1:45 PM - 3:15 PM
[O11-P127] Derivation of the Optimal Number of Gears for the Planet Drives Cages Using VBA: Update of the Mechanical Planetarium!
Keywords:Planetarium, Planet Drives Cages, Orbital path of a planet, Gear
[Background and Purpose]
Mechanical planetariums have been used for over 100 years, starting in 1923. But recently, digital planetariums have become more popular because they are easier to use and take up less space. Still, the machines inside digital planetariums are very complex.
This study looks at how planets are shown in a mechanical planetarium called the “Minolta Planetarium MS-10”(made by KONICA MINOLTA,INC.). The goal is to check how accurate the planet movements are in the MS10 compared to the real movements of the planets. This research also suggests ways to make the MS10 more accurate.
[Method]
In the MS10, a part called the "planet drives cage" is used to show the motion of the planets. This machine uses many gears with different numbers of teeth to create the movement. Because there were no official design documents for the MS10, the number of teeth on each gear was counted by hand. (Figure 1)
The study found that the ratio of Earth's orbit time to the orbit times of the other planets could be reproduced by using four or six gears.
Since the MS10 was made in 1966, the orbit times of the planets have changed slightly. Updated data was taken from a recent paper [1], and the new ratios were used as target values. (Table 1)
To find better gear combinations, a program written in VBA (Visual Basic for Applications) was used. This program tested new combinations that used the same number of gears and the same range of teeth as the original MS10.
[Results]
For Mercury, Venus, and Mars, better gear combinations were found. These new combinations showed the orbit times more accurately than the original MS10. (Figure 2)
The study compared the errors between the old MS10 values and the improved values to see how close they were to the real planet data. (Table 2)
[Discussion]
For Mercury, Venus, and Mars, which use four gears, the program successfully found better combinations. But for Jupiter and Saturn, which use six gears, the program needed too many calculations and couldn’t finish. In the future, a new method will be developed to help find better gear combinations for these two planets.
In the course of the study, a simple model of a planet drives cage was constructed. The next step is to design and build a new "planet drives cage" using the improved gear combinations from this study.
[References]
[1] J.L. Simon, P. Bretagnon, J. Chapront, M. Chapront-Touzé, G. Francou, J. Laska, "Numerical expressions for precession formulae and mean elements for the Moon and the planets", ASTRONOMY AND ASTROPHYSICS, vol. 282, 663-683, 1994
Mechanical planetariums have been used for over 100 years, starting in 1923. But recently, digital planetariums have become more popular because they are easier to use and take up less space. Still, the machines inside digital planetariums are very complex.
This study looks at how planets are shown in a mechanical planetarium called the “Minolta Planetarium MS-10”(made by KONICA MINOLTA,INC.). The goal is to check how accurate the planet movements are in the MS10 compared to the real movements of the planets. This research also suggests ways to make the MS10 more accurate.
[Method]
In the MS10, a part called the "planet drives cage" is used to show the motion of the planets. This machine uses many gears with different numbers of teeth to create the movement. Because there were no official design documents for the MS10, the number of teeth on each gear was counted by hand. (Figure 1)
The study found that the ratio of Earth's orbit time to the orbit times of the other planets could be reproduced by using four or six gears.
Since the MS10 was made in 1966, the orbit times of the planets have changed slightly. Updated data was taken from a recent paper [1], and the new ratios were used as target values. (Table 1)
To find better gear combinations, a program written in VBA (Visual Basic for Applications) was used. This program tested new combinations that used the same number of gears and the same range of teeth as the original MS10.
[Results]
For Mercury, Venus, and Mars, better gear combinations were found. These new combinations showed the orbit times more accurately than the original MS10. (Figure 2)
The study compared the errors between the old MS10 values and the improved values to see how close they were to the real planet data. (Table 2)
[Discussion]
For Mercury, Venus, and Mars, which use four gears, the program successfully found better combinations. But for Jupiter and Saturn, which use six gears, the program needed too many calculations and couldn’t finish. In the future, a new method will be developed to help find better gear combinations for these two planets.
In the course of the study, a simple model of a planet drives cage was constructed. The next step is to design and build a new "planet drives cage" using the improved gear combinations from this study.
[References]
[1] J.L. Simon, P. Bretagnon, J. Chapront, M. Chapront-Touzé, G. Francou, J. Laska, "Numerical expressions for precession formulae and mean elements for the Moon and the planets", ASTRONOMY AND ASTROPHYSICS, vol. 282, 663-683, 1994