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Calculate the scaled planet diameters and planet-sun distances for a solar system model. Enter scale or diameter or distance, select to show table and/or map below, select options, then press Calculate.
- Solar System Model Links
Click the links below to go to the Solar System Scale Model...
- Instructions for Website Developers
Model distance of planet from the sun. Location parameters;...
- Solar System Model Links
You can use the center of mass formula. Set the origin of your coordinate system at the center of the Earth, then $\vec{r}_1 = \vec{0}$ and $\vec{r}_2 = d$ and $$r_{center} = \frac{m_1r_1+m_2r_2}{m_1+m_2} = \frac{m_2}{m_1+m_2} \cdot d$$ as you have as well.
A sheet is provided in this module with scale distances to be used with the planet sheets. See also http://www.exploratorium.edu/ronh/solar_system/ for other/custom scales.
distance scale 1 cm : 1 astronomical unit (note the mention of lower-case) or 149,597,870.7 km. Provide a simple ruler, a pencil, and an example, and have students make their own to take home. Tape the information onto the back of the sheet, for those who want to keep the actual numbers.
This data will allow you to make a scale model of the solar system. For younger students, do a distance-only model. For older students, you might want to scale the size of the planets to the same scale as for the distances.
Understanding the size differences of objects in the solar system as well as their correct distances from each other is important. There are many good projects that will show you how to make your own scale model.
Calculate using a spreadsheet: Download the Scale Distance spreadsheet (XLSX or CSV). Create a formula in your spreadsheet that will calculate the distance from the Sun to each planet (in centimeters) in your model. The formula should multiply the AU value by the number of centimeters you want each AU to represent, your scale value.
