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Question:
It is my understanding that the orbits of the planets are influenced mainly by the mass of the sun, with some lesser influences from other orbiting bodies. How is it possible for the sun to exert a gravitational pull on bodies so far away to keep them in orbit, especially with the high velocities these bodies orbit at? As massive as the sun is, I cannot imagine how it would hold the outer planets in its grasp, being so minuscule a body in respect to the distances involved.



Replies:
The Sun is hardly "minuscule," as it comprises practically all of the mass of the Solar System. The force of gravity decreases as the square of the distance from the attracting object (1/d^2), which never actually goes to zero, no matter how large the distance d becomes.

The Solar System also orbits the center of the Milky Way galaxy, although that is much farther away than the Sun is from the planets. Our galaxy, in turn, is being pulled toward the Virgo cluster of galaxies, which is farther still...

Richard Barrans
Department of Physics and Astronomy
University of Wyoming


Great question. It’s true that even distant planets have fairly high orbital (“tangential”) velocities, although the velocities do decrease with distance from the sun. But what’s more critical is the *angular* velocity. For example, Pluto (ignoring its recent demotion from “planetary” status) is tangentially whizzing through space fairly quickly, but because it takes nearly 250 earth years to orbit the sun, its angular velocity is not high, and that’s what determines centrifugal force.

To see this mathematically, recall centripetal force is m*v^2 (where v is tangential velocity) and gravitational force is g*m1*m2/r^2. Setting these forces equal to each other, you arrive at G*m = r*v^2 (m here is the sun’s mass). G and m are constants, so this says as r (planets distance to sun) multiplied by *tangential* (not angular) velocity equals a constant. If you make a table of the planetary distances and their corresponding *tangential* velocities squared, and multiply them, you’ll see a pattern emerge.

On a related topic, some people (my younger self) have been puzzled that both Jupiter and Pluto could both be outer planets and have stable orbits with such a mass difference (when younger, I thought Jupiter should be "flung off"). You have probably realized that planetary *mass* plays no role. Massive planets have stronger gravitational force, but that’s balanced by an equally stronger centrifugal force, and vice versa.

P. Bridges



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