Linear equations and the discovery of Ceres

Guiseppi Piazzi Discovered Ceres on Jan. 1, 1801

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Linear equations and the discovery of Ceres

• Piazzi collected 22 observations over 40 nights

• Ceres then vanished behind the sun’s rays, on Feb. 11

• Piazzi’s data consisted of triplets (time, angle1, angle2) giving position of asteroid at different times

• Piazzi’s observations published in September

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Linear equations and the discovery of Ceres

• Astronomers wanted to recover Ceres’ orbit.• Carl Gauss, 24, tackled the problem.• Gauss had to solve a system of 17-by-3 system of

linear equations (17 equations in 3 unknowns).• Sir Isaac Newton said such orbit calculations were

“among the toughest problems in astronomy.”• Gauss’ work led him to discover least squares

approximation (we’ll discuss that later) and what we now call Gauss-Jordan elimination.

• Gauss made his computations in only a few weeks. On Dec. 7 astronomers found Ceres, exactly where Gauss said it would be!

(Left) Carl Friedrich Gauss, considered one of the

three greatest mathematiciansof all time (along with

Archimedes and Sir Isaac Newton).

(Right) Gauss at 24, when he computedthe orbit of Ceres.

(Left) Gauss’ sketch of the orbit of Ceres.

(Right) Image of Ceres from the Hubble telescope.

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“. . . for it is now clearly shown that the orbit of a heavenly body may be determined quite nearly from good observations embracing only a few days; and this without any hypothetical assumption.’’

Carl Friedrich Gauss