|MadSci Network: Astronomy|
Hi, Brent The masses of the planets don't matter when determining their orbits. What counts on this situation is the equilibrium between the gravitational attraction and the centripetal force. Look at these equations: Fc = (mv^2)/r and Fg = (GMm)/r^2 Where Fc is the centripetal force, Fg the gravitation, m is planet's mass, M is Sun's mass, v is the orbital velocity of the planet (which is really not constant, but we can consider it this way) and r is the orbit's radius. G is the gravitation constant. Its value is 6.67E-11 m^3/(s^2 * kg). The orbits are stable, otherwise we wouldn't be here to discuss this problem! So, the attractive force (gravity) has to be equal to the centripetal force, which tends to make the planet escape from its orbit. Fc = Fg (mv^2)/r = (GMm)/r^2 and with some simple manipulation: r = (GM)/v^2 As you can see, the radius of the orbit doesn't depend on the planet's mass. It depends only on the Sun's mass, and inversely on square velocity. What determines the position of the planets in any solar system is the system's initial conditions, which aren't well known... yet! The initial angular momentum, the mass distribution discontinuities in the dust cloud that originated our solar system (or any other), and some other factors, were the conditions that led the planets to be arranged this way. Yes, they were "built" about 5 billion years ago on almost the same orbit they have today! Any cruel doubts to email@example.com D!
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