Thank you for the advice. I had already tried, and tried again, checking the "Use world file to define the coordinates of the raster". This does not seem to be helping.
I have also double checked that my datum is the same for both images. I am using D_Titan_2000. My low resolution, basemap, is the world map of Titan and I trying to layer high resolution TIFF images onto this. All images are TIFF files with corresponding TFW files. I have selected the D_Titan_2000 datum for all of the images.
The problem I am still having is that ArcMap is placing all the high resolution images in the upper left corner of the basemap.
Thank you!