-    the gravity field is a static field
-    the image of the sun came from 8 minutes ago

To calculate any gravity related phenomenon we have to know the location of the earth in the gravity field. We can only deduct that from the image of the sun, which is from 8 minutes ago. Hence t should be replaced by t-r/c.

If r/c is 8 minutes, this is an experiment that verifies the speed of the light is c. Not the speed of the gravity unfortunately.

So any idea can be generated by a pat on the head has been patted hundreds of years ago.