A

Step 1: Identify the key parameters.
The distances from the planet to the Sun are given as r1 (maximum distance) and r2 (minimum distance). We can denote the semi-major axis (a) and semi-minor axis (b) of the elliptical orbit as follows:

• a = (r1 + r2) / 2
• b = \sqrt{r1 \cdot r2}

Step 2: Understand angular momentum in elliptical orbits.
The angular momentum J of a planet in an elliptical orbit about the Sun is given by:
J = m * v * r
where v is the tangential velocity and r is the distance from the Sun to the planet.

Step 3: Calculate tangential velocity.
To find the velocity, we will use the conservation of angular momentum. The angular momentum at the farthest point (maximum distance r1) and the closest point (minimum distance r2) is equal.
This means:
J = m * v1 * r1 = m * v2 * r2
Therefore, expressing v from this gives us two equations.

• v1 = \frac{J}{m * r1}
• v2 = \frac{J}{m * r2}

Using Kepler's laws, the relation between the semi-major axis and the orbital period T can yield the semi-major axis value used in averages.

Step 4: Express the angular momentum.
By utilizing the specific angular momentum in orbit, which utilizes the average distances and mass of the Sun (M_s):
Angular momentum can also be expressed as: J = m \sqrt{G M_S (2 / r1 + 1 / r2)}, where G is the gravitational constant.

Step 5: Conclusion.
Upon evaluating the expressions, the final angular momentum relative to the Sun as center takes relevance using the average and proportionalities established within classical mechanics and gravitational influences.
Thus, we can finalize the angular momentum expression.
Therefore, the answer is proportional to the average distances of the ellipse and gives a constant mass-ratio relation returning:
Answer: Therefore, A.