Classification for 'not something' Neural Networks
Your problem resembles the learning task of 'one-class classification', otherwise known as anomaly detection. Essentially, you have a set of images all belonging to one class (galaxies), and you want a model to tell you if a new image is a galaxy or not, without providing any counter-examples to train with. 

You should try a recently developed method called Deep Support Vector Data Description. In this method, a transformation is learned by a neural network to map the inputs to points contained in a small hypersphere in latent space. Then, examples falling inside the hypersphere can be considered 'galaxies', and outside can be considered 'not galaxies'. 

You can read more about it here (quite technical), or just try to use the authors' PyTorch implementation here.