Python GDAL: degrees to meters without reprojecting

I am trying to get senseful results in my Python script. I want to measure distance between features in a shapefile. I'm working with the SRS: GCS_WGS_1984, so my units are in degrees. But for the user, it would be better to have these units in meters, for more comprehension.
How can I convert degrees into meters? I'd like to not reproject my shapefile...