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  • 2022-06-13 04:45
matlab方位角计算代码太空工程 太空工程课程作业 第1部分第1.1部分-使用TLE数据以及轨道特性与任务之间的关系进行卫星仿真 介绍 SARAL和O3B FM07都是最近三年内发射的卫星。 这两颗卫星都用于地球探测或通信任务,但它们的倾斜度大不相同,这使得它们在研究中非常有趣。 报告的这一部分将研究如何调整其轨道性能以执行其任务。 LEO中的卫星-SARAL SARAL与ARgos和ALtika一起代表Satelite。 它是近地轨道卫星。 该卫星由印度空间研究组织(ISRO)和CNES运营。 SARAL于2013年2月23日发射升空,其任务是研究海洋环流和海面高程。 为了执行任务,SARAL配备了高度计和数据收集系统作为有效载荷。 AL的名称代表ALTIKA,因为AlLTIKA是高度计,也是卫星的有效载荷。 高度计在Ka波段工作。 卫星提供的高度测量将对海面高度的测量产生影响,并减少制图误差。 然后由ARGOS数据收集系统完成数据收集,因此将这两个系统结合起来便得到了SARAL的名称。 轨道参数卫星规格轨道类型:太阳同步发射质量:407千克近地点:791.1km预期寿命:5年Ap
# SpaceEngineering Space Engineering Course Work Part 1 Part 1.1 - Satellite Simulation Using TLE Data and Relation Between Orbital Properties and Mission Introduction SARAL and O3B FM07 are both satellites that have been launched within the last three years. Both satellites are used for earth sensing or communication missions but they have very different inclination which makes them very interesting to research. This section of the report will investigate how their orbital properties are adjusted to perform their mission. Satellite in LEO - SARAL SARAL stands for Satelite with ARgos and ALtika. It is a Low Earth Orbit satellite. The satellite is operated by Indian Space Research Organisation (ISRO) and CNES. SARAL was launched on February 23rd, 2013 with the mission of studying ocean circulation and sea surface elevation. To perform the mission, SARAL is equipped with altimeter and data collection system as its payloads. The AL in its name stands for ALTIKA as AlLTIKA is the altimeter and also the payload of the satellite. The altimeter operates at Ka band. The altimetric measurements provided by the satellite will have an impact on the measurement of sea surface height and reduce mapping error. The data collection is then done by the ARGOS data collection system so the two systems combined resulted in the name SARAL. Orbital Parameters Satellite Specifications Type of Orbit: Sun-Synchronous Launch Mass: 407 kg Perigee: 791.1km Expected life time: 5 years Apogee: 791.6 km Inclination: 98.5 o Period: 100.5 minutes Semi Major Axis: 7162 km Eccentricity: 0.0000401 TLE: 1 39086U 13009A 16062.90226953 +.00000026 +00000-0 +25963-4 0 9997 2 39086 098.5412 251.8101 0000401 050.0426 310.0793 14.32253629157651 Satellite in MEO - O3b FM07 O3b FM07 is part of the O3b satellite constellation. The main purpose of the satellite constellation is telecommunications. To perform its duties, the satellite is equipped with twelve Ka band antennas and provides high speed internet and broadcasts to people in remote area, which is actually what the name of the "Other 3 Billion" satellite network is referencing to.The O3b FM07 was launched on July 10, 2014 and today the satellite network has more than 12 in the orbit. Orbital Parameters Satellite Specification Perigee: 8069.5 km Launch Mass: 650 kg Apogee: 8076.6 km Inclination: 0.0359o Period: 287.9 minutes Semi Major Axis: 14444 km Eccentricity: 0.0002445 TLE 1 40081U 14038C 16062.74115278 -.00000022 +00000-0 +00000-0 0 9994 2 40081 000.0359 353.2540 0002445 324.0770 042.6465 05.00115716029950 Methodology To simulate the orbit of each satellite in 3D over a 24-hour period, the basic Keplerian orbital model is used. The seven key orbital parameters required to find the location of satellite in any given time are inclination (i), right ascension of the ascending node (Ω), eccentricity of the orbit (e), argument of perigee (ω), mean anomaly of the orbit (Mo), time (t) and the semi major axis of the orbit (a). These parameters can be found by examine the satellite’s TLE. After these parameters are defined, they are inputted into the Keplerian orbital calculation function. This function first calculates the mean anomaly at a given time by using 𝑀 = 𝑀𝑜 + 𝑛(𝑡 − 𝑡0) where 𝑛 = √𝜇/𝑎3 and 𝑡 − 𝑡0 will equal to the time stamp in the Matlab code. The next step is to find the eccentric anomaly at the given mean anomaly. This can only be done by using iterative method to solve 𝐸 − 𝑒 𝑠𝑖𝑛(𝐸) − 𝑀 = 0 The iteration is initialized using E0 = M and the next iteration value is found using 𝐸𝑖+1 = 𝐸𝑖 − (𝐸 − 𝑒 𝑠𝑖𝑛(𝐸) − 𝑀 )/(1 − 𝑒 cos(𝐸)) with the eccentric anomaly, E, found, the true anomaly can then be found by rearranging the equation below tan (𝜃/2) = √((1 + 𝑒)/(1 − 𝑒)) x tan (𝐸/2) the true anomaly gives the angle the satellite is at in the orbit so now we just need to find the distance to get the location of the satellite at a certain time in orbit. The distance r is found by using 𝑟 = 𝑝/(1+𝑒 𝑐𝑜𝑠𝜃) where p is the semilatus rectum and can be found using p = a x (1-e2). With distance and true anomaly know, we know have the Perifocal frame in polar form and we can convert this to Cartesian form easily as we have all the parameters required to do so. We are then required to transfer the coordinates from Perifocal frame to ECI frame which can also be performed by using the transfer matrix and the result will give us the 3D orbit for satellite. We have also set the time step in the Matlab code as well so it only plots the orbit over a 24 hour period. The next step is to plot a ground trace of the orbit. To do this, we simply need to find the satellite's position in ECEF coordinates. This is simply executed by the eci2ecef function in Matlab which utilizes the transfer matrix between the two coordinates systems. Part 1.2 - Orbital Simulation with Perturbation Introduction Orbital perturbation can come from many different sources such as Earth oblateness, gravity harmonics, solar/lunar gravity forces, aerodynamic drag and solar radiation. Perturbations are external disturbances that affect the ideal orbital dynamics. The magnitude of perturbations of each different source depends on the altitude of the orbit. Gravitational forces are the most significant perturbation especially on LEO satellites as they have lower altitude. On the other hand, perturbations caused by atmospheric drag decreases significantly as altitude increase since there is less resistance in outer space. Another perturbation is the attraction force of the moon and sun. These perturbations increase slowly as altitude increase since the higher the altitude, the closer the satellite will be to them and there will be stronger attraction forces between them. This also stands true for other planet attraction forces which can cause perturbations as well, but they are less significant as they are not as close to the satellite compared to the moon or Earth nor do they have the same attraction force as the sun. The dominant perturbing source that will be investigated is called J2 zonal perturbations. It is the most significant perturbation source after gravitational forces especially for LEO satellites. The effect of J2 perturbation drops with increase in altitude but is still significant for a large range of altitudes that are close to Earth. J2 perturbation is investigated here and not gravitational forces perturbation because J2 perturbation is more related to the orbital parameters of the satellite. J2 zonal perturbation is the result of the effect of Earth oblateness. This is mostly due to the Earth's spin and results in a gradual change in the ascension of the ascending node and argument of perigee. The change in ascension of the ascending node occurs because there is more attraction in Earth's equator since the poles are flatter so the satellite accelerates towards the equator more. As a result, this extra acceleration also causes the change in argument of perigee since the orbit is no longer a closed ellipse due to the change in force components. Methodology To simulate the modified perturbation orbit model, a starting true anomaly is first found using the same method as Part 1. With the true anomaly of the starting position found, we can now compute the equinoctial elements model since we have all the classical orbital parameters required to calculate the orbit. The conversions equations can be simply applied and are shown in appendix. This gives us the six parameters required and we need to introduce perturbations into equinoctial model. To do this we express the J2 perturbation as a perturbing acceleration on the two-body equation of motion. This acceleration is express as 𝑥̇ and is known as the sate rate equations. 𝑥̇ = 𝑨(𝑥)Δ(𝑥) + 𝒃(𝑥) and x matrix containing the 6 equinoctial elements that
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