Geo Station Keeping Elements
Orbital elements useful when describing motion of geosynchronous satellites, computed with respect to the Earth TrueOfDate system, as a function of time.
The literature contains a variety of metrics that have been found useful for describing and maintaining geosynchronous orbits. The elements are categorized as:
- Angle representing location in orbit
- Inertial angles (measured from Earth TrueOfDate X-axis)
- Mean Longitude, True Longitude, True Right Ascension, Mean Right Ascension
- Geodetic angles (measured from Earth Fixed X-axis)
- Geodetic Mean Longitude, Geodetic True Longitude, Geodetic True Longitude At Time Of Perigee, Geodetic Mean Right Ascension, Geodetic Longitude
- Drift in orbit (as compared to ideal motion whose rate is the sidereal rotation rate of the Earth (360.985612287742 deg/day))
- Mean Drift Rate (with dimension AngleRate)
- Drift Rate factor (non-dimensional)
- These values are provided in two forms: (i) based on two-body motion; and (ii) incorporating the effects of Earth oblateness represented by J2.
- Eccentricity vector
- The location of the eccentricity vector within the orbit plane.
- Defined in the same manner as equinoctial elements h and k.
- Inclination vector
- The vector whose direction is the lines of nodes, with magnitude depending on the inclination angle.
- Different investigators use different magnitudes--several versions of the inclination vector (each with different magnitudes) are provided below.
- Some investigators (e.g., Soop) use the term 'inclination vector' to actually locate the projection of the unit angular momentum vector in the XY-plane, which is perpendicular to the line of nodes. The UnitAngularMomentum vector is provided separately below.
Reference: Handbook of Geostationary Orbits, E. M. Soop, 1994, DOI 10.1007/978-94-015-8352-7.
Available for these objects: Satellite
Type: Time-varying data.
Availability: Reports | Graphs | Dynamic Displays | Strip Charts
Data Provider Elements
| Name | Dimension | Type | Description |
|---|---|---|---|
| Time | Date | Real Number or Text | Time. |
| Geodetic Longitude | Longitude | Real Number or Text | The detic longitude (i.e., angle from the Earth Fixed X-axis locating the position vector onto the Earth Fixed XY plane). Longitude increases in the direction found using the right-hand rule about the Earth Fixed Z-axis. |
| Mean Longitude | Longitude | Real Number or Text | Mean longitude, computed with respect to Earth TrueOfDate axes. The value is the sum of mean anomaly, argument of perigee and raan. A measure of the location within the orbit based on time. Note: Soop's use of the term mean longitude really refers to Geodetic True Longitude. |
| Geodetic Mean Longitude | Longitude | Real Number or Text | The difference between Mean Longitude and Mean GHA. It is a measure of location in orbit relative to the Earth Fixed X-axis, but still based upon time. |
| True Longitude | Longitude | Real Number or Text | True longitude, computed as the angle between the position vector and the X-axis of the equinoctial axes, computed with respect to Earth TrueOfDate axes. The value is the sum of true anomaly, argument of perigee and raan. Soop denotes this by s but calls it right ascension. |
| Geodetic True Longitude | Longitude | Real Number or Text | The difference between True Longitude and Mean GHA. It is a measure of the position vector relative to the Earth Fixed X-axis. Soop denotes this by lambda but calls it mean longitude. |
| Geodetic True Longitude At Time Of Perigee | Longitude | Real Number or Text | The difference between True Longitude and Mean GHA, computed at the estimated time of perigee using the current osculating elements. It is a measure of the position vector relative to the Earth Fixed X-axis. Soop denotes this by lambda_0 but calls it mean longitude at epoch, where the epoch t_0 has been chosen here to be the time of perigee. |
| True Right Ascension | Longitude | Real Number or Text | The dihedral angle between the Earth TrueOfDate X-axis and the projection of the position vector into the Earth TrueOfDate XY-plane, measured about the Earth TrueOfDate Z-axis. Note: Soop's use of the term right ascension really refers to True Longitude. |
| Mean GHA | Longitude | Real Number or Text | The angle between the Earth Fixed X-axis and the Earth TrueOfDate X-axis. The Earth Fixed XY plane is the same as the Earth TrueOfDate XY plane. The sidereal Greenwich Hour Angle (GHA) that accounts for the difference between UT1 and UTC time scales, but does not include equation of the equinox. |
| Mean Right Ascension | Longitude | Real Number or Text | Mean right ascension, defined as arctan(cos(inclination angle) * tan(mean longitude)), computed with respect to Earth TrueOfDate axes. |
| Geodetic Mean Right Ascension | Longitude | Real Number or Text | The difference between Mean Right Ascension and Mean GHA. The difference is a measure of location in orbit relative to the Earth Fixed X-axis. |
| Semi-major Axis | Distance | Real Number or Text | A measure of the size of the orbit. Orbits with eccentricity <1 are ellipses, with major and minor axes identifying the symmetry axes of the ellipse, the major axis being the longer one. The value is half the length of the major axis. |
| Mean Motion (TwoBody) | AngleRate | Real Number or Text | A measure of the osculating period of the orbit, expressed as an angular rate. The value is 2pi rad / orbit_period. |
| Mean Motion (J2) | AngleRate | Real Number or Text | A measure of the period of the orbit, expressed as an angular rate, where the effect of the secular drift of mean anomaly, argument of perigee, and raan caused by J2 is included. The value is 2pi rad / orbit_period. |
| Mean Drift Rate (TwoBody) | AngleRate | Real Number or Text | The difference between Mean Motion (TwoBody) and the sidereal rotation rate of the Earth (i.e., the mean GHA rate, with value 360.985612287742 deg/day). This value is often used in lieu of the Semi-major Axis when describing geosynchronous motion; however, it is only a fair approximation to the rate of the mean longitude because it ignores the secular drift caused by the oblateness of the Earth represented by J2. |
| Mean Drift Rate (J2) | AngleRate | Real Number or Text | The difference between Mean Motion (J2) and the sidereal rotation rate of the Earth (i.e., the mean GHA rate). This is a better approximation of the rate of the mean longitude because it incorporates the secular drift caused by the oblateness of the Earth represented by J2. |
| Drift Rate factor (TwoBody) | Unitless | Real Number or Text | A non-dimensional measure of mean longitudinal drift, defined as D = -1.5 * (semi-major axis - a_GEO)/a_GEO, where a_GEO is the semi-major axis value whose mean motion n_GEO = sqrt(mu/a_GEO^3) is equal to the sidereal rotation rate of the Earth (i.e., the mean GHA rate, with value 360.985612287742 deg/day). Soop denotes this by D and calls it drift rate. The drift rate, defined as the drift rate factor multiplied by the sidereal rotation rate of the Earth, is only a fair approximation to the rate of the mean longitude because it ignores the secular drift caused by the oblateness of the Earth represented by J2. |
| Drift Rate factor (J2) | Unitless | Real Number or Text | A non-dimensional measure of mean longitudinal drift, defined as D = -1.5 * (semi-major axis - a_J2)/a_J2, where a_J2 is the semi-major axis value whose mean motion, when computed including the effect of the oblateness of the Earth represented by J2, is equal to the sidereal rotation rate of the Earth (i.e., the mean GHA rate, with value 360.985612287742 deg/day). The drift rate, defined as the drift rate factor multiplied by the sidereal rotation rate of the Earth, is a better approximation to the rate of the mean longitude because it incorporates the secular drift caused by the oblateness of the Earth represented by J2. |
| Eccentricity | Unitless | Real Number | The magnitude of the eccentricity vector. A measure of the shape of the orbit. Values <1 indicate an ellipse (where zero is a circular orbit) and values >1 indicate a hyperbola. |
| Ecc_x | Unitless | Real Number | The component of the eccentricity vector, computed with respect to Earth TrueOfDate axes, along the X-axis of the equinoctial axes. This is the same value as the element 'k' of equinoctial elements, where k = e * cos(omegaBar), where omegaBar = raan + argument of perigee. The eccentricity vector points from the center of the Earth to the location of perigee (as computed using osculating orbital elements at the current time) with a magnitude equal to the eccentricity of the orbit. |
| Ecc_y | Unitless | Real Number | The component of the eccentricity vector, computed with respect to Earth TrueOfDate axes, along the Y-axis of the equinoctial axes. This is the same value as the element 'h' of equinoctial elements, where h = e * sin(omegaBar), where omegaBar = raan + argument of perigee. The eccentricity vector points from the center of the Earth to the location of perigee (as computed using osculating orbital elements at the current time) with a magnitude equal to the eccentricity of the orbit. |
| Declination | Angle | Real Number or Text | The angle between the position vector and the XY-plane of the Earth TrueOfDate axes. The angle is positive when the Z component is positive. |
| Cos(incl) | Unitless | Real Number | The value of cos(inclination angle), where the inclination angle is defined with respect to Earth TrueOfDate axes. |
| Inclination | Angle | Real Number or Text | The angle between the orbit plane and the XY plane of Earth TrueOfDate axes. |
| Incl_x(incl) | Angle | Real Number or Text | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its X-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as the inclination angle itself. |
| Incl_y(incl) | Angle | Real Number or Text | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its Y-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as the inclination angle itself. |
| Sin(incl) | Unitless | Real Number | The value of sin(inclination angle), where the inclination angle is defined with respect to Earth TrueOfDate axes. |
| Incl_x(sin_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its X-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as sin(inclination angle), so that the reported value is the same as -UnitAngularMomentum_y. |
| Incl_y(sin_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its Y-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as sin(inclination angle), so that the reported value is the same as UnitAngularMomentum_x. |
| Sin(half_incl) | Unitless | Real Number | The value of sin(0.5 * inclination angle), where the inclination angle is defined with respect to Earth TrueOfDate axes. |
| Incl_x(sin_half_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its X-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as sin(0.5 * inclination angle). |
| Incl_y(sin_half_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its Y-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as sin(0.5 * inclination angle). |
| 2 Sin(half_incl) | Unitless | Real Number | The value of 2.0 * sin(0.5 * inclination angle), where the inclination angle is defined with respect to Earth TrueOfDate axes. |
| Incl_x(2_sin_half_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its X-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as 2.0*sin(0.5 * inclination angle). |
| Incl_y(2_sin_half_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its Y-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as 2.0*sin(0.5 * inclination angle). |
| Tan(half_incl) | Unitless | Real Number | The value of tan(0.5 * inclination angle), where the inclination angle is defined with respect to Earth TrueOfDate axes. |
| Incl_x(tan_half_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its X-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as tan(0.5 * inclination angle), so that the reported value is the negative of the element 'q' of equinoctial elements, where q = tan(0.5 * inclination angle) * cos(raan). |
| Incl_y(tan_half_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its Y-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as tan(0.5 * inclination angle), so that the reported value is the same as the element 'p' of equinoctial elements, where p = tan(0.5 * inclination angle) * sin(raan). |
| 2 Tan(half_incl) | Unitless | Real Number | The value of 2.0 * tan(0.5 * inclination angle), where the inclination angle is defined with respect to Earth TrueOfDate axes. |
| Incl_x(2_tan_half_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its X-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as 2.0*tan(0.5 * inclination angle). |
| Incl_y(2_tan_half_incl) | Unitless | Real Number | The component of the inclination vector, computed with respect to Earth TrueOfDate axes, along its Y-axis. The inclination vector lies along the line of nodes. The magnitude of the inclination vector has been chosen as 2.0*tan(0.5 * inclination angle). |
| UnitAngularMomentum_x | Unitless | Real Number | The component of the unit angular momentum vector (i.e, the unit vector along crossProduct(position, velocity)) along the X-axis of the Earth TrueOfDate axes. The value will equal sin(inclination angle)*sin(raan). |
| UnitAngularMomentum_y | Unitless | Real Number | The component of the unit angular momentum vector (i.e, the unit vector along crossProduct(position, velocity)) along the Y-axis of the Earth TrueOfDate axes. The value will equal -sin(inclination angle)*cos(raan). |
| UnitAngularMomentum_z | Unitless | Real Number | The component of the unit angular momentum vector (i.e, the unit vector along crossProduct(position, velocity)) along the Z-axis of the Earth TrueOfDate axes. The value will equal cos(inclination angle). |