what is the least squares method of Gauss? What application does it have in astronom?

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what is the least squares method of Gauss? What application does it have in astronom?

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“Least squares” analysis is a tool in statistics for finding lines or curves given a set of data.

Historically it was developed by Gauss to find the location of Ceres, [this blog post has a nice deep dive on the background](https://www.actuaries.digital/2021/03/31/gauss-least-squares-and-the-missing-planet/).

Gauss had only a handful of data points for when and where Ceres had been spotted by astronomers before it got too close to the Sun to be visible. Astronomers were trying to predict where it would be so they could spot it again, but were having a lot of trouble predicting from so few data points, and those data points had potential errors or uncertainties in them.

So essentially Gauss was trying to take a handful of points of data (the observations), and match them to an ellipse or curve (the actual path). Gauss’s breakthrough was to look for the curve that minimised the squares of the distance between each point and the curve. So you get your trial curve, you measure the distance from each of your points to the curve, you square those distances, and add them all together. And you then adjust your curve so that you get the smallest sum of the squares (the “least squares”); and that resulting curve will probably be the best approximation to the actual curve from the data.

And Gauss’s method (having to invent a much of new maths to do this, and requiring a lot of calculations by hand) worked; he was able to predict the path of Ceres accurately enough for astronomers to find it again.