Orbital

Part 1 Orbital

Why a Sat. remains in ?

Bcs the centrifugal caused by the Sat. around is counter- balanced by the Earth's Pull. Kepler’s Laws

The () which the earth follows the same laws that govern the motion of the around the .

J. Kepler (1571-1630) was able to derive empirically three laws describing planetary motion  I. Newton was able to derive Keplers laws from his own laws of mechanics [gravitation theory] Kepler’s 1st Law (Law of Orbits)

The path followed by a Sat. (secondary body) orbiting around the body will be an . The center of () of a two-body system is always centered on one of the foci (earth center). Kepler’s 1st Law (Law of Orbits)

The eccentricity (abnormality) e:

a 2  b2 e  a b- semiminor axis , a- semimajor axis

VIN: e=0  0

For equal time intervals, a Sat. will sweep out equal areas in its orbital plane, focused at the barycenter

 VIN: S1>S2 at t1=t2  V1>V2 Max(V) at Perigee & Min(V) at Apogee Kepler’s 3rd Law (Harmonic Law)

 The of the periodic time of orbit is proportional to the cube of the mean distance between the two bodies.  a 3  n 2

 n- of Sat. (radian/sec) ,   - earth geocentric = 3.986005x1014  The mean distance is equal to the semimajor axis a

VIN: With n in rad/sec, the in sec. : P=2/n Kepler’s 3rd Law (Harmonic Law)

In English: Orbits with the same semi-major axis will have the same period Examples Examples Definition  A set of mathematical parameters that enables us to accurately describe satellite motion

Purpose  Discriminate one satellite from other  Predict where a satellite will be in the future or has been in the past  Determine amount and direction of maneuver or Orbital Elements

 Semi-Major Axis (Size)  Eccentricity (Shape)  Inclination  (Orientation)  Argument of Perigee  Time (Location within orbit) 

Equatorial Plane

Inclination ( i)

Orbital Plane Inclination

Prograde: 0  i < 90

Equatorial: i= 0 or 180

Retrograde: : i = 90 90  i < 180

i

Argument of  Perigee ()  Right ascension()

Direction of True satellite motion Anomaly () Locate with Respect to Space Orbital Elements Definition  A set of mathematical parameters that enables us to accurately describe satellite motion

Purpose  Discriminate one satellite from other satellites  Predict where a satellite will be in the future or has been in the past  Determine amount and direction of maneuver or perturbation Orbital Elements

 Semi-Major Axis (Size)  Eccentricity (Shape)  Inclination  Right Ascension (Orientation)  Argument of Perigee  Epoch Time (Location within orbit)  True Anomaly – Mean Anomaly Example Example Orbit Perturbations