A. Write a program that calculates the elevation of the Sun...

a. Write a program that calculates the elevation of the Sun as viewed from any fixed point on Mercury's equator, assuming zero axial tilt. You should start at local noon and assume any location on Mercury's orbit.
b. Present the results of that program for two Mercury years.

Key Concepts

Planetary Orbital Mechanics

This concept encompasses the study of how planets move in their orbits around the Sun, primarily governed by Kepler's laws. It explains the elliptical shape of orbits and the varying orbital speed, both of which influence the observed motion of the Sun relative to an observer on the planet. Understanding these principles is crucial when modeling the changing solar elevation over time.

Planetary Rotation and Timekeeping

The rotation of a planet determines the cycle of day and night, and hence phenomena like local noon. This concept addresses how a planet's rotation period, axial tilt, and spin-orbit resonance (when applicable) influence local time measurements and the progression of solar elevation. Accurate timekeeping based on these factors is essential for correctly simulating the Sun's position throughout a day or over longer time periods.

Celestial Coordinate Systems

This concept involves understanding how positions of celestial objects are mapped relative to an observer on a rotating body. In astronomical calculations, transforming between different coordinate systems—such as equatorial, ecliptic, and horizontal—is essential for accurately determining the apparent position and elevation of the Sun in the sky.

Solar Elevation Calculation

Calculating the Sun's elevation is a key aspect of observational astronomy. It entails determining the angular height of the Sun above the horizon, which depends on the observer's location, the time of day, and the celestial mechanics of the planet. This concept uses trigonometric formulas that combine the effects of the planet's rotation and orbital position.

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