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Kepler's Laws of Planetary Motion

 

Kepler's Third Law Formula

\( P^2 \;=\; a^3  \)     (Kepler's Third Law Simplified)

\( P^2 \;=\;  \dfrac{ 4 \cdot \pi^4  }{ G \cdot ( M + m ) } \cdot a^3   \)     (Kepler's Third Law General Form)
Symbol English Metric
\( P \) = Planet's Distance from the Sum \(mi\)  \( mi \) 
\( a \) = Planet's Orbit Semi-major Axis \(mi\) \( mi \)
\( \pi \) = Pi \(3.141 592 653 ...\) \(3.141 592 653 ...\)
\( G \) = Gravitationa Constant \(lbf-ft^2 \;/\; lbm^2\) \(N - m^2 \;/\; kg^2\)
\( M \) = Central Body Mass \(lbm\) \(kg\)
\( m \) = Orbating Body Mass \(lbm\) \(kg\)

Kepler's laws of planetary motion are a set of three fundamental laws.  These laws describe the motion and behavior of planets and other celestial bodies in the solar system.  These laws revolutionized our understanding of planetary motion and laid the foundation for Isaac Newton's laws of motion and the law of universal gravitation.  Kepler's laws have played a crucial role in shaping our knowledge of celestial mechanics and continue to be relevant in modern astronomical research and space exploration

Kepler's First Law (Law of Orbits)
The orbit of every planet is an ellipse with the sun at one of the two foci. In simpler terms, the orbit of a planet is not a perfect circle but an elongated shape called an ellipse.
 
Kepler's Second Law (Law of Areas)
A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.  This means that a planet moves faster when it is closer to the Sun (at perihelion) and slower when it is farther away (at aphelion).  In other words, a planet's speed varies throughout its orbit, but the area it sweeps in a given time remains constant.
 

Kepler's Third Law Formula

\( P^2 \;=\; a^3  \)     (Kepler's Third Law Simplified)

\( P^2 \;=\;  \dfrac{ 4 \cdot \pi^4  }{ G \cdot ( M + m ) } \cdot a^3   \)     (Kepler's Third Law General Form)
Symbol English Metric
\( P \) = Planet's Distance from the Sum \(mi\)  \( mi \) 
\( a \) = Planet's Orbit Semi-major Axis \(mi\) \( mi \)
\( \pi \) = Pi \(3.141 592 653 ...\) \(3.141 592 653 ...\)
\( G \) = Gravitationa Constant \(lbf-ft^2 \;/\; lbm^2\) \(N - m^2 \;/\; kg^2\)
\( M \) = Central Body Mass \(lbm\) \(kg\)
\( m \) = Orbating Body Mass \(lbm\) \(kg\)
Kepler's Third Law (Law of Periods)
The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.  This law establishes a relationship between the orbital periods and distances of different planets, showing that the farther a planet is from the Sun, the longer its orbital period.

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