Saturday, August 03, 2013

DESIGNING 2 YEAR RESONANCE

Period (T) of Asteroid Orbit
T= 2 yr = 730.5 days 
Semimajor Axis (a)
a = ∛(T2) = 1.58 AU
Perihelion (q)

q = a - c
    Focus (c)

c = a - q
    c2 = a2 -2aq + q2  
Semiminor Axis (b)

b2 = a2 - c2  
b2 = 2aq - q2  = q (2a - q)
b = √(q (2a - q))
Semi Latis Rectum ()
  = b2 / a
q
b
(AU)(AU)(AU)
0.10.550.19
0.20.770.37
0.30.930.54
0.41.050.70
0.51.150.84
0.61.240.97
0.71.311.09
0.81.371.19
0.91.431.29
11.471.37
For an orbit to be two years, semimajor axis, a, must be exactly 1.58 AUs in length.
All other parameters can vary within certain ranges.
Examples are shown in table to left.
Orbit's closest point to Sol, perihelion (q), independently varies from .1 AU to 1.0 AU;
q is kept no larger than 1.0 AU to assure intersection with Earth orbit.
Semiminor axis, b, depends on q and a.
Semilatus rectum, , depends on b and a.
Thanks to JPL/NASA for following:



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