astro: June 2015

As described in this MPML message, an interesting study is under way: its goal is to
measure the perihelion precession rates for a number of objects to quantify the effects of general relativity (GR) and solar oblateness.

More at http://mel.epss.ucla.edu/jlm/research/NEAs/GR/

Based on this list, we can get the following data:

Symbol	Description
H	Absolute magnitude
a	Semi-major axis (au)
e	Eccentricity
i	Inclination (deg)
P	Orbital period (days)
SLR	Semilatus rectum (au)
dr	Range rate due to GR/J2 (km/y)
dw	Perihelion shift (asec/century)
arc	Length of optical arc
nobs	Number of optical observations

Let's visually see how SLR, dr and dw are related:

Graph 1 - dw vs SLR (parameter = quartile of dr)

Graph 2 - dw vs dr (parameter = quartile of SLR)

Graph 1 - dw vs SLR (parameter = quartile of dr)

> quantile of dr (km/y)
     0%     25%     50%     75%    100% 
 48.800  55.425  66.300  80.300 171.000

Graph 2 - dw vs dr (parameter = quartile of SLR)

> quantileof SLR (au)
     0%     25%     50%     75%    100% 
0.17400 0.37400 0.48550 0.58675 0.66400

It seems to me that both graphs show (as expected) that the more an asteroid comes near the sun the more important is the dr effect.

The same is true for the dw effect but I do not understand this:

dw belongs to an area defined by two almost linear boundaries (the slope of the higher boundary is greater than the slope of the lower boundary , thus we see a "triangular shape"...)
Why does this happen?

Multiple regression

Coming back to easier considerations, there may be another way to show the relation between dw, dr and SLR.

Look at the multiple regression fit that predicts dw based on SLR and dr taking into
account the interaction between SLR and dr:

> summary(fit)

Call:
lm(formula = dw ~ SLR * dr, data = p)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.15438 -0.30660  0.04085  0.24131  3.13628 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -27.820350   0.981042 -28.358  < 2e-16 ***
SLR          -6.124334   1.318151  -4.646 1.15e-05 ***
dr            0.146494   0.006126  23.912  < 2e-16 ***
SLR:dr        1.038595   0.028026  37.059  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5601 on 90 degrees of freedom
Multiple R-squared:  0.9863, Adjusted R-squared:  0.9859 
F-statistic:  2163 on 3 and 90 DF,  p-value: < 2.2e-16

dw - Fitted values vs original values

This is the normal probability plot used to see how much the residuals of the model are
normally distributed:

Kind regards,
Alessandro Odasso

Due to their earth like orbit, these low delta-v asteroids move slowly when seen from earth. The resulting movement is very nice.

I tried to visualize asteroids which are likely to be lunar ejecta. I also add Bennu that moves much faster but it is interesting to see how it gets "near" to the earth during the Osiris-REx mission

All the other asteroids are sorted by Delta-V.

The last two asteroids have a very low eccentricity.

The following graphs show their movement in the next 10 years: