Whilst we are thinking about orbital mechanics, I want to comment that there is

Question

Whilst we are thinking about orbital mechanics, I want to comment that there is an interesting relationship between the Solar System planet’s semi-major axis and a simple numerical series. The relationship states that the semi-major axis of planets in our Solar System conforms to (where 10 = 1 AU): a=4+n Where a = semi-major axis n = 0, 3, 6, 12, 24, 48... n, with the exception of the first step, has each value is twice the previous value. Thus the 3rd planet from the Sun (Earth) has a semi-major axis (a) = 4+6 = 10, or 1AU. Compare this relationship to the actual distances of the planets in our Solar System. Computer their percentage difference from reality.

Explanation / Answer

The semi-major axis a=4+n now in our solar system we have 9planets

using the formula we get semi-mjor axis of Mercury a= 4+0=4/10AU =.4AU

semi-major axis of Venus a=4+3=7/10AU .7AU

semi-major axis of earth a=10/10=1AU

semi-major axis of Mars a= 4+12= 16/10=1.6AU

semi-major axis of Jupiter= 4+ 24= 2.6AU

semi-major axis of Saturn= 4+48=5.2AU

semi-major axis of Uranus= 4+96= 10AU

semi-major axis of Neptune= 4+192=19.6AU

semi-major axis of pluto= 4+ 384=38.8AU

Now in reality semi major distance in AU is given below

In relality the percentage difference are:

Mercury: .4-.38/.38*100= 5.26%

Venus: .73-.7/.73*100=4.10%

Earth: 0% (no percentage difference)

Mars: 1.6-1.5/1.5*100= 6.67%

Jupiter: 5.2-2.6/2.6*100=50%

Saturn:9.5-5.2/9.5*100=45.2%

Uranus: 19.2-10/19.2*100=47.9%

Neptune: 30-19.6/30*100=34.67%

Pluto: 39.5-38.8/38.8*100=1.8%

Planet distance(AU) Mercury .38 Venus .73 Earth 1 Mars 1.5 Jupiter 5.2 Saturn 9.5 Uranus 19.2 Neptune 30 Pluto 39.5

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