The orrery was designed in Solidworks. Before design however, I needed to figure out all of the gears. My original goals was to make an orrery that was as accurate as I can make it. Every planet is mounted to the central shaft. This means to sets of gears between every planet. One going away from the shaft, and one going back to it. An even set of gears means that the direction of rotation is the same for every planet.
There is a catch however. In order to get back to the central shaft after each set, the sum of the top gears and the bottom gears must be the same. If this is not the case, the gears will not have the same hub to hub distance and will not line up. In order to properly calculate the ratios with this added challenge, I made an excel sheet with all possible ratios from 10 to 40 with 2 sets of gears. I simply enter the ratio, and the sheet lights up all of the gears that will product something close to that ratio.
Accuracy of the gear ratios
The next bit is a bit technical. It tells a bit about how accurate the orrery is relative to the real solar system and what gear ratios were used. This was a good part of the design process, so I wanted to include it in this Instructable.
The orrery starts at the sun. The sun rotates differently depending on where you measure, because it is plasma, not a solid. On the poles it spins every 34.4 days, on the equator it spins every 25.05. The orrery was designed with the sun making 1 revolution being 25 days.
Mercury has an orbital period of 87,9691 days. A ratio of 1:3,5187 is required relative to the sun. The gears 30:38 and 18:50 were used to create a ratio of 1:3,5185. This has an accuracy of 99,993%.
Venus has an orbital period of 224,701 days. A ratio of 1:2,5534 is required relative to mercury, and 1:8,9851 relative to the sun. The ratios 22:39 and 25:36 are used, giving a total ratio of 1:2,5527. The accuracy to the sun is 99,963%.
Earth has an orbital period of 365,256 days. A ratio of 1:1,6260 is required relative to Venus, and 1:14,61 relative to the sun. The ratios 27:31 and 24:34 are used, giving a total ratio of 1:1,6265. The accuracy to the sun is 99,995%.
Mars has an orbital period of 686,971 days. A ratio of 1:1,881 is required relative to Earth, and 1:27,481 relative to the sun. The ratios 29:35 and 25:39 are used, giving a total ratio of 1:1,8828. The accuracy to the sun is 99,911%.
Jupiter has an orbital period of 4332,59 days. A ratio of 1:6,3051 is required relative to Mars, and 1:173,27 relative to the sun. The ratios 12:40 and 18:34 are used, giving a total ratio of 1:6,2963. The accuracy to the sun is 99,948%.
Saturn has an orbital period of 10759,22 days. A ratio of 1:2,48398 is required relative to Jupiter, and 1:430,41 relative to the sun. The ratios 19:35 and 23:31 are used, giving a total ratio of 1:2,4828. The accuracy to the sun is 99,902%.
The moon spins relative to the earth. Every rotation of the earth is 365,256 days. The moon has an orbital period of 27,322 days. A ratio of 13,3685:1 is required relative to earth. The ratio used is 136:11 is used, giving 12,3636:1. This might seem like I messed up, but this is what makes spinning gears so difficult. When the earth spins around the sun once, the moon now makes 12,3636 revolutions relative to the earth. But the earth also makes one revolution which is added to the rotation of the moon. The total is 13.3636. The accuracy to the earth is 99,963%.
The further you get from the sun, the more difficult it is to keep accurate. This orrery stays well within 0.1% accuracy on all planets and the moon. This is more than accurate enough for me. I hope no one disagrees with me on this.