How did Gauss find the orbit of Ceres using least squares?

[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.