YARKOVSKY EFFECT AND SOLAR RADIATION PRESSURE DETERMINATION
The orbit of smallsized asteroids can be affected by nongravitational perturbations. When this happens, nongravitational forces need to be taken into account in the orbit determination process since they are as important as collisions and gravitational perturbations for the overall understanding of the asteroid orbital evolution.
The Yarkovsky effect and the Solar Radiation Pressure (SRP) are nongravitational perturbations that can be modelled knowing the physical properties of asteroids, and whose consequences on the motion can be measured from accurate astrometry. The knowledge of the physical properties of asteroids is usually not sufficient to produce the thermophysical models needed for the computation of the Yarkovsky acceleration. Nevertheless, it can often be measured as a semimajor axis drift if the astrometric dataset contains extremely accurate observations (e.g. radar data), or if the observations span a sufficiently long time interval. In (Farnocchia et al. 2013), a list 21 NEAs with a measurable semimajoraxis drift is provided.
Since 2013, the number of asteroids for which it is possible to detect the Yarkovsky effect has grown. This is due to the increased quality and time span of the observations, and to new radar measurements that have since become available. We are able to detect the Yarkovsky effect for more than 40 NEAs, employing a high precision dynamical model, including the Newtonian attraction of 16 massive asteroids and the planetary relativistic terms, and a suitable astrometric data treatment. Hereinafter, we present a list of objects with a significant detection of the Yarkovksy effect and which have a value compatible with the Yarkovsky mechanism.
The inclusion of nongravitational perturbations also affects the results of the impact monitoring, as for (410777) 2009 FD, (29075) 1950 DA, (99942) Apophis and (101955) Bennu. Currently, these cases are the only ones for which the impactor tables are computed by including the Yarkovsky effect.
THE METHOD
Yarkovsky effect
We started our procedure taking into account the list of objects in the NEODyS database having a semimajor axis formal uncertainty less than 3· 10^{9}. For each one of them we performed an orbital fit for the intial conditions together with the Yarkovsky parameter A2.
After the A2 parameter determination, to discern the significance of the estimated semimajor axis drift, we considered the signaltonoiseratio (SNR) of the A2 parameter, selecting those object with SNR ≥ 3, and by carefully analyzing peculiar cases. In particular, we computed a reliability parameter S to check if the value computed is physically realistic and consistent with the presumed Yarkovsky mechanism. In order to compute S, we made use of the calibration for the Yarkovsky effect used in (Spoto et al. 2015), if the needed physical information were available, or we used the simplified computation as in (Farnocchia et al. 2013). Then we selected those object with S ≤ 1.5, even if a further analysis was needed to handle specific cases.
Direct solar radiation pressure
For particularly small objects, it is meaningful to include also the solar radiation pressure in the orbital fit. We computed the areatomass ratio (A/M) from a spherical model, and we converted it into the parameter A1, coefficient of the radial acceleration in the nongravitational model. These computations have been done for the four objects also the JPL currently has in its Small Body Database. They are 2011MD, 2012LA, 2006RH120 and 2009BD.
RESULTS
Hereinafter, a table summarizes the results obtained by the computation explained in the previous section, sorted for decreasing SNR. We report only the valid detection (i.e. SNR ≥ 3 and S ≤ 1.5). This is a work in progress, therefore further analysis will be done on the remaining objects. A paper containing all the results is in preparation.


The following table is for the four objects for which we computed also the A1 parameter.
Object name  A2  SNR  A1  SNR 

10^{15} au/d^{2}  10^{15} au/d^{2}  
2009BD  1143.12 +/ 79.89  14.31  54204.91 +/ 7796.41  6.95 
2006RH120  50468.80 +/ 3786.68  13.33  124007.53 +/ 4743.11  26.14 
2011MD  19726.28 +/ 27035.20  0.73  80554.42 +/ 18970.72  4.25 
2012LA  4906.52 +/ 12832.10  0.38  81155.96 +/ 16299.59  4.98 