This paper presents a data driven approach to space object characterisation through the application of machine learning techniques to observational light curve data. One-dimensional convolutional neural networks are shown to be effective at classifying the shape of objects from both simulated and real light curve data. To the best of the authors’ knowledge this is the first generalised attempt to classify the shape of space objects using real observational light curve data.It is also demonstrated that transfer learning is successful in improving the overall classification accuracy on real light curve datasets. The authors develop a simulated light curve dataset using a high fidelity three-dimensional ray-tracing software. The simulator takes in a textured geometric model of a Resident Space Object as well as its ephemeris and uses ray-tracing software to generate photo-realistic images of the object that are then processed to extract the light curve. Models that are pre-trained on the simulated dataset and then fine-tuned on the real datasets are shown to outperform models purely trained on the real datasets. This result indicates that transfer learning will allow organisations to effectively utilise deep learning techniques without the requirement to build up large real light curve datasets for training.