Issue 51

Over the summer, Jack Anthony will break down each of the six orbital elements required to uniquely identify a specific orbit and satellite in that orbit. This week we examine eccentricity. For those who can’t wait the entire summer, please visit Jack’s “Orbit Element Dance” on YouTube and you’ll find a 1:02 video featuring Jack in his driveway demonstrating this highly effective way to learn about the 6 classical orbital elements (COE). Orbit Element Dance.

Jack uses the STP method of remembering the 6 COEs: Size, Shape, Tilt, Twist, Position of Perigee and Position of the Satellite at a particular time.

The second “S” in the STP way of remembering the 6 Classical Orbital Elements is SHAPE. The shape of an orbit is described by the ECCENTRICITY orbital element (denoted as “e”). A circular orbit has an eccentricity of 0. For closed ellipses orbiting Earth, eccentricity values are 0 to less than 1. An eccentricity of 1 is a parabola and greater than 1 is a hyperbola.

If eccentricity is around .7 to .99, it is an elongated orbit – very eccentric. This article examines a favorite high-eccentricity orbit with e=.737.

Eccentricity can be used with semi-major axis to answer key questions about an orbit. In ellipse geometry, eccentricity is determined from the major axis and the distance between the two foci: e = 2c/2a = c/a. If the orbit is circular, the foci are on top of one another and 2c=0, so eccentricity is 0.

Given e and a, you can calculate radius of perigee and apogee: Radius Perigee = a × (1-e) and Radius Apogee = a × (1+e). Subtract Earth’s radius (6378 km) to calculate altitude: Altitude Perigee = Radius Perigee – 6378 km and Altitude Apogee = Radius Apogee – 6378 km.

The Molniya orbit is a Highly Elliptical Orbit (HEO) with eccentricity around .737. It has a low perigee and a far-out apogee. Russia introduced this orbit in the 1960s because access to geosynchronous orbits from high-latitude launch sites was a propulsive challenge.

A sample HEO uses a=26600 km, e=.737 and inclination 63.4°. The orbital period is about 720 minutes or 11.99 hours. The example gives perigee altitude = 618 km and apogee altitude = 39826 km.

Kepler’s Second Law states that an orbiting body sweeps out equal area in equal time. The spacecraft is slowest at apogee and fastest at perigee. For the example HEO, the satellite moves through the perigee region in less than two hours and spends more than ten hours with “hang time” above the northern hemisphere.

Another non-circular orbit is the Tundra orbit. It is geosynchronous with a period of 23 hr 56 min 4 sec, a semi-major axis of 42164 km, eccentricity typically between .2 and .3, and inclination 63.4°. Next time: Tilt of an orbit – inclination.