Arrowstar
Probenaut
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- May 23, 2008
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Hi all,
I've been looking into alternative methods to determine the flight path of a body other than by direct numerical integration of Newton's second law (sum the gravity forces, determine velocity, determine position). In particular, I've been thinking about how I might use mechanical energy relationships to determine the flight path of an orbit. Since the total mechanical energy of an ideal orbit is constant, this would appear to be a great way to determine velocities/positions directly.
I've run into two problems. First, when looking at kinetic energy, I notice that the velocity vector is replaced with the scalar velocity magnitude, removing any direction information from that vector. This is obviously a problem, as not knowing which way you're traveling means you can't propagate your orbit. Second, when dealing with potential energy, how does one deal with multiple sources of gravity? It's real easy when you're a block floating above a flat plate with only one gravity source, but it seems to get more complicated when you attempt to put said block around the Sun with the various planets acting on it.
Are these issues resolvable? Using energy/work seems like an advantageous way to do things, if you can get it to work. Any tips or insight would be appreciated!
Thanks!
I've been looking into alternative methods to determine the flight path of a body other than by direct numerical integration of Newton's second law (sum the gravity forces, determine velocity, determine position). In particular, I've been thinking about how I might use mechanical energy relationships to determine the flight path of an orbit. Since the total mechanical energy of an ideal orbit is constant, this would appear to be a great way to determine velocities/positions directly.
I've run into two problems. First, when looking at kinetic energy, I notice that the velocity vector is replaced with the scalar velocity magnitude, removing any direction information from that vector. This is obviously a problem, as not knowing which way you're traveling means you can't propagate your orbit. Second, when dealing with potential energy, how does one deal with multiple sources of gravity? It's real easy when you're a block floating above a flat plate with only one gravity source, but it seems to get more complicated when you attempt to put said block around the Sun with the various planets acting on it.
Are these issues resolvable? Using energy/work seems like an advantageous way to do things, if you can get it to work. Any tips or insight would be appreciated!
Thanks!
