China
Africa
Explore chapters and articles related to this topic
Attitude Determination Using Two Vector Measurements – TRIAD Method
Published in Chingiz Hajiyev, Halil Ersin Soken, Fault Tolerant Attitude Estimation for Small Satellites, 2020
Chingiz Hajiyev, Halil Ersin Soken
In the analyses, the satellite’s orbital parameters are assumed as: inclination i = 97°; right ascension of the ascending node Ω = 15°; eccentricity e = 0 and orbital altitude of h = 550 km. The Earth radius is R = 6378.14 km; the Earth angular velocity is; the Earth magnetic field moment is M = 7.86 × 1015 Wb ⋅ m; the magnetic tilt angle is ε = 11.4°. The accuracy of the orbital parameters i, Ω and u are 5e-6 rad, 1e-5 rad and 1.5e-4 rad, respectively. The attitude sensors’ accuracy is ~1° for magnetometer, 0.1° for sun sensor and 0.36° for horizon sensor (horizon sensor determines the roll and pitch angles). It is assumed that eccentric anomaly is equal to the mean anomaly. Only one orbital period was simulated. In Figure 5.4, the change of the satellite attitude accuracy throughout the orbit is shown when the first algorithm (SUN-MAG) is used (required accuracy is 1°). As accuracy characteristics pitch (θ), yaw (ψ) and roll (φ) angles’ variances are taken. The results for the second and third algorithms are given in Figures 5.5 and 5.6, respectively.
Defense Information, Communication, and Space Technology
Published in Anna M. Doro-on, Handbook of Systems Engineering and Risk Management in Control Systems, Communication, Space Technology, Missile, Security and Defense Operations, 2023
Mean anomaly, M—the angle between the perigee and an imaginary satellite that travels in a circular orbit that has the same focus and the period as the actual satellite but does so with a constant speed (called the mean motion). When the eccentric anomaly has been calculated from Eq. 5.11 the mean anomaly can be calculated by Kepler’s equations as: M=E−esinE
A problem-based learning proposal to teach numerical and analytical nonlinear root searching methods
Published in International Journal of Mathematical Education in Science and Technology, 2022
Juan Luis González-Santander, Fernando Sánchez-Lasheras
Nonlinear equations are found in many branches of Applied Mathematics, Physics, and Engineering, but very few of them can be solved analytically. The impact of this fact on teaching at undergraduate level has been highly significant. For instance, in the calculation of planetary elliptic orbits, we need to evaluate the roots of Kepler's equation, where E is the eccentric anomaly, ϵ is the eccentricity and M the mean anomaly. The solution of Kepler’s equation can be formulated analytically as where Jn denotes the Bessel function of the first kind, and the sum in (1) converges for ϵ < 1 like a geometric series with ratio (Colwell, 1993):