2
$\begingroup$

Including all objects gravitationally bound to the Sun, how many atoms are there in our solar system?

$\endgroup$
  • 8
    $\begingroup$ Have you done any work to get an estimate? $\endgroup$ – Bill N Jul 22 '15 at 22:28
  • 3
    $\begingroup$ Hint: By far, most of the mass is in the Sun. $\endgroup$ – pela Jul 22 '15 at 22:36
3
$\begingroup$

Giving that most of the solar system's mass is concentrated in the sun, you may say that the order of magnitude of the number of atoms in the sun and in the solar system is the same. Thus, we may find this number by using the sun's mass and dividing it by the hydrogen's mass, because the sun is composed of it almost entirely: $$\frac{M_s}{M_h}=\frac{2\cdot10^{30}}{1.67\cdot10^{-27}}=1.2\cdot10^{57}$$

So the order of magnitude of the number of atoms in the solar system is $10^{57}$.

$\endgroup$
  • $\begingroup$ I believe this answer is wrong, as explained in my answer (the sun does not consist of atoms). $\endgroup$ – Floris Oct 23 '18 at 14:29
  • $\begingroup$ I believe that the notion of "what is an atom" is really subjective. A proton, after all, is treated as an ion all the way in chemistry, for example. Well, would you say that a chloride is not an atom? Either way, it is a problem of semantics, not physics. $\endgroup$ – Franklin Nov 16 '18 at 1:22
  • $\begingroup$ when a nucleus still has some of its electrons it is reasonable to call it an atom. When it has none it starts to look very much not like an atom. Yes, it’s a matter of opinion - I gave you mine and we may have to agree to disagree. $\endgroup$ – Floris Nov 16 '18 at 1:26
  • $\begingroup$ I understand your position, and do agree to disagree. (: $\endgroup$ – Franklin Nov 17 '18 at 16:59
10
$\begingroup$

A very brief Google search gets you the number 1,192,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (approximately $10^{57}$ atoms)- but in fact this is wrong. That value is derived from the mass of the objects of the solar system (mostly the Sun) divided by the mass of a proton (which is what most of the Sun is made of).

But the question asks for the number of atoms in the solar system. Since the Sun is a plasma ball, most of its mass is not in the form of atoms. We are then left with estimating the number of atoms in the rest of the solar system, for which we need the composition of the various planets. The largest objects in the solar system (after the Sun) are:

Name     radius    mass 
          (km)    (kg)
Jupiter  71492  1.90E+27
Saturn   60268  5.68E+26
Neptune  24766  1.02E+26
Uranus   25559  8.68E+25
Earth     6378  5.97E+24

Of these, Jupiter is about 71% of the total mass of non-Sun objects; everything including Earth is 99.8% of the mass.

To get to the number of atoms, we need a reasonable estimate of the atomic composition. According to this link 80-some percent of the mass of the giant gas planets is Hydrogen and Helium. This means that we would get an upper limit on the number of atoms if we just took the mass of these five, and pretended it was all hydrogen:

Total mass: 2.67E27 kg; mass of proton 1.67E-27; number of atoms on the order of $10^{54}$.

That is three orders of magnitude smaller than the answer you get when you include the Sun. Of course not all of the Sun is fully ionized - see this paper for a painfully detailed calculation of the degrees of ionization. But the photosphere (where the non-plasma parts of the Sun are) is a very small (and low density) fraction of the Sun; including it properly is well outside of the scope of your question, I'm sure.

$\endgroup$
  • $\begingroup$ 10^57 atoms in the solar system according to Floris, times 10^11 stars in the milky way, times 10^11 galaxies in the observable universe equals 10^77 atoms. On the low end I think. $\endgroup$ – Alex Jul 22 '15 at 22:41
  • 1
    $\begingroup$ @Alex indeed if you follow the link it states clearly that it estimates a lower limit for the number of atoms in the universe. Note also that the answer really addresses "nuclei" since the sun is a plasma and therefore not really comprised of atoms. And it contains the majority of mass in the solar system. $\endgroup$ – Floris Jul 22 '15 at 22:59
  • 1
    $\begingroup$ That's funny, I asked a trick question and didn't know it. $\endgroup$ – Alex Jul 22 '15 at 23:11
  • 2
    $\begingroup$ You are technically correct, the best kind of correct. +1 $\endgroup$ – Jim Jul 23 '15 at 18:42
  • 1
    $\begingroup$ The gravitational acceleration at the photosphere is 28g. Since it is unlikely that there is no hydrogen above the photosphere, there would be a significant portion of atoms on the sun that should be counted. $\endgroup$ – LDC3 Aug 2 '15 at 15:23

protected by Qmechanic Oct 23 '18 at 12:34

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?

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