Given the current state of the Solar System if the mass of a planet - say Mercury were to be increased or decreased would it still orbit at the same distance from the Sun or would more or less mass move it to a greater or lesser orbital distance?
Okay, I am nothing more than an amateur astronomer. Here is my understanding of the above question. If this is wrong or oversimplified let me know...I am sure someone will do just that
For a revolving or rotating system with
no outside force applied...
Angular Momemtum= mass X velocity X radial distance from the center
This must be conserved, that is the product of m times v times r must remain constant...
example 1. when a spinning skater compresses herself by withdrawing her arms and crouching she is decreasing the radius of the system, since her mass remains the same, her velocity must increase...so she spins faster
example 2. likewise when a sportscar enters a turn, the driver presses on the gas pedal accelerating the vehicle, since mass is the same, the radial distance from the center must decrease...so the car tightens the curve
Now for the Mercury question, assuming no outside (electrical or otherwise?) force is applied, if Mercury gained mass then conservation of angular momemtum would demand that it's orbital velocity and distance from the Sun (or some combination thereof) decrease, that is move into a smaller orbit.
If Mercury lost mass- some combination of increases in orbital velocity and distance from the Sun would be required, but...
A complication however, Keplers Laws of Planetary Motion would require that planets on inner orbits have a greater orbital velocity than planets on orbits that are further out. So if Mercury increased mass and moved into a smaller orbit then it's orbital velocity must increase accordingly, so an increase in mass could only result in a smaller orbit (not a decrease in orbital velocity), and vice versa for a decrease in mass.
So,
mass - increase, then distance from the Sun - decrease.
mass - decrease, then distance from the Sun - increase.
Again, I am strict amateur, corrections anyone?
Nick