Here is the work-script for chapter 2

2.1 Orbits

18 September 2017

Then we turned to Orbital Mechanics. Important are: Kepler's laws, Newton's Universal law of Gravitation and Newton's 2nd Law of Motion.

With Newton's laws we can describe the motion of a satellite. It is a motion in a plane. The position of a satellite in space at any time is given by the set of 6 Keplerian Elements, or Keplerian Orbital Elements. NASA, for example, gives these Elements in a two-line format . Click here for examples.

We talked about the Vernal Equinox, the zero coordinate point for the geocentric equatorial coordinate system. This coordinate system is generally used for positions of celestial sources. The coordinates are expressed in right ascension (RA) and declination (dec.). It is also the position through which the orientation of the orbital plane is linked to the celestial reference frame. The vernal equinox is also used in terms of a time. At the vernal equinox and six months later at the autumnal equinox, the Sun is at particular locations in the geocentric equatorial coordinate system. At which ones? When is exactly the autumnal equinox?

What are the coordinates in RA and dec. today? Then we used as an example a set of Keplerian orbital parameters and properly positioned a satellite in three-dimensional space around a globe with the use of cardboard models for the orbital plane and the orbital ellipse. The motion of the satellite and its position at any given time are given by the solution of the differential equation derived from Newton's laws and the Keplerian Elements.

We learned about the geocentric equatorial

coordinate system and RA (right ascension) and dec (declination as the celestial coordinates of a spacecraft or a celestial source). The Gaia satellite of ESA has just released a preliminary catalogue of positions of stars, galaxies and quasars in RA and dec that in 2020 will include 1 billion sources. That catalogue of sources will define the most accurate celestial reference frame. Then we started on the Orbit Perturbations. We talked about the effects of the equatorial bulge and looked at numerical examples.

We practised visualizing the Keplerian orbit parameters and the vernal equinox. Then we continued with the orbit perturbations. We finished talking about the effects due to the equatorial bulge. We learned about effects of the equatorial ellipticity and then about third body effects on the Keplerian orbital parameters, the atmospheric drag and the solar radiation pressure.

We finished the orbit perturbations. Look at LAGEOS for a satellite of which the orbit can be determined very accurately. Look here for the latest GRACE results in the form of gravitational deviations from a geoid. We started with the coordinate transformations: perifocal coordinate system, geocentric equatorial coordinate system, topocentric horizon coordinate system.

We continued with the coordinate systems and then covered LST, GST, UT. mean sidereal day and mean solar day and introduced the antenna look angles.

2 October

We computed the look angles and the range to a satellite.

We computed the visibility of a geostationary satellite and talked about Earth eclipse and sun transit outage.

We talked about the launch vehicles, e.g.: Delta, Ariane, Proton, HV, GSLV, Long March and SpaceX

Look here for the launch of Gravity Probe B. Look here for the launch of Radioastron. Look here for the first ballistic rocket launches in 1942. Here is the Saturn V rocket with Apollo 11 on top which took the first men to the moon and back.

Wernher von Braun, head of V2 and the American rocket program development up to Saturn V, here with US president Kennedy.