So We Really Don’t Orbit the Sun

Image courtesy of space.com
Image courtesy of space.com

Whether or not we consider Pluto a planet, it orbits the sun just like Earth and everything else we call a planet. Right?

Yes and no. While the sun lies roughly at the center of the solar system, there’s nothing in physics that sets it apart from any other celestial body in this system. Let’s start off with the basics.

Image courtesy of csep10.phys.utk.edu
Image courtesy of csep10.phys.utk.edu

As per the diagram, if two bodies of masses m1 and m2 exist without outside forces acting on them, then the center of mass (also known as center of gravity) is somewhere along the line of distance between them. Given the masses of the bodies, one can determine where this point is as per the relation

m1r1 = m2r2

Of course, this is not something you’ll find on planetary scales, for two reasons:

  1. Celestial bodies are always being influenced by outside forces.
  2. Solar systems are comprised of many bodies, not just two.

In systems with many bodies, you’ll need x, y, and z coordinates to find the center of mass, and you’ll have to have an equation for each coordinate. The equations look like this:

Image courtesy of hyperphysics.phy-astr.gsu.edu
Image courtesy of hyperphysics.phy-astr.gsu.edu

You really don’t need to grasp these equations; just know that you need the masses and distances from other bodies on all the bodies present in the system.  The center of mass of a system of bodies is a single point–not one of the bodies themselves.

Of course, in a system of bodies like the solar system, with something gigantic roughly in the center and smaller bodies within its gravitational grasp, it’s going to look like the planets orbit the sun. But what these bodies actually orbit is a location called the barycenter. Since the solar system is in constant motion, the location is always changing.

Something else to note: the sun orbits the barycenter too! Any star that has bodies in orbit does this. In fact, a relatively recent discovery in astronomy started with noticing the “wobble” in stellar positions.  Only stars with bodies in orbit (planets) will do this because it is the gravitational influence from these nearby bodies that causes the star to revolve about its barycenter in addition to its own rotation.

Related Links:

http://astro.unl.edu/naap/esp/centerofmass.html

https://en.wikipedia.org/wiki/Orbit

http://www.realclearscience.com/blog/2014/08/technically_the_earth_does_not_orbit_the_sun.html

http://www.qrg.northwestern.edu/projects/vss/docs/space-environment/3-orbital-lengths-distances.html

http://spaceplace.nasa.gov/review/dr-marc-solar-system/planet-orbits.html

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