Is it against the law to privately sun bath au natural in your own back yard?
You can get arrested for public exposure if anyone can see you sunbathing in the nude on your own property, there have been arrests of individuals inside their homes who were nude in front of windows, so it would be illegal unless no one could possibly see you. Starts getting a little vague with airborne observation.
“Is it against the law to privately sun bath au natural in your own back yard?”
So long as it’s not visible from public, no. And if that’s the case then you have a reasonable expectation of privacy and the courts will be on your side in such cases.