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When you use the Small-Body Data Browser of JPL Solar System Dynamics and do the search for asteroid 2015 YA, and after that push the [ show orbit diagram ] button, you can see that on october 12, 2018 this asteroid will have a close encounter with Venus.

With the present knowledge of 2015 YA and its orbital elements and perturbations , is it possible to predict how close the encounter will be and what will be the necessary calculations ?

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    $\begingroup$ You would not want to use an osculating orbit for a question like this. Osculating orbits are phony orbits and valid for only one instant in time. I think you'd like to ask about the real predicted trajectory in the best possible ephemeris. $\endgroup$ – uhoh Jul 14 '18 at 9:05
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    $\begingroup$ @uhoh Yes you're right, i will change the sentence somewhat. $\endgroup$ – Conelisinspace Jul 14 '18 at 9:22
  • $\begingroup$ How close is the encounter when compared to the diameter of Venus? $\endgroup$ – Uwe Jul 14 '18 at 12:59
  • $\begingroup$ @Uwe Close encounter in km please . Is this time the asteroid not big enough for you ? :) $\endgroup$ – Conelisinspace Jul 14 '18 at 14:59
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The JPL Small Body Database has the answer to the specific question in its Close Approach Table (only some columns kept here):

Date/Time (TDB) Time Uncertainty (days_HH:MM) Body Nominal Distance (au) Minimum Distance (au) Maximum Distance (au)

2018-Oct-19 15:01 03:08 Venus 0.083402183093844 0.0807857117393986 0.0861169334256464

0.083 au is about 12.4 million kilometers, or roughly 2,000 Venusian radii. In other words, not close.

In the longer term, 2015 YA's passes by Venus, Mars and Earth make its orbit interesting in the long term. There have been several studies, of which the most accessible seems to be C de la Fuente Marcos and R de la Fuente Marcos's "A trio of horseshoes: past, present and future dynamical evolution of Earth co-orbital asteroids 2015 XX169, 2015 YA and 2015 YQ1" (2016):

Its orbital elements show that its path is more eccentric (e = 0.27914) and less inclined (i = 1◦. 6) than that of 2015 XX169 . This opens the possibility of closer encounters with the Earth —its MOID with our planet has a value of 0.0036 AU— and even relatively close approaches to both Venus (at per- ihelion) and Mars (at aphelion). Evolving within this dynamical context, 2015 YA must be less stable than 2015 XX169. It is however a member of the NHATS list, NASA’s list of viable NEAs for an actual human exploration mission.

This asteroid is currently a member of the Aten dynamical class but before its recent encounter with the Earth on 2015 December 15 it was an Apollo. It will remain as an Aten for the next 142 years and then return to the Apollo dynamical class. Its short-term dynamical evolution is displayed in Fig. 4 (nominal orbit). It arrived very recently to the Earth co-orbital zone and it may leave in a few hundred years. Its orbital evolution is far more chaotic than that of 2015 XX169. As in the previous case, the object follows an asymmetric horse- shoe path with respect to the Earth with the value of the relative mean longitude librating around 180◦, but enclosing 0◦(see Fig. 4, panel C). The short-term evolution of the value of its semi-major axis is rather irregular (see Fig. 4, panel D) although it switched between the Apollo and Aten dynamical classes very recently and it will switch back to Apollo in the future.

If we just want to understand the general pattern, it's possible to extrapolate the general motion:

The past long-term evolution of 2015 YA strongly suggests that its semi-major axis started to reach values similar to that of our planet nearly 30 kyr ago (see Fig. 6). It also includes phases in which the behaviour of the argument of perihelion is consistent with what is expected when a Kozai resonance is in effect (see Fig. 6, panel G) but the evolution of the eccentricity (see Fig. 6, panel E) does not exhibit the oscillatory behaviour that is observed, for instance, in the case of 2015 XX169. The positions of the nodes oscillate more or less regularly (see Fig. 6, panel H) and the closest encounters with our planet often coincide with the time when both nodes are in the path of the Earth. The dynamics of this object is currently controlled by encounters with Venus and the Earth-Moon system, but Mars may also be an important perturber in the future.

But our measurements are (currently) poor, and the the orbit it substantially chaotic, so that even after a few hundred years we can't make precise predictions:

The analysis of the effect of the errors in Table 1 on the evolution of the orbital parameters displayed in Fig. 5 shows that the value of its Lyapunov time was very short —below 100 yr— in the past and it will be only slightly longer in the future (a few hundred years).

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  • $\begingroup$ @ Thank you very much for this extensive answer ! Chaotic creatures, those asteroids ! $\endgroup$ – Conelisinspace Jul 15 '18 at 10:33

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