Keplerain elements: Orbit plane Satellite perigee 00 Verna equator equinox Node Greenwich i Inclination Q2 Right Ascension of ascending node o Argument of perigee v True anomaly 02/20/02 12.540Lec05
02/20/02 12.540 Lec 05 6 Keplerain elements: Orbit plane Node i ω Ω ν Z θ 0 Greenwich Vernal equinox Satellite perigee equator i Inclination Ω Right Ascension of ascending node ω Argument of perigee ν True anomaly
Keplerain elements in plane Satellite Apogee a ae vEv Perigee Focus Center of Mass a semimajor axIs V True anomaly b semiminor axis E Eccentric anomaly e eccentricity M Mean anomaly 02/2002 12.540Lec05
02/20/02 12.540 Lec 05 7 Keplerain elements in plane a Focus Center of Mass ae Satellite Apogee Perigee b E ν r a semimajor axis b semiminor axis e eccentricity ν True anomaly E Eccentric anomaly M Mean anomaly
Satellite motion The motion of the satellite in its orbit is given by M(1)=n(t-70) E(t=M(t+esin e(t) vt)=tan e sin e(t/(1-ecose(t) (cos e(t-e/(1-ecose(t)) To is time of perigee 02/20/02 12.540Lec05
02/20/02 12.540 Lec 05 8 Satellite motion • The motion of the satellite in its orbit is given by • T o is time of perigee M ( t ) = n ( t − T0 ) E ( t ) = M ( t ) + esin E ( t ) ν( t ) = tan −1 1 − e 2 sin E ( t)/ ( 1 − ecos E ( t)) (cos E ( t ) − e)/ ( 1 − ecos E ( t)) ⎡ ⎣ ⎢ ⎤ ⎦ ⎥