ABSTRACT

The purpose of this team project was to investigate the motion of celestial bodies. First, we derived Kepler's Laws. We were then able to calculate a planet's angle in orbit in relation to its perihelion by translating an ellipse, expressed in polar coordinates, and constructing an auxiliary circle. By introducing spherical trigonometry, we were able to track a body's movement on the celestial sphere. In addition, we used trigonometry to calculate the angles of a rotation of a shadow at different times of day, and constructed a sundial. Finally, we successfully unified our studies of Kepler's Laws, the geometry of ellipses, and spherical trigonometry to pinpoint the position of the Sun and planets on the celestial sphere at any given time. Our findings could be further applied to the movement of other celestial bodies.