## Checking Carl Sagan’s astrology math

Give the following a watch:

It’s a good overview on why astrology is garbage, but for this particular post I want to focus on the last minute where Carl Sagan compares the gravitational influences of both Mars and a child’s obstetrician. It’s a fairly simple calculation to check, so let’s do the math:

The relevant equation is Newton’s Law of Universal Gravitation

$\displaystyle F = G \frac{ M_1 M_2 }{ r^2 }$

Now to pick some rough values. For the mass of the adult obstetrician, I’ll select 80 kg (176 lbs) as reasonable, while 3 kg for an infant seems within the usual range. Right at birth, say the center of mass of the obstetrician is 1 m away from the infant. Thus we have

$\displaystyle F_O = (6.67 \times 10^{-11} \mbox{ Nm}^2\mbox{kg}^{-2})\frac{(80 \mbox{ kg})(3 \mbox{ kg})}{ (1 \mbox{ m})^2} = 1.6 \times 10^{-8} \mbox{ N}$

Now, the distance between Mars and Earth is constantly changing as they sweep out different orbits at different rates, and since we’re discussing any arbitrarily-timed birth I’ll take the average value of 1.7 AU (where 1 AU is the semimajor axis of Earth, at about 150 million km). The mass of Mars is $\displaystyle 6.42 \times 10^{23} \mbox{ kg}$. Therefore,

$\displaystyle F_M = (6.67 \times 10^{-11} \mbox{ Nm}^2\mbox{kg}^{-2})\frac{(6.42 \times 10^{23} \mbox{ kg})(3 \mbox{ kg})}{ (1.7 \times 1.50 \times 10^{11} \mbox{ m})^2} = 2.0 \times 10^{-9} \mbox{ N}$

Which is an order of magnitude smaller force. Ol’ Carl was right. If you time it right so that Mars is at closest approach you can at best have the two forces roughly equal, which is no help to the astrologers.

While it’s not necessary that a physical phenomenon have a presently explained physical mechanism to be true, it is pretty damning to go so long without being able to propose any even plausible mechanism (this is a problem that many pseudosciences face, which is often explained with synonyms for magic like “vital force” or “ghosts”). Nevermind that astrology is physically baseless, but also first cousin to racism since it sorts and judges people based off their birth, not the actions they take in life.