Discovering Ceres: Gauss and the Least Square Approach

[mitchell2007]

I've been reading 'Measuring the World' by D. Kehlmann, i have reached to the part when Gauss using the least square approach (¿? still not 100% sure) discovered the orbit of 'Ceres' but my question is How did he get it??.. assuming the orbit is elliptic and using some possible meditions how could you get the trajectorie of an asteroid or something similar?, thanx.

 

[ObsessiveMathsFreak]

Very elegantly.

 

[charng]

I am familiar with the work of Carl Friedrich Gauss and his contributions to mathematics and astronomy. In the case of discovering the orbit of Ceres, Gauss used a mathematical technique known as the least square approach.

The least square approach is a method of finding the best fit line or curve for a set of data points. In this case, Gauss used observations of Ceres's position in the sky over a period of time to determine its orbit. He then used the least square approach to calculate the most likely trajectory that would fit those observations.

The key to this approach is the assumption that the orbit of Ceres is elliptical. This is a common assumption in astronomy, as many celestial bodies, including planets and asteroids, have elliptical orbits around the sun. Using this assumption, Gauss was able to use his mathematical skills to calculate the parameters of the ellipse, such as its semimajor axis and eccentricity, which would describe Ceres's orbit.

In addition to the assumption of an elliptical orbit, Gauss also needed accurate measurements of Ceres's position in the sky. This is where his meticulous observations and measurements came into play. By using precise instruments and careful observations, Gauss was able to gather the necessary data to apply the least square approach and determine Ceres's orbit.

Overall, Gauss's use of the least square approach in discovering the orbit of Ceres showcases the power of mathematics and the importance of accurate measurements in scientific research. It also highlights the importance of making assumptions based on previous knowledge and observations in order to make new discoveries.