TY - JOUR

T1 - Averaged Equations of Motion for a Perturbing Acceleration which Is Constant in Various Reference Frames

AU - Sannikova, T.N.

AU - Kholshevnikov, K.V.

PY - 2014

Y1 - 2014

N2 - The motion of a zero-mass point under attraction to the central body and a disturbing acceleration $\mathbf P$ is considered. We suppose the vector $\mathbf P$ being constant in three mostly used in astronomy reference frames: the main inertial one $\mathcal O$, and two orbital ones $\mathcal O_k$ with $x$-axis directed along the radius-vector if $s=1$, and along the velocity vector if $s=2$. The ratio of $|\mathbf P|$ to the main acceleration due to the attraction to the central body is supposed to be small. Averaging transform is applied to the equations in osculating elements in the first order with respect to the small parameter. Closed expressions for the functions describing the change of variables as well as for the right-hand parts of equations in averaged elements are obtained. All functions appeared in the frames \mathcal O$, $\mathcal O_1$ are elementary; elliptical integrals emerge in the frame $\mathcal O_2$. All quantities we need are developed in series in powers of the eccentricity $e$ converg

AB - The motion of a zero-mass point under attraction to the central body and a disturbing acceleration $\mathbf P$ is considered. We suppose the vector $\mathbf P$ being constant in three mostly used in astronomy reference frames: the main inertial one $\mathcal O$, and two orbital ones $\mathcal O_k$ with $x$-axis directed along the radius-vector if $s=1$, and along the velocity vector if $s=2$. The ratio of $|\mathbf P|$ to the main acceleration due to the attraction to the central body is supposed to be small. Averaging transform is applied to the equations in osculating elements in the first order with respect to the small parameter. Closed expressions for the functions describing the change of variables as well as for the right-hand parts of equations in averaged elements are obtained. All functions appeared in the frames \mathcal O$, $\mathcal O_1$ are elementary; elliptical integrals emerge in the frame $\mathcal O_2$. All quantities we need are developed in series in powers of the eccentricity $e$ converg

KW - Averaged equations

KW - disturbing acceleration

U2 - 10.1134/S1063772914120099

DO - 10.1134/S1063772914120099

M3 - Article

VL - 58

SP - 945

EP - 953

JO - Astronomy Reports

JF - Astronomy Reports

SN - 1063-7729

IS - 12

ER -