14) holds if the radius r is replaced by the semimajor axis a:
When the outer particle approaches the moon, the particle is slowed down (loses angular momentum) and, provided the initial difference in semimajor axis is not too large, the particle drops to an orbit lower than that of the moon.
Therefore the system is deterministic and at any given time the orbital elements of the particle (such as its semimajor axis and eccentricity) can be calculated from its initial position and velocity.
2065 for the semimajor axis and eccentricity, respectively.
The corresponding initial values of the heliocentric semimajor axis and eccentricity are a [sub.
Figure 7 shows the variation of the semimajor axis of the asteroid, a, over the same time interval as shown in Fig.
FIGURE 7 The semimajor axis as a function of time for an object using the same starting conditions as in Fig.
FIGURE 10 The semimajor axis as a function of time for an object using the same starting conditions as in Fig.
The semimajor axis of the elliptical orbit has now increased to a little more than 1 a.
At that time the semimajor axis returns to being a little smaller than 1 a.
So why does the semimajor axis of 1986 TO's orbit fluctuate - with a period of nearly eight centuries - between being a little smaller and a little larger than 1 a.
My diagram at top left illustrates the variation of the orbit's semimajor axis.