Introducing 1 AAU (Areal Astronomical Unit) for the area of a circle of radius 1 AU, how do you find 4-sd values in AAU, fot the orbital areas of solar planets?

1 Answer
Oct 5, 2016

Mercury:.1498 AAU Venus: .5232 AAU Earth 1 AAU
Mars: 2.320 AAU Jupiter: 27.09 AAU Saturn: 91.81 AAU
Uranus: 368.6 AAU Neptune: 903.0 AAU.

Explanation:

The orbital areas in AAU are

Mercury:0.1498 AAU

Venus: 0.5232 AAU

Earth 1 AAU

Mars: 2.320 AAU

Jupiter: 27.09 AAU

Saturn: 91.81 AAU

Uranus: 368.6 AAU

Neptune: 903.0 AAU.

A MON AVIS: Using AAU as areal unit, we get the direct

comparison with the area for the Earth orbit which is nearly

$1 A A U$

$= \pi A {U}^{2} = 70307$ trillion sq. km, nearly.

The formula for conversion is

$1 A U = \sqrt{\frac{1}{\pi} A A U} = 0.5642 \sqrt{A A U}$

Cross check: $1 A U = 0.5642 \sqrt{70307 X {10}^{12}} = 1.496 X {10}^{8} k m$

I also extend this definition for volume of a unit sphere as SAU:

1 SAU

= volume of a sphere of radius 1 AU

$= \frac{4}{3} \pi A {U}^{3}$.

For length, this unit is LAU.

1 LAU

= circumference of a circle of radius 1 AU

$= 2 \pi A U$

= 939,951,145 km, nearly.