# Planetary Systems

How does one know the correct position of planets in relation to the sun when viewing the solar system from different angles makes the appearance of the planets different? I would think that it would require a satellite to orbit in a circular pattern above and below the entire solar system to get correct bearings.

-

## 1 Answer

One perspective (heh) involves the following relation among position vectors: $$\vec{r}_{A\rightarrow C} = \vec{r}_{A\rightarrow B} + \vec{r}_{B\rightarrow C}.$$ These position vectors can be for anything; object $A$ could be a house, object $B$ an ant, and object $C$ a leaf on the river. Here's a diagram to help:

So if you want to know the position of object $C$ relative to object $A$ (the bold dark arrow), you just have to know the position of some other object $B$ relative to those others.

To answer your question, you can apply this same idea to the solar system: $$\vec{r}_{\mathrm{Sun} \rightarrow X} = \vec{r}_{\mathrm{Sun} \rightarrow \mathrm{Earth}} + \vec{r}_{\mathrm{Earth} \rightarrow X}.$$ Or in pictures:

The position of planet $X$ relative to the sun (bold dark arrow, which is what we want) can be found if we know Earth's position relative to the Sun and planet $X$'s position relative to Earth. In this way, measurements of a planet's position as measured from here on Earth can be used to get a map of the solar system..

There is the added complication of knowing distance to planets and coming up with a convenient coordinate system in order to actually come up with values for these position vectors. Others may have better information on that.

-
ok, can you dumb that down into laymen's terms, I'm just a curious, not a physics major. –  user42744 Apr 4 '14 at 16:35
The paragraph that starts with "The position of planet $X$" summarizes how it could be done. You only need to know where Earth is relative to the Sun, and where the planet is relative to Earth. I'll try to get some diagrams up. –  BMS Apr 4 '14 at 16:36
Thanks, but again, isn't that based on perspective from planet to sun. It sounds the basis of our solar system and how it looks is directly related from Earth's perspective. –  user42744 Apr 4 '14 at 16:40
No need to accept this answer if you don't believe it addresses your concern. Others may come along and do a better job. –  BMS Apr 4 '14 at 18:21
That never happens. I accept it from the standpoint that our perception of the solar system is based off every things position relative to the earth. That's how I am perceiving it. –  user42744 Apr 4 '14 at 18:26