Light curves are plots of brightness measured over time. In the field of Space Situational Awareness (SSA), light curves of Resident Space Objects (RSOs) can be utilized to infer information about an RSO such as the type of object, its attitude, and its shape. Light curves of RSOs in geostationary orbit (GEO) have been a main research focus for many years due to the availability of long time series data spanning hours. Given that a large portion of RSOs are in low Earth orbit (LEO), it is of great importance to study trends in LEO light curves as well. The challenge with LEO light curves is that they tend to be short, typically no longer than a few minutes, which makes them difficult to analyze with typical time series techniques. This study presents a novel approach to observational LEO light curve classification. We extract features from light curves using a wavelet scattering transformation which is used as an input for a machine learning classifier. We performed light curve classification using both a conventional machine learning approach, namely a support vector machine (SVM), and a deep learning technique, long short-term memory (LSTM), to compare the results. LSTM outperforms SVM for LEO light curve classification with a 92% accuracy. This proves the viability of RSO classification by object type and spin rate from real LEO light curves.