question about kepler's law?

Question

Kepler's third law states that the square of the orbital perod is equal to the cube of the semi major axis of the orbit.

I have difficulty understanding this could some one please break it down in simpler terms so I can understand it better?

Answer 1

The period, P, is the time, in years, that it takes the planet to make one complete orbit. By definition one year is the period of Earth's orbit.

The semi-major axis, A, is basically the average distance from the sun, measured in Astronomical Units (AU). By definition one AU is the semi-major axis of the Earth's orbit.

P squared = A cubed.

So the Earth has P of 1 year and A of 1 AU. 1 squared equals 1 cubed. That is a trivial example.

Jupiter has P a little under 12 years, so for Jupiter 12 squared equals A cubed. 12 squared is 144, so A is the cube root of 144, or a little over 5. Jupiter is a little over 5 AU from the Sun.

Answer 2

This is known as the harmonic law and gives the relationship between the size of the orital of a planet and its time of revolution.

Kepler's third law - sometimes referred to as the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets. Unlike the first and second laws, which describe the motion characteristics of a single planet, the third law makes a comparison between the motion characteristics of different planets. The comparison being made is that the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets. As an illustration, consider the orbital period and average distance from sun (orbital radius) for earth and mars as given in the table below.

Planet ___ Period(s) ___ AverageDist. (m) ___T2/R3(s2/m3)

Earth____3.156 x 107 s __1.4957 x 1011 ____ 2.977 x 10-19

Mars_____5.93 x 107 s ___2.278 x 1011______ 2.975 x 10-19


Observe that the T2/R3 ratio is the same for earth as it is for mars. In fact, if the same T2/R3 ratio is computed for the other planets, it will be found that this ratio shows approximate agreement with the same value for both earth and mars (see table below). Amazingly, every planet has the same T2/R3 ratio.

Planet_____Period(yr)______Ave.Dist. (au) ____T2/R3(yr2/au3)

Mercury ____0.241 ________ 0.39 ____________ 0.98

Venus_______0.615 _______ 0.72 ____________1.01

Earth _______1.00 _________1.00 ____________1.00

Mars ________1.88_________1.52 ____________1.01

Jupiter________11.8________ 5.20_____________0.99

Saturn________29.5_________9.54___________1.00

Uranus________84.0_________19.18__________1.00

Neptune________165_________30.06__________1.00

Pluto __________248__________39.44_________1.00


(NOTE: The average distance value is given in astronomical units where 1 a.u. is equal to the distance from the earth to the sun - 1.4957 x 1011 m. The orbital period is given in units of earth-years where 1 earth year is the time required for the earth to orbit the sun - 3.156 x 107 seconds. )


Kepler's third law provides an accurate description of the period and distance for a planet's orbits about the sun. Additionally, the same law which describes the T2/R3 ratio for the planets' orbits about the sun also accurately describes the T2/R3 ratio for any satellite (whether a moon or a man-made satellite) about any planet. There is something much deeper to be found in this T2/R3 ratio ratio - something which must relate to basic fundamental principles of motion.

Answer 3

You should try Wikipedia before asking here.