Kepler's second law says that a. planetary orbits are ellipses with the Sun at one focus. b. the square of a planet's orbital period equals the cube of its semimajor axis. c. net forces cause changes in motion. d. planets move fastest when they are closest to the Sun.

Planetary motion refers to the way planets move around the Sun. This concept is essential in understanding how our solar system works. Basically, planets follow a path called an orbit.
These orbits aren't perfect circles but are more oval-shaped, or elliptical.
The Sun isn't at the center of the orbit but at one of the two foci of the ellipse.
This means that the distance between a planet and the Sun changes as the planet moves around its path.
As planets travel, their speed varies due to gravitational forces. They move faster when they are closer to the Sun and slower when they are farther away. Understanding these patterns helps us predict the position of planets in the future and offers insights into other astronomical phenomena.

Orbital mechanics is the science of describing the motions of planets and other objects in space. It deals with determining the positions and velocities of objects and predicting their future movements.
The key component here is gravity, which is the force that pulls objects together. Due to gravity, a planet is pulled towards the Sun as it goes along its orbit. The balance between this gravitational pull and the planet’s speed keeps it in its elliptical path.
According to Newton’s Law of Universal Gravitation, every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.
This law helps explain why planets don’t fly off into space or crash into the Sun.
Applying this law, we can derive formulas to calculate the positions and velocities of objects in space at any given time.

Johannes Kepler formulated three fundamental laws to describe planetary motion. These laws are:

• First Law (Law of Ellipses): Planets move in elliptical orbits with the Sun at one focus. This means that the shape of a planet's orbit is an ellipse rather than a perfect circle.
• Second Law (Law of Equal Areas): A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This indicates that a planet moves faster when it is closer to the Sun and slower when it is further away.
• Third Law (Law of Harmonies): The square of a planet's orbital period (the time it takes to complete one orbit) is proportional to the cube of the semimajor axis of its orbit (half the longest diameter of the ellipse). This law reveals a precise, mathematical relationship between the time a planet takes to orbit the Sun and its average distance from the Sun.

Together, these laws provide a comprehensive understanding of how planets orbit the Sun. They are crucial for astronomers and scientists to predict planetary positions and understand the dynamics of our solar system.