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首页> 外文期刊>International Journal of Applied Mathematics and Theoretical Physics >Numerical Model of Perturbated Earth's Satellite Orbit
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Numerical Model of Perturbated Earth's Satellite Orbit

机译：摄动地球卫星轨道的数值模型

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The study aimed to develop a two-dimensional numerical model of a perturbed Earth's satellite orbit under the influence of the Moon. The first step was to model, numerically, the Earth-satellite orbit. The interaction was assumed to be first order. The basis of the model was that for two-dimensional motion, influence in the radial direction does not affect the motion in the tangential direction and vice versa. Based on this, the satellite's motion was decomposed into radial and tangential directions. The trajectory was segmented into time intervals and the curve swept over each interval was approximated as a straight line with the assumption that acceleration in each interval was constant. Equations of constant accelerated motion were used to describe the motion of the satellite over each interval. When the model results were compared with the exact solution, for an elliptical orbit, they matched perfectly well over the entire orbit with a maximum relative error of 0.079%. When it was tested for other orbits, circular, hyperbolic, etc., it retained all of them according to theoretical predictions. The model was then extended to incorporate the effects of the Moon by launching the satellite at quarter, half and three-quarter distance from Earth to Moon. A circular orbit was used to model the effects of the Moon. The acceleration results of the model were compared with theoretical predictions. The corresponding errors in the acceleration for the three positions of launch were 0.019% and 0.20%. This showed that this model is applicable for predicting perturbated satellite orbit and it can be applied with any extra force to describe perturbated orbit of the satellite. It can also be used to model the trajectory of projectile motion, of which the exact solution is incapable of generating. Since this model gives the speed of the satellite at any instant, it can be applied when the orbit needs to be changed as it can be used to compute the required new speed.
机译：该研究旨在建立一个受月球影响的地球卫星轨道的二维数值模型。第一步是对卫星地球轨道进行数值模拟。假定交互是一阶的。该模型的基础是，对于二维运动，径向方向的影响不影响切线方向的运动，反之亦然。基于此，卫星的运动被分解为径向和切线方向。轨迹被划分为时间间隔，并且假设每个间隔的加速度是恒定的，则在每个间隔上扫描的曲线近似为一条直线。恒定加速运动方程用于描述每个间隔内卫星的运动。当将模型结果与精确解进行比较时，对于椭圆轨道，它们在整个轨道上完全匹配，最大相对误差为0.079％。当测试其他轨道，圆形，双曲线等轨道时，它根据理论预测保留了所有轨道。然后，通过从地球到月球的四分之一，一半和四分之三距离发射卫星，扩展了该模型以包含月球的影响。圆形轨道用于模拟月球的影响。模型的加速结果与理论预测值进行了比较。发射的三个位置的加速度的相应误差分别为0.019％和0.20％。这表明该模型适用于预测卫星的扰动轨道，并且可以用任何额外的力来描述卫星的扰动轨道。它也可以用来模拟弹丸运动的轨迹，而精确的解决方案无法生成。由于此模型可以随时提供卫星的速度，因此可以在需要更改轨道时应用它，因为它可以用于计算所需的新速度。

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