SolunarForcast.com
There are several "solunar" activity charts out there and they do not all agree. I have used the same one since the late 1960s and have them to be extremely accurate. Field & Stream magazine used to publish them monthly and you could order a booklet that contained the entire year in advance, which is what I did. These days you can subscribe to them online at solunarforcast.com.
There are other factors besides the position of the sun and the moon that effect the activity of game and fish that must also be taken into account. Barometric pressure will trump all other factors, especially for fish. When barometric pressure is low the fish are almost completely inactive and feed best during periods of high pressure. The key is to pick a time when both are favorable, high barometric pressure and a Major or Minor Activity time. If these don't coincide with my free time then I elect to do chores around the house. That way I don't waste my time and keep my wife happy. She understands how the solunar tables work and doesn't give me any grief when I take off to go hunting or fishing.
For deer hunting the rut trumps all other factors, but the deer are still more active during Major or Minor times during the rut than other times during the day. If you have limited time, try to pick a Major Time to hunt. If you have unlimited time, spend the whole day hunting during rut.
Back in the early 70s some of my co-workers challenged me to "prove it" when I told them about Solunar Tables. We were within a quarter mile of a small lake on the edge of town, so I told them that I would bring my fishing tackle with me the next day and take them to the lake to "prove it". Three of them piled into my car during our lunch hour at noon and we drove to the lake. I caught a fish on almost every cast using a small spoon with a green and yellow frog pattern at noon under a bright sun in the middle of the summer.
I can't prove it to you, but you can prove it to yourself IF you follow the tables AND take into account the other important factors such as barometric pressure and the rut.