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user2554
user2554
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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:"there are "...$kM$ 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.

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 $kM$ stars, and assuming uniform prior distribution (Gauss writes in his note:"there are $kM$ 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.

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.

Source Link
user2554
user2554
  • 4.7k
  • 1
  • 14
  • 22

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 $kM$ stars, and assuming uniform prior distribution (Gauss writes in his note:"there are $kM$ 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.