Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. This paper demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and trigonometric methods, which are much simpler than the original derivation depicted by Kepler. The established law of equal area for the Earth was applied to analyse the angular velocity or the reciprocal of the distance--for the Earth's orbit around the Sun--and can be defined as a periodic function by analysing the available data, which help explain the law of ellipses for the Earth. (Contains 4 tables and 3 figures.)