7
$\begingroup$

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?

$\endgroup$
17
$\begingroup$

Yes, it is.

Applying basic principles articulated by Newton the 17th Century, every pair of bodies with mass attract each other in the form of gravity. That force is proportional to the product of their masses and inversely proportional to the distance between them.

So every grain of sand does exert a gravitational force on the sun. But using another principle from Newton, Force = (mass)x(acceleration). So while there is a force on the sun, the sun's mass cancels out of the calculation of acceleration. As the grain of sand's mass is so tiny, the acceleration the sun experiences as a consequence of the force exerted by the grain of sand is practically non-existent.

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.

$\endgroup$
  • $\begingroup$ +1 Where $G$ is the gravitational constant (big "G"): en.wikipedia.org/wiki/Gravitational_constant $\endgroup$ – Ergwun May 27 '12 at 1:53
  • 1
    $\begingroup$ Based on a quick search (eg. here) that acceleration is a few orders of magnitude too high. It is even more trivial than this estimate. The chemical make up and fineness of the sand is all important, but looks like a heavy grain would only be ~25mg. $\endgroup$ – Richard May 27 '12 at 6:21
  • $\begingroup$ There are gravitational effects to parts of a body. While the earth itself is a rigid solid, the oceans are not. Hence they will react to gravity from the moon and sun by rising towards them. Tidal forces can also melt the surface of a wayward planet and break apart an un-dense stray comet. $\endgroup$ – Jesvin Jose May 27 '12 at 7:09
  • $\begingroup$ 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 $1.77 \times 10^{-6} \ m/s$ $\endgroup$ – Simon S May 27 '12 at 12:53

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.