Kepler’s Laws

Johannes Kepler stated the three laws of planetary motion. These laws are what are known today as Kepler’s laws and they describe the motion of the planets. He discovered these laws through the help of Tycho Brahe’s studies collections because he was in charge of them when Brahe died.

The first law states that “Every planet has an elliptical orbit with the Sun at one focus.” Having an elliptical orbit means that the sum of the distances of each orbital point to a point called the focus is constant. The first law states that the Sun is a focus of the orbit of every planet in the solar system. The claims of the Ptolemaic and Copernican systems stated that the orbits of the planets follow a circular path or a superposition of circular paths. Johannes Kepler discovered the elliptic path of the orbits of the planets after studying Tycho Brahe’s observations and study collections and he proved this through his calculations. The elliptical orbit of the planets is an effect of the force of gravity. Most of the planets follow an elliptical orbit with low eccentricity. Other heavenly bodies such as asteroids also follow an elliptical orbit, with high eccentricity, with the Sun at one of its foci. The eccentricity of an ellipse describes its shape, that is, an ellipse with low eccentricity has a geometric shape that is close to a circle and an ellipse with high eccentricity has a geometric shape that is close to an oval or a stretched circle.

The second law states that “For equal intervals of time, the line that joins the planet to the Sun sweeps out equal areas.” Consider that when the planet earth is following its elliptical orbit for one day or 24 hours, an area is covered by the earth’s path in its orbit and it is described by the line that joins the earth to the sun. The second law states that for a 24-hour time interval, this area is always the same wherever the earth on the point of its orbit is. Since the Sun is at one focus of the elliptical orbit of every planet, the planets move faster when they are closer to the sun because the areas that they sweep are the same when they are farther from the sun.

The third law states that “The square of the period of a planet’s orbit is directly proportional to the cube of the semi-major axis of the planet’s orbit.” This law is described by the equation P2=ka3 where P is the planet’s orbital period, k is the proportionality constant and a is the planet orbit’s semi-major axis. The proportionality constant is the same for all planets. This law implies that the time it takes the planet to orbit around the sun or what is known as its orbital period increases as its distance from the sun, which is directly related to its orbital path’s semi-major axis, also increases. Mercury, which is the nearest planet to the sun, takes the shortest time to orbit around the sun and Pluto, which is the farthest plant from the sun takes the longest time to orbit around the sun. The third law was what other scientists and astronomers used to calculate for orbital periods of satellites and other heavenly bodies.

Kepler’s Laws of Planetary Motion have been very useful for other scientists and astronomers to understand the orbital paths of the planets, satellites, and moons.

Johannes Kepler stated the three laws of planetary motion. These laws are what are known today as Kepler’s laws and they describe the motion of the planets. He discovered these laws through the help of Tycho Brahe’s studies collections because he was in charge of them when Brahe died. 

Nikola Tesla’s Principles

The AC motors used in electrical power systems are mostly induction motors. Nikola Tesla invented the AC induction motor after first discovering the principle of rotating magnetic field.

The principle of rotating magnetic field is basically shown when two coils of wire perpendicular to each other can rotate a magnetic field if the coils are supplied with 90 degrees out of phase AC current.

The  Two-phase Induction Motor

Nikola Tesla’s two-phase induction motor consists of two sets of wire coils surrounding the core of a motor. The two sets of coils are perpendicular to each other. The coils act as electromagnets when alternating current passes through them. The polarity of the coil electromagnets changes when the direction of the current flow reverses. The current that passes through the first coil creates a magnetic field around the coil and this causes the coil to turn. When the direction of the current flow that passes through the first coil reverses, a magnetic field is produced around the second coil. This process produces a rotating magnetic field. This theory of operation of a rotating magnetic field makes up the induction motor with only the rotor moving.

The Tesla Coil

The Tesla coil, which is also one of Nikola Tesla’s inventions, is instrumental in developing wireless communication especially in radio communications. The Tesla coil is a type of an air-core transformer with the primary and secondary windings set at resonance. A resonance is a condition of an electrical circuit in which the combination of the alternating currents impedance values cancel out. The Tesla coil demonstrates properties of insulators and conductors in interaction with electric fields in high frequency.

The Tesla coil consists of a primary winding, a secondary winding, a transformer, and two high-voltage capacitors. The transformer consists of an iron core in which coils of copper wire are wound around its hollow center. The iron core inside the transformer acts as an electromagnet when an alternating current is passing through the transformer and this will produce a magnetic field around the primary winding. The electrical energy stored in the capacitors is then converted to magnetic energy. When the frequency in the primary winding is high enough, a magnetic field will be produced in the secondary winding.

The Tesla Turbine

One important contribution of Nikola Tesla to the area of energy conversion is his invention of what is known today as the Tesla Turbine. The Tesla turbine is a bladeless turbine that uses the boundary layer effect to cause the rotor disk of the turbine to move in the direction of the fluid. The boundary layer effect is defined as the interaction of a fluid with a solid surface with the boundary layer as the disk surface in which the thin layer of fluid is interacting with. The adhesive property of fluids causes fluid molecules to reduce speed and stick above the metal surface of the rotor disk. These molecules will cause the fluid flow above them to slow down. The viscous property of fluids causes the fluid molecules to keep from separating. This whole process creates a pulling force that causes the rotor disk to move in the direction of the fluid.

The AC motors used in electrical power systems are mostly induction motors. Nikola Tesla invented the AC induction motor after first discovering the principle of rotating magnetic field.