A speed of the palnet at the perihelion P be `V_(p)` and the sun -planet distance SP be `r_(P)` as shown in fig. Relate `{r_(p),v_(p)}` to the corresponding quantities at the aphelion `{r_(A),V_(A)}`. Will the planet take equal times to traverse BAC and CPB?

Explanation

To solve the problem, we need to relate the quantities at perihelion (point P) and aphelion (point A) for a planet orbiting the sun. We will also determine whether the time taken to traverse the arcs BAC and CPB is equal.

### Step 1: Understand the conservation of angular momentum
The angular momentum \( L \) of a planet in orbit is given by the formula:
\[ L = m \cdot v \cdot r \]
Where:
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