Final answer:
The semi-major axis of Halley's Comet can be calculated using Kepler's Third Law. The mass of the Sun can also be inferred from orbital data. The comet's perihelion and aphelion distances are derived from its eccentricity and semi-major axis, and the variation in kinetic energy between these points is due to the conservation of energy.
Step-by-step explanation:
Analysis of Halley's Comet's Orbit
The semi-major axis of the orbit is derived from Kepler's Third Law of Planetary Motion, which is generally used to determine the size of orbits. Since Halley's Comet has an orbital period of 76 years, we can calculate the semi-major axis using the formula T^2 = a^3, where T is the period in Earth years and a is the semi-major axis in Astronomical Units (AU). Solving for a gives us Halley's semi-major axis.
To find the mass of the Sun by exploiting Halley's orbital data, one can rearrange Kepler's Third Law and use the gravitational constant, although the mass of the Sun can be considered a known constant in these calculations.
The aphelion and perihelion (the farthest and closest points to the Sun in Halley's orbit) can be calculated using the orbit's eccentricity and semi-major axis.
Concerning the kinetic energy at perihelion and aphelion, it's important to look at the principles of conservation of energy in elliptical orbits to understand how the kinetic energy varies at different positions in the orbit. At perihelion, the comet is fastest and thus has the highest kinetic energy. We can relate the kinetic energies at aphelion and perihelion by considering the potential energy differences and the conservation of total mechanical energy in the comet's orbit.