WEBVTT 00:00:00.000 --> 00:00:02.860 This is Giancoli Answers with Mr. Dychko. 00:00:04.250 --> 00:00:07.560 In the first case, acceleration due to gravity will be capital G times 00:00:07.730 --> 00:00:11.840 some original mass divided by some original radius squared. 00:00:12.570 --> 00:00:13.970 And then in the second case, 00:00:14.080 --> 00:00:16.210 we have a different mass and a different radius, 00:00:16.420 --> 00:00:18.340 and we are told that the mass two is 00:00:18.500 --> 00:00:20.500 twice mass one, with double the mass, 00:00:20.860 --> 00:00:22.650 and the radius in the second case is 00:00:22.810 --> 00:00:25.320 triple the radius in the first case so 3 times r 1. 00:00:25.860 --> 00:00:27.600 So we make substitutions for each of these 00:00:27.600 --> 00:00:30.530 in the second case 00:00:30.820 --> 00:00:32.200 for acceleration due to gravity. 00:00:32.600 --> 00:00:34.570 So we have capital G times 00:00:34.740 --> 00:00:37.160 2 m 1 instead of m 2 00:00:37.420 --> 00:00:40.890 and we have 3 r 1 instead of r 2. 00:00:41.240 --> 00:00:45.220 By the way, I should have a square there, that's better. 00:00:49.730 --> 00:00:52.220 This 3 on the bottom becomes 9 00:00:52.220 --> 00:00:53.420 because it gets squared 00:00:53.680 --> 00:00:58.010 and so we have two-ninths times capital G m 1 over r 1 squared 00:00:58.130 --> 00:01:01.130 and this whole thing is the acceleration due to gravity, in the first case, 00:01:01.130 --> 00:01:04.320 before you doubled the mass and tripled the radius. 00:01:04.980 --> 00:01:07.450 So that means that 00:01:07.660 --> 00:01:08.930 the acceleration due to gravity 00:01:08.930 --> 00:01:12.460 changes by a factor of two-ninths, in the second case, 00:01:12.460 --> 00:01:14.920 after you double the mass and triple the radius.