we calculate the minuscule accelerations that the planets and other bodies gravitationally exert on the sun:
a = F/sunmass = G*planetmass/r^2
(if you want force, equal and opposite unlike acceleration, multiply by sunmass 1.988e+30 kg. however, sunmass and G are not known to high precision, but the gravitational parameter G*M is known to high precision for many solar system bodies. therefore, calculating acceleration is not limited by low precision of G.)
for distance r we use orbital semimajor axis. bodies represent the mass of the entire planetary system including all moons, unless otherwise indicated.
2.091e-07 m/s^2 Jupiter
2.774e-08 m/s^2 Venus
1.8501e-08 m/s^2 Saturn
1.803e-08 m/s^2 Earth (including moon)
1.781e-08 m/s^2 Earth (alone)
6.570e-09 m/s^2 Mercury
8.242e-10 m/s^2 Mars
7.049e-10 m/s^2 Uranus
3.354e-10 m/s^2 Neptune
2.3e-10 m/s^2 Milky Way galaxy (this value was looked up, not calculated)
1.6e-13 m/s^2 Alpha Centauri A + Alpha Centauri B
2.831e-14 m/s^2 Pluto (including Charon)
2.523e-14 m/s^2 Pluto (alone)
8.7e-15 m/s^2 Sagittarius A*
Jupiter has by far the greatest effect moving the sun.
the Alpha Centauri system exerts a greater pull on the sun than Pluto does.
the centripetal acceleration that keeps the sun orbiting the Milky Way is greater than the acceleration caused by Pluto. however, the component of that galactic orbital acceleration caused by Sagittarius A-star, the supermassive black hole at the center of the galaxy, is less than Pluto.
how do these accelerations compare to those seen in exoplanets discovered by the radial velocity method (Doppler shifts)? to "hot Jupiters" discovered by the transit method?
units --version
GNU Units version 2.27
for i in mercury venus earth mars jupiter saturn uranus neptune pluto; do echo $i; units --output-format %.3e "G ${i}mass / (${i}sundist_min/2 + ${i}sundist_max/2)^2"; done | perl -nlwe 'if(/Definition: (.*)/){ $_=$1; s,m / s,m/s,; print"$_ $planet"; }else{ die unless /(.)(.*)/; $planet=(uc$1) . $2;}' | sort -gr
_onlypluto = (1/G) 869.3 km^3 / s^2
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