The period of Comet Halley is approximately 76 years. Its perihelion position is 0.6 au from the Sun, so its aphelion distance from the Sun is approximately

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Comet Halley's orbit can be analyzed using Kepler's laws, specifically the law of orbits, which tells us that the orbit of a planet (or comet, in this case) is an ellipse with the Sun at one of the two foci. The semi-major axis (a) of this ellipse is the average of the perihelion (closest approach to the Sun) and aphelion (farthest distance from the Sun) distances. Given the period (P) of 76 years and the perihelion distance of 0.6 AU, we can use the formula for the semi-major axis in relation to the period (from Kepler's third law, $P^2 = a^3$ for objects in the Solar System when P is in years and a is in astronomical units, AU) to find the semi-major axis and then solve for the aphelion distance. However, without doing the calculations explicitly, we know the aphelion distance must be significantly greater than the perihelion distance to account for the long period and the elliptical nature of the orbit. Among the options given, 35 AU is the only one that fits this requirement, as it is much greater than the perihelion distance, indicating a highly elliptical orbit that would take approximately 76 years to complete.

The Period of Comet Halley Is Approximately 76 Years