# Grain of sand attracting the sun?

My friend keeps telling me that according to physics...

"The sun attracts a grain of sand on the earth with the same force that the grain of sand attracts the sun"

or

"A grain of sand on the earth attracts the sun"

Is that true? Does in theory a grain of sand really attract the sun?

Formalizing these statements, let M be the mass of the sun, m the mass of the grain of sand. The magnitude of the gravitational force exerted by the grain of sand on the sun is $$F = \frac{GMm}{r^2}$$ where $G = 6.63 \times 10^{-11}$ and $r = 1.5 \times 10^{10} \ m$ and thus the acceleration the sun experiences towards the earth as a consequence of the grain of sand is $$a = \frac{Gm}{r^2} \approx 3 \times 10^{-34} \ m/s^2$$ where we approximated $m = 1 \ gram$. Hence the acceleration is not zero, but it is functionally nothing.
• +1 Where $G$ is the gravitational constant (big "G"): en.wikipedia.org/wiki/Gravitational_constant Commented May 27, 2012 at 1:53
• I will confess I didn't bother looking up the mass of a grain of sand but estimated it, because we can see that even if the estimate of 1 gram were off by 10 or even 20 orders of magnitude the acceleration would still negligible. By way of comparison, the acceleration of the sun due to the entire mass of the earth is only $1.77 \times 10^{-6} \ m/s$ Commented May 27, 2012 at 12:53