Cartesian Orbital Elements in Satellite Initial State

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Questions and Answers

What is the unit of the semimajor axis 'a' in the classical orbital elements?

Astronomical Unit

Radian

Meter (correct)

Kilometer

What is the range of values for the orbital plane inclination 'i'?

[0, 180] deg (correct)

[0, 360] deg

[0, 90] deg

[0, 45] deg

What is the definition of the right ascension of the ascending node 'Ω'?

The angle between the equatorial plane and the orbital plane

The angle between ê1 and the axis of nodes n̂ (correct)

The angle between the line of nodes and the eccentricity vector

The angle between the Earth's axis and the orbital plane

What is the range of values for the eccentricity 'e'?

[0, 1] Signup and view all the answers

What is the purpose of the Cartesian orbital elements?

To describe the position and velocity of a satellite in ECI coordinates Signup and view all the answers

What is the definition of the anomaly of the periapsis 'ω'?

The angle between the line of nodes and the eccentricity vector Signup and view all the answers

What is the unit of the mean anomaly at epoch 'M0'?

Degree Signup and view all the answers

What is the range of values for the mean anomaly at epoch 'M0'?

[0, 360] deg Signup and view all the answers

What is the direction of the periapsis equivalent to?

Eccentricity vector Signup and view all the answers

Which Cartesian coordinate system is centered at the spacecraft center of mass?

Hill Cartesian Coordinate System Signup and view all the answers

What is the classical orbital element that is singular for equatorial orbits?

Orbital inclination Signup and view all the answers

What is the direction of the orbital angular momentum vector?

Perpendicular to the orbital plane and positive Signup and view all the answers

What is the direction of the vector p̂2 in the Perifocal CCS?

Defines together with ê1 the orbital plane Signup and view all the answers

What is the condition under which the Perifocal CCS is inertially-fixed?

In the absence of orbital perturbations Signup and view all the answers

What is the set of classical orbital elements?

{a, e, i, Ω, ω, M0} Signup and view all the answers

What is the direction of the vector ĥ3 in the Hill CCS?

Perpendicular to the orbital plane and positive Signup and view all the answers

What is the sign of the flight-path angle γ?

Same as the sign of sin f Signup and view all the answers

What is the shape of the orbital trajectory when e = 0?

Circular Signup and view all the answers

What is the value of radial velocity for a satellite on a circular orbit?

Zero Signup and view all the answers

What is the relationship between h and µR?

h = µR Signup and view all the answers

What is the value of the orbital speed for a satellite on a circular orbit?

Constant and equivalent to vt Signup and view all the answers

What is the shape of the orbital trajectory when e ≠ 0?

Elliptical Signup and view all the answers

What is the definition of the flight-path angle?

The angle between the radial and tangential velocity Signup and view all the answers

What is the equation for the orbital radius r(f) when e = 0?

r(f) = R = p Signup and view all the answers

Study Notes

Cartesian Orbital Elements

The Cartesian orbital elements are used to describe the initial state of a satellite in ECI (Earth-Centered Inertial) coordinates.
The Cartesian orbital elements are represented by the vector ce containing the initial position and velocity components: r1, r2, r3, r˙1, r˙2, r˙3.

Classical Orbital Elements

The classical orbital elements are a, e, i, Ω, ω, M0.
a is the orbit semimajor axis.
e is the orbit eccentricity, ranging from 0 to 1.
i is the orbital plane inclination, ranging from 0 to 180 degrees.
Ω is the right ascension of the ascending node (RAAN), ranging from 0 to 360 degrees.
ω is the anomaly of the periapsis, ranging from 0 to 360 degrees.
M0 is the mean anomaly at epoch, ranging from 0 to 360 degrees.

Perifocal Coordinate System (PCS)

The PCS is inertially fixed only in the absence of orbital perturbations.
The PCS has three base vectors: p̂1, p̂2, p̂3.
p̂1 is in the direction of the periapsis (equivalent to the eccentricity vector).
p̂2 defines the orbital plane together with ê1.
p̂3 is perpendicular to the orbital plane and positive in the direction of the orbital angular momentum.

Hill Cartesian Coordinate System (Hill CCS)

The Hill CCS is centered at the spacecraft center of mass.
The Hill CCS has three base vectors: ĥ1, ĥ2, ĥ3.
ĥ1 is in the direction of the instantaneous satellite position (radius vector).
ĥ2 is in the transversal direction, defining the orbital plane together with ĥ1.
ĥ3 is perpendicular to the orbital plane and positive in the direction of the orbital angular momentum.

Circular Orbit

A circular orbit has an eccentricity e equal to 0.
The orbital trajectory is a circle with a radius R coincident with the semilatus rectum.
The satellite flies at a constant orbital speed, equivalent to its transversal velocity, while the radial velocity stays zero.
The angular momentum h is related to the orbital radius R by the equation h = µR.

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Description

This quiz covers the use of Cartesian orbital elements in determining the initial state of a satellite in ECI coordinates, including position and velocity.