Final answer:
Following the third-quarter moon phase on July 2, the next waning gibbous phase would likely occur around August 1. This is due to the lunar cycle taking about 29.5 days to complete.
Step-by-step explanation:
The lunar cycle, including phases such as the waning gibbous, takes approximately 29.5 days to complete. Following the third-quarter moon phase, the moon enters the waning crescent phase before transitioning to the new moon. After the new moon, the moon goes through the waxing crescent and first quarter phases before reaching the waxing gibbous phase. Thus, if the third-quarter moon is on July 2, the next waning gibbous will be about two weeks before this, around June 18. However, the waning gibbous phase immediately following July 2 would be about a month later, around August 1.
Learn more about Lunar Cycle