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Saturday, October 8, 2016

Amor - H mag vs Tisserand (ONLY Tp < 3)

I refer to my previous post. Following some comments from Alan Harris, I have re-drawn the relation H mag vs Tisserand with respect to a planet with generic semi-major axis ap taking into account ONLY those asteroids that have Tp < 3.

Amor - Method 1
Method based on Spearman correlation.

Having filtered only those asteroids that have Tp < 3, I have to restrict the range where the semimajor axis ap can vary:

0.35 AU <= ap <= 3 AU

For the purpose of the next plot, this is a table showing the orbital parameters of the planets:


Semimajor
Axis
(AU)
Orbital
Period
(yr)
Orbital
Speed
(km/s)
Orbital
Eccentricity
(e)
Inclination
of Orbit
to Ecliptic
(°)
Rotation
Period
(days)
Inclination
of Equator
to Orbit
(°)
Mercury 0.3871 0.2408 47.9 0.206 7.00 58.65 0
Venus 0.7233 0.6152 35.0 0.007 3.39 -243.01* 177.3
Earth 1.000 1 29.8 0.017 0.00 0.997 23.4
Mars 1.5273 1.8809 24.1 0.093 1.85 1.026 25.2
Jupiter 5.2028 11.862 13.1 0.048 1.31 0.410 3.1
Saturn 9.5388 29.458 9.6 0.056 2.49 0.426 26.7
Uranus 19.1914 84.01 6.8 0.046 0.77 -0.746* 97.9
Neptune 30.0611 164.79 5.4 0.010 1.77 0.718 29.6
 This is the plot showing the correlation between H mag and Tp calculated for various values of semimajor axis ap expressed in AU:
I have added the following vertical lines, showing the ap of the planets:
  • blue line - Mercury
  • green line - Venus
  • red line - Earth
  • magenta line - Mars
I wonder whether the planets are truly responsible for the peaks that we see in this plot.
This is probably true for Earth, because the peak is located at ap = 1.0 AU
Not clear if we can claim that this is true for Mercury and Venus.
In the case of Mars, this is less convincing: the peak next to Mars is not located at ap=1.52 AU but slightly greater.

Boxplot for ap=0.3871 AU

we only have 79 asteroids, with tp < 3, belonging to these Tp quartiles.
> summary(p1$tsquartile)
[-0.299,2.34]   (2.34,2.58]   (2.58,2.89]      (2.89,3]
           20            20            19            20



Boxplot for ap=0.7233  AU
In this case we have 746 asteroids with T<3
> summary(p1$tsquartile)
[-0.198,2.68]   (2.68,2.85]   (2.85,2.94]      (2.94,3]
          187           186           187           186

Boxplot for ap=1.0 AU
In this case we have 3668 asteroids with T<3
> summary(p1$tsquartile)
[-0.15,2.82]  (2.82,2.93]  (2.93,2.97]     (2.97,3]
         917          917          917          917


Boxplot for ap=1.65 AU
It turns out that the peak next to Mars semimajor axis is located at about ap= 1.65 AU
In this case we have 5617 asteroids with T<3
> summary(p1$tsquartile)
[-0.0765,2.66]    (2.66,2.75]    (2.75,2.83]       (2.83,3]
          1405           1404           1404           1404



Finally, I would like to see if the method2 based on Chi-squared test gives a similar answer.

Amor - Method2
Method based on Chi-squared statistic (see previous post):

In this case the effect of Mercury (if real) can not be seen.
Much more clear, if real, the effect of Earth and Mars ... some doubts about Venus.


Cheers,
Alessandro Odasso

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