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