On the impact of the Yarkovsky effect on Apophis’ orbit

In October 2009, a new set of optical observations of Apophis, a potentially hazardous asteroid, was published. These data have significantly expanded the interval of observations and their total number. In the article we compare the results of refinement of Apophis’ orbit made at the Jet Propulsion Laboratory (JPL, United States), the University of Pisa (Italy), and the Institute of Applied Astronomy (IAA) of the Russian Academy of Sciences with consideration for new observations. New orbits lead to a significant decrease in the probability of Apophis’ collision with the Earth in 2036. As a result of processing a large number of observations of asteroids approaching the Earth and main belt asteroids less than 40 km in size, with a large number of optical and, in many cases, radar observations in different oppositions, one of the authors revealed that additional acceleration affects their motion. This acceleration can be represented by the transversal component A ₂ in the orbital coordinate system. The presence of this acceleration can be interpreted as the Yarkovsky effect. The statistical properties of distribution of A ₂ for asteroids, for which it is determined quite reliably, evidence in favor of this interpretation. The value of additional acceleration for bodies the size of Apophis falls in the range ±10⁻¹³ AU/day². In this paper we have calculated the probability of Apophis colliding with the Earth in 2036 at different values of the transversal component of additional acceleration A ₂. For the resulting points, a plot of the probability of the collision against the A ₂ value has been constructed. At A ₂ = −8.748 × 10⁻¹⁴ AU/day² (and zero values of the radial A ₁ and normal A ₃ components) the nominal solution for Apophis’ orbit on April 13, 2029, is only 90 m from the middle of a “keyhole” 600 m in width, which leads to a collision of Apophis with the Earth in 2036. Since the scattering ellipse in the target plane in 2029 significantly overlaps the keyhole, the probability of collision at the given additional acceleration value is 0.0022. This result has been verified by the Monte Carlo method. Tests of 10000 random sets of orbital elements, which were found taking into account their correlation, have shown that 22 cases have resulted in virtual asteroids colliding with Earth in 2036. A plot of the probability of the collision against the value of A ₂ has been constructed.     

Spatial and temporal variations in infrared emissions of the upper atmosphere. 2. 15-μm carbon dioxide emission

The results of rocket and satellite measurements of carbon dioxide emissions at a wavelength of 15 μm in the upper atmosphere have been systematized and analyzed. Analytical expressions describing the dependence of the altitude distribution of 15-μm CO₂ emission intensity and its variation in the altitude range from 100 to 130 km on the season, latitude, and solar activity have been obtained.     

Seasonal and Long-Term Changes in the Intensity of O2(b1Σ) and OH(X2Π) Airglow in the Mesopause Region

Geomagnetism and Aeronomy - Spectral observations of the mesopause airglow at the Zvenigorod Scientific Station have been used to obtain the midnight emission intensities of molecular oxygen...     

The influence of the correlations between an asteroid’s orbital parameters on the estimation of the probability of planetary collision by the Monte Carlo method

The probability of an asteroid colliding with a planet can be estimated by the Monte Carlo method, in particular, through the statistical simulation of the possible initial conditions for the motion of an asteroid based on the probability density distribution set by the respective covariance matrix to be further projected with the orbital model onto the supposed time point of the collision. Hence, the collision probability is calculated as the ratio between the number of projected (virtual) asteroids striking the planet and their total number. The main problem is that different elements of the initial conditions (orbit or state vector) are correlated and, therefore, cannot be simulated independently. These correlations are reflected in the nondiagonal covariance matrix of the solution. The matrix is diagonalized by an orthogonal transformation. In the uncertainty domain constructed from the diagonal matrix elements, the initial values for each of the six orbital elements are simulated independently from the other elements, but with the accounting for their normal distribution. The program for calculating the normal distribution is based on the central limit theorem. Each sample of the initial values for the six orbital elements is transferred to the initial reference frame using an inverse transformation. Then, numerical integration is used to track the asteroid’s motion along the respective orbit to predict a possible impact event. Asteroids 99942 Apophis and 2007 WD5 are used as examples to show that disregarding the correlations when diagonalizing the covariance matrix to set the initial conditions may seriously distort the collision probability estimates. The paper gives the probabilities of the collisions of Apophis with the Earth and asteroid 2007 WD5 with Mars calculated by the author from observation sets showing nonzero collision probabilities. The author’s estimates are compared to those calculated by NASA.