Okay, I have it. Finally a purely mathematical proof that Bonz's theory can't work.<br /><br />Alright, so one of Bonz's assumptions is that the moon and the earth are increasing at the same rate, i. e. in the time that the earth doubles in size, the moon also doubles in size.<br /><br />So the ratio of earth's radius to the moon's radius must at all times be the same. Let's call it k. This means that k must be the same at t = 0, t = 1, etc.<br /><br />Let's see if it holds up. Let's take t = 0 and t = 86, 400 (the number of seconds in a day) and check k to see if it is indeed the same.<br /><br />Let t be time, R the radius of earth, r the radius of the moon, G be "gravitational" acceleration on the earth, g be "gravitational" acceleration on the moon, and k be the ratio of the earth's radius to the moon's radius.<br /><br />At t = 0<br />R = 6, 378, 100 m<br />r = 1, 737, 400 m<br />G = 9.8 m/s^2<br />g = 1.6 m/s^2<br /><br />So we calculate k = R/r and get 3.67<br /><br />At t = 86, 400<br />We find the new radii. We know the new radius will be = old radius + 1/2at^2. So let's calculate<br /><br />New R = Old R +Gt^2/2 = 6, 378, 400 + (9.8)(86, 400)^2/2 = 36, 584, 682, 100 m<br /><br />New r = Old r + gt^2/2 = 1, 737, 400 + (1.6)(86, 400)^2/2 = 5, 973, 705, 400 m<br /><br />Now let's calculate k at t = 86, 400. According to Bonz, it should be the same<br /><br />k = 36, 584, 682, 100/5, 973, 705, 400 = 6.12<br /><br />In other words k is not the same at t = 0 as it is at t = 86, 400, whick SHOULDN'T be the case according to Bonz, but it is. Under Bonz's assumpsions k would have to be the same at all times in order for proportions to remain the same. But under his other assumptions (the outward acceleration is constant) this cannot be the case.<br /><br />QED