Near-circular satellite orbits in an oblate, diurnally varying atmosphere

1983 ◽  
Vol 389 (1796) ◽  
pp. 153-170 ◽  
Keyword(s):  
Gravitational Field ◽  
Differential Equations ◽  
Diurnal Variation ◽  
Numerical Solution ◽  
Initial Conditions ◽  
Satellite Orbits ◽  
Atmospheric Parameters ◽  
Orbital Elements ◽  
Air Drag ◽  
Circular Satellite

The influence of air drag and the geopotential on near-circular satellite orbits, eccentricity e < 0.01, is considered. A model of the atmosphere is adopted that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation. Differential equations governing the variation in e and the argument of perigee ω are derived by combining the effects of air drag with those of the Earth’s gravitational field. These are solved numerically using initial conditions obtained from a series of computed orbits of the satellite 1963-27 A. The behaviour of the orbital elements predicted by the numerical solution is compared with the observed elements to test the developed theory, and to obtain values of atmospheric parameters at heights near 400 km.

A method for the estimation of errors propagated in the numerical solution of a system of ordinary differential equations

1966 ◽  
Vol 25 ◽  
pp. 281-287 ◽  
Author(s):  
P. E. Zadunaisky
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Initial Conditions ◽  
Current Theory ◽  
Numerical Process

Let bex′=f(t,x) a system of ordinary differential equations, with initial conditionsx(a) =s, which is integrated numerically by a finite difference method of orderpand constant steph.To estimate the truncation and round-off errors accumulated during the numerical process it is established a method based on the current theory of the asymptotic behaviour (whenh→0) of errors. This method should avoid the main difficulties that arise when the results of the theory must be applied to practical cases. The method has been successfully tested and applied to estimate the errors accumulated in a numerical computation of planetary perturbations on the orbit of a comet.

The advance of the perigee of a satellite in a rotating oblate atmosphere with a diurnal variation in density

1983 ◽  
Vol 389 (1797) ◽  
pp. 433-444 ◽  
Keyword(s):  
Diurnal Variation ◽  
Scale Height ◽  
Satellite Orbits ◽  
Third Order ◽  
Air Drag ◽  
Small Eccentricity ◽  
Density Scale

The effect of air drag on satellite orbits of small eccentricity, 0.01 ≾ е ≾ 0.2, is considered. A model of the atmosphere that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation, is adopted. The equation governing the changes due to drag in the argument of perigee ω , during one revolution of the satellite, is integrated with the assumption that the density scale height H is constant. The resulting expression for e ∆ ω is presented to third order in e . Compact expressions for e ∆ ω and e ∆ ω / ∆ T D , where ∆ T D is the corresponding change in the period, are obtained when H is allowed to vary with altitude. It is shown that there is an equivalence between the variable- H and the constant- H equations, provided that the value of H used in the latter is chosen appropriately.

The numerical solution of linear stiff differential equations

1972 ◽  
Vol 71 (3) ◽  
pp. 505-515 ◽  
Author(s):  
J. R. Cash
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Initial Conditions ◽  
Stiff Differential Equations ◽  
General Method

AbstractA general method is given and illustrated by application to particular cases for obtaining subdominant solutions of stiff difference and differential equations, i.e. when rapidly varying solutions – transients or otherwise – are possible but are in fact excluded by the initial conditions.

The numerical solution of systems of stiff ordinary differential equations

1974 ◽  
Vol 76 (2) ◽  
pp. 443-456
Author(s):  
J. R. Cash
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Complete Solution ◽  
Step Length ◽  
Rate Of Change ◽  
First Order ◽  
Stiff Ordinary Differential Equations ◽  
Iterative Procedures

AbstractAlgorithms are developed for the numerical solution of systems of first-order ordinary differential equations, the solutions of which have widely different rates of variation. The iterative procedures described use a step length of integration proportional to the rate of change of the required slowly varying solution in a region of integration, where either the transient components of the complete solution have become negligible compared with the chosen working accuracy or in a region where rapidly increasing components of the solution are theoretically possible but are made absent by the initial conditions. Several numerical examples are given to demonstrate the algorithms.

Effects of air drag on near-circular satellite orbits

1964 ◽  
Vol 1 (5) ◽  
pp. 513-519 ◽  
Author(s):  
J. OTTERMAN ◽  
K. LICHTENFELD
Keyword(s):  
Satellite Orbits ◽  
Air Drag ◽  
Circular Satellite
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