The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C, are $K_A$, $K_B$ and $K_C$ respectively. AC is the major axis, and SB is perpendicular to AC at the position of the Sun S (S is the Sun at one focus; A and C are the two ends of the major axis -- one is perihelion, the other aphelion; B lies on the orbit directly above S, on the semi-latus rectum). Then (NEET 2018)

Step 1. Total mechanical energy is conserved along the orbit: $E=K+U=K-\dfrac{GMm}{r}=\text{constant}$, so $K=E+\dfrac{GMm}{r}$ -- kinetic energy is larger wherever $r$ is smaller.

Step 2. A and C are the two ends of the major axis (one perihelion, one aphelion -- the closest and farthest points from the Sun S). B is the point on the orbit where SB is perpendicular to the major axis; this is the semi-latus-rectum point, whose distance from the focus $S$ always lies strictly between the perihelion and aphelion distances. …

Use total-energy conservation (K = E + GMm/r) together with the dist …

• Assuming B (on the semi-latus rectum) is equidistant from the two apsides, instead of strictly between them. …