IEEE Aerospace and Electronic Systems Magazine - August 2020 - 17

Cataldo et al.
Another important parameter is the objects revolution
period, which is directly related with the orbital major
semiaxis and calculated as
sﬃﬃﬃﬃﬃ
a3
T ¼ 2p
:
m

(4)

The motion of an object on these orbits around a central
body can be written as the composition of the motion part
ruled by the Newton laws and a sum of several perturbative
forces. In particular, accordingly with the "two-body
problem" [28], the motion law can be written as
€r ¼ À

Figure 1.
Orbital parameters.

(5)

where r is the position vector of the object with respect to
the center of mass of the body, r ¼ jrj and api is the ith
perturbative force. Perturbative forces include [28]:

where
a is the orbital major semiaxis (meters or kilometers);
e is the eccentricity, which determines the amount
by which the orbit differs from a perfect circle;
i is the inclination angle of the orbital plane (i.e., the
plane in which the orbit lies) with respect to the
Earth's equatorial plane;
V is the longitude of the ascending node, i.e., the
angle measured with respect to the Earth's equatorial plane between the ascending node (V) and the
first point of aries (g);
v is the argument of the periapsis, i.e., the angle
between the body's ascending node and the orbit's
periapsis;
n is the true anomaly, i.e., the angle between the
direction of the periapsis and the current position of
the object.
The ascending node is the point where the orbit passes
through the Earth's equatorial plane and the object is traveling south-to-north. The longitude of the ascending node
is measured counterclockwise (as seen from the north). For
noninclined orbits (i ¼ 0), the ascending node (and thus its
longitude) is not defined. For computational convenience,
if i ¼ 0, then V is conventionally also set to zero.
In this article, we are only interested in closed orbits
for which the eccentricity is a nondimensional number
greater than (or equal to) zero but less than one. For closed
orbits, the Keplerian parameters univocally identify an
ellipse in 3-D space, knowing that one of the ellipse's
focuses coincide with the center of the Earth, except for
the true anomaly. The true anomaly is the only orbital
parameter that changes in time because it identifies the
current position of the object on its orbit.
AUGUST 2020

n
X
m
r
þ
api
r3
i¼1

Atmospheric drag, mainly for LEO objects;
Solar radiation pressure;
Earth radiation pressure;
Third-body effect from the moon and sun;
Lorentz forces and Van Allen belt distortion, mainly
for high eccentricity orbits.
It is worth pointing out that, for IOD, just gravitational
field nonuniformities and atmospheric drag can be considered as perturbative forces, while the others can be neglected.

USER REQUIREMENTS
As already mentioned, the main goal of this article is to propose and test a multibistatic radar system making use of
radio-telescopes as receivers for space surveillance applications and optimized for RSO IOD. Such systems should
have the operational capability to help in creating and
maintaining a catalog of RSOs to be shared worldwide.
Cataloging space objects requires an expensive network of
sensors that are capable of periodically observing objects
and determining any changes in their orbital elements and
of continually performing orbit determination calculations.
To achieve this goal, a set of system functionalities
have been identified:
Detection of new RSOs;
Tracking of new RSOs;
Initial orbit propagation of new RSOs;
RSO's feature extraction and classification;
Orbit confirmation and creation of a new object in a
catalog.

IEEE A&E SYSTEMS MAGAZINE

IEEE Aerospace and Electronic Systems Magazine - August 2020

Table of Contents for the Digital Edition of IEEE Aerospace and Electronic Systems Magazine - August 2020