Kepler's+Third+Law+(1618)

 =The square of the orbital period is proportional to the cube of the the orbit's semi major axis.= = = Kepler’s laws imply that the speed of revolution of a planet around the sun is not uniform, but changes throughout the planet’s “year.” It is fastest when the planet is nearest the sun (called the //perihelion//) and slowest when the planet is farthest away (//aphelion//). The third law means that if //Y// is the length of a planet's year, that is, the time it takes the planet to make a complete revolution about the sun, and if we denote by //a// the length of the semimajor axis of the planet’s orbit, then the quantity //Y2/a3// is the same for every planet (and comet, and other satellite) in the solar system. Thus, if a planet’s orbit is known, the length of it’s year can be immediately calculated, and //vice versa//. Kepler’s laws were empirical, that is, they were derived strictly from careful observation and had no purely theoretical foundation. However, about 30 years after Kepler died, the English mathematician and physicist Sir Isaac Newton derived his inverse square law of gravity, which says that the force acting on two gravitating bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Kepler’s laws may be derived from this theoretical principle using calculus.

or Ta2 / Tb2 = Ra3 / Rb3


 * Square of any planet's orbital period (sidereal) is proportional to cube of its mean distance (semi-major axis) from Sun
 * Mathematical statement: T = kR3/2, where T = sideral period, and R = semi-major axis
 * Example - If a is measured in astronomical units (AU = semi-major axis of Earth's orbit) and sidereal period in years (Earth's sidereal period), then the constant k in mathematical expression for Kepler's third law is equal to 1, and the mathematical relation becomes T2 = R3

Planets distant from the sun have longer orbital periods than close planets. Kepler's third law describes this fact quantitatively. "The [|square] of the [|orbital period] of a planet is directly [|proportional] to the [|cube] of the [|semi-major axis] of its orbit." Symbolically: where //P// is the orbital period of planet and //a// is the semimajor axis of the orbit. The [|proportionality constant] is the same for any planet around the sun. So the constant is 1 ([|sidereal year])2([|astronomical unit])−3 or 2.97473×10−19 s2m−3. See the actual figures: [|attributes of major planets]. For example, suppose planet A is four times as far from the sun as planet B. Then planet A must traverse four times the distance of Planet B each orbit, and moreover it turns out that planet A travels at half the speed of planet B. In total it takes 4×2=8 times as long for planet A to travel an orbit, in agreement with the law (82=43). This law used to be known as the **harmonic law Example: []**


 * Planetary Data**
 * Planet || Period of revolution || Period of rotation || Semi major axis( A U ) || ||
 * ^  || around the sun (in Years) || around own axis ||^   ||^   ||
 * Mercury || 0.241 || 58.6 days || 0.387 || ||
 * Venus || 0.615 || 243 days || 0.723 || ||
 * Earth || 1.00 || 23 h 56 m 4 s || 1.00 || ||
 * Mars || 1.88 || 24 h 37 m 23 s || 1.524 || ||
 * Jupiter || 11.86 || 9 h 50 m || 5.203 || ||
 * Saturn || 29.46 || 10 h 25 m || 9.54 || ||
 * Uranus || 84.01 || 710 h 50 m || 19.18 || ||
 * Neptune || 164.79 || 16 h || 30.07 || ||
 * Pluto || 248.43 || 6.4 days || 39.44 || ||