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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.
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.
Scale Model of the Solar System Goals: To get an idea of the scale of the solar system with the sizes of the planets. To be able to correctly change from “real” distances to scale distances. What You Turn In:
Using data from text appendix, determine how far the center of mass of the Earth-moon system is from the center of Earth. Compare this distance to the radius of Earth, and comment on the result. Ignore the other objects in the solar system.
At the 1" solar scale, the distances between planets can be up to 100 feet. Strongly suggest at least two presenters - three preferred. One each at the Sun, Neptune and walking back
Some Solar System models attempt to convey the relative scales involved in the Solar System in human terms. Some are small in scale (and may be mechanical—called orreries)—whereas others extend across cities or regional areas. [63]
Distances in the Solar System • Distance to Venus can be obtained using radar ranging • Send signal, determine how long it takes to return • Radio waves move at the speed of light, which is known (3 × 108 m/s) • Calculate distance: distance = (speed of light) (time taken× for signal to return)/2
