  We present an experimental study of the Rydberg $^1S_0$- and $^1P_1$- series
of ytterbium for principal quantum numbers in the range of $n=70$ to $90$. The
study is performed using trap loss spectroscopy in a magneto-optical trap
operating on the $6^1S_0 \rightarrow 6^1P_1$ transition at $399\,\text{nm}$.
Compared to the commonly used Rydberg spectroscopy method using
field-ionization and ion detection, trap loss spectroscopy is significantly
simpler and requires a less sophisticated experimental setup. Using this method
we determine relative values of the scalar and tensor electric polarizabilities
of both, $6sns\,^1S_0$- and $6snp\,^1P_1$- Rydberg states.
