### Orbital Elements and the Dangers of Space Debris

Satellites revolving around the Earth travel in either a circular or elliptical orbit. These orbits range in altitudes from 200- 2000 km for LEO, all the way up to 35,786 km for geostationary orbits (GEO) [12]. The velocities of the satellites throughout their orbits are proportional to the altitudes. For example, the ISS is in a circular orbit at an altitude of roughly 350 km. This corresponds to an orbital velocity of 7.7 km/s (17,200 mph) and the station completes a full orbit of the earth in just over 90 minutes [4]. On the other hand, a spacecraft designed to transmit a satellite TV broadcast would be designed to reside in GEO, travel at 3.3 km/s (7,400 mph) and have a period of 24 hours.

The angle between the orbital plane of the satellite and the equatorial plane of the Earth may also vary. The angle between the two planes is called the inclination angle of the orbit. To visualize the inclination angle, imagine you are standing up straight, your waist is Earth's equator, and you are holding a hula hoop to symbolize the orbit of a satellite. If you place your hands on the sides of the hula hoop, level with your waist, and hold it parallel to the ground, the orbit has zero inclination. If you keep your hands level with your waist but start to twist the hula hoop up, pivoting it about a line drawn from one hand, through your waist, to the other hand, you are changing the inclination of the orbit. If you now rotate your shoulders so instead of being at your sides, your right hand is slightly in front of you and your left is slightly behind, you have changed the right ascension of ascending node (RAAN) of the orbit. The orbital inclination and right ascension of ascending node are important parameters for understanding how space debris can affect other spacecraft.

NASA Orbital Debris Program Office

Even though they have new orbits, the majority of the fragments are still clustered relatively close together immediately after impact and follow the same general orbital trajectory of the original satellite. Over time, however, these orbits begin to disperse due to what is called the regression of nodes [11]. If the Earth were a perfect sphere with evenly distributed mass, the gravitational pull would always be directly towards the center of the planet and in the plane of the orbit. Earth actually has slight bulge around the equator, causing part of the gravitational force vector to be out of the orbit plane, which in turn causes the right ascension of the ascending node, or RAAN. The gravitational force of the Sun and the Moon also contribute to the regression of nodes, but Earth’s oblateness is the dominating factor [11]. The rate at which the node regresses is a function of the inclination and period of the orbit. After a fragmentation event, the debris is cast into orbits with different periods and inclination angles, and each orbit changes orientation at a different rate. Over time the orbits begin to spread out because of the variance in nodal regression rate. In the case of the Fengyun 1-C anti-satellite weapons test, since the debris was distributed across such a wide range of altitudes and orbital periods, the precession rates caused the fragments to envelope the globe and create a shell of orbiting debris in a short period of time, roughly 12 months [14]. Within one year, the orbital debris had almost completely encircled the Earth, clearly indicating the worldwide risk posed by fragmentation events.