It is only when one has a lot of good data over time that one sees that they are ellipses.
The case of Gauss computing the orbit of Ceres (which I am now surprised to find was not just a case of plug in the data and run least squares over a class of simple orbital models) suggests that intelligence coupled with the determination/capability to work through long chains of computation can substantially reduce the amount of data required for inference.
Gauss made that computation after he already had Newton’s laws and Kepler’s work behind him. He knew that the result had to be very close to an ellipse and that any deviation was going to be from nearby planets, and he knew the rough order of magnitude from that. If he had just had the small amount of data he had, and had no idea what the orbit should look like he wouldn’t have been able to do so.
The case of Gauss computing the orbit of Ceres (which I am now surprised to find was not just a case of plug in the data and run least squares over a class of simple orbital models) suggests that intelligence coupled with the determination/capability to work through long chains of computation can substantially reduce the amount of data required for inference.
Gauss made that computation after he already had Newton’s laws and Kepler’s work behind him. He knew that the result had to be very close to an ellipse and that any deviation was going to be from nearby planets, and he knew the rough order of magnitude from that. If he had just had the small amount of data he had, and had no idea what the orbit should look like he wouldn’t have been able to do so.