# Several questions about Gauss's contributions to observational astronomy

I just want to check if anyone has additional information about a private astronomical research begun by Gauss in 1819, which dealt with the "movements of the solar system" in the galaxy (motion of the solar system relative to the fixed stars). In addition to the material in his nachlass (volumes 6 and 11:1), I found several interesting sources which show that through his correspondences and unpublished fragments Gauss was involved in attempts to try and define the movement of the sun by the statistical motion of the fixed stars.

Since i'm completely unfamiliar with those scientific matters, my question is therefore intended to be a framework for learning in a general way on this aspect of observational astronomy (i.e, mathematial tools, methodology) by achieving better understanding of Gauss's work on this. To be more specific, these are my questions:

• One such correspondence is his 1838 letter to Argelander (just Google "On a Letter from Gauss to Argelander" and you will find it). My first question is therefore a request for explanation of what Gauss actually did in this letter.
• In Gauss's werke, volume 11-1, p.390, appears a short note "About the frequency of optical double stars". Despite it's neglible length, Martin Brendel (the editor of Gauss's astronomical works) comments on it lengthfully, and the interesting title of the note just makes my curiousity greater. So my second question is just for explanation.
• Any additional useful information will be blessed.

As i said several times before, one of my main objectives in using this site is to gain a complete picture of all of Gauss's contributions to math and science, so once again, i appologize for being so annoying and tedious with my obssesive questions-asking about Gauss.

• The paper "On a letter from Gauss to Argelander" seems clear. It explains what Gauss did in his letter. By analyzing the "proper motion" of the stars in the sky, he made the conclusion about the motion of the Sun.. with respect to what? It does not specify clearly. Well probably with respect to the imaginary "center" of the local stars cluster. – Alexandre Eremenko Jul 4 '19 at 20:49

Concerning the note "About the frequency of optical double stars", i think that Gauss attempted to solve in this note a kind of probabilistic problem that is relevant to astronomy. Gauss tries to find a pattern in the most updated maps of stars up to his time - what is the fraction of double stars in a ball (sphere with volume) centred at the earth, among a total of $$kM$$ observed stars, and assuming uniform prior distribution (Gauss writes in his note:"...$$kM$$ stars scattered without a rule")? A double optical star is actually two stars whose angular distance on the celestial sphere doesn't exceed $$\lambda$$.

Gauss gives the answer in a form of a Poisson distribution with a rate parameter $$\omega$$ for which he gives a formula in terms of $$\lambda, M, k$$. This note is therefore noteworthy for two reasons:

• The first mathematician to apply Poisson distribution for describing statistical behaviour of stars is, according to wikipedia, Simon Newcomb. Gauss's attempt therefore preceeds him.

• I guess the main problem is how to evaluate the rate parameter $$\omega$$, and that is what Brendel attempts to reconstruct in his commentary on Gauss's note.

I'm still not sure if Gauss tries to solve this problem on a sphere or on a ball; it's more reasonable that he tries to solve it on a ball because in this way his calculation has direct relevance to astronomy.