To page 23 in the book: the discovery of Ceres

200 years ago, the 1. January 1801, the Italian astronomer Giuseppe Piazzi (1746-1826) discovered Ceres, the first and largest asteroid. Ceres is a rock of 914 km diameter. Roughly speaking, what Gauss was is to describe the Keplerian orbit of Ceres with a few parameters. From the observations, the parameters can then be solved via a linear system of equations similar than in one of the homework problems, where you have to fit a cubic curve from 4 observations.

By the way: Gauss, who predicted the position of Ceres from observations was essentially doing what you did when solving problem 30. He parameterized the Keplerian orbit of Ceres with some parameters and new the position at certain times. This led to a linear system of equations.
Apropos homework for monday: in section 1.3:
Problems 4,14,26*,34,48,50
Office hours: reminder: Mo, We 14-15, starting next monday.

Orbital elements of Ceres

    Diameter       Mass    Rotation    Orbital   Spectral   Semimajor     Orbital        Orbital     
      (km)       1015 kg     Period     Period     Class       Axis      Eccentricity   Inclination   
    --------     -------   --------    -------   --------   ---------    ------------   -----------  
    960 x 932     870,000   9.075 hrs   4.60 yrs      C       2.767 AU       0.0789       10.58 deg  
Source: Nasa

Pictures and infrared picture of Ceres