Orbital elements are a set of parameters used to describe the shape, position, motion and other attributes of satellite orbits, which can also be calledNumber of tracksThe combination is not fixed and can be adjusted according to different types of satellite orbits or to better describe the satellite movement.[1]
Orbital elements areTwo body problemDescription inCelestial motionA group ofFundamental constant, used to calculate the position and speed of celestial bodies at any time.There are many forms of basic constants, but there are simple conversion relations between groups in different forms.The three components of the coordinate and velocity of the celestial body's position at a certain time are one of them.Kepler elements are commonly used, which have obvious geometric significance.
Artificial earth satelliteThere are 6 Kepler elements in an elliptical orbit.They determine the size, shape and spatial orientation of the orbit, and give the starting point for measuring the time of movement.The six elements are:
Track semimajor axis
(a）: Its length is half of the long axis of the ellipse, and can be measured in kilometers or the equatorial radius of the earth or astronomical units.according toKepler's third lawThere is a definite conversion relationship between the semi major axis and the operating cycle.
Track eccentricity
(e）: is the ratio of the distance between the two focuses of the ellipse and the major axis.When the eccentricity is 0, the orbit is circular;When the eccentricity is between 0 and 1, the orbit is elliptical, and the larger the eccentricity is, the flatter the ellipse will be;When the eccentricity is equal to 1, the orbit is a parabola;When the eccentricity is greater than 1, the orbit is hyperbolic.The semimajor axis of a parabola is infinite, and the semimajor axis of a hyperbola is less than zero.
Rail inclination
(i）: The included angle between the orbital plane and the equatorial plane of the earth is measured by the included angle between the north pole direction of the earth axis and the normal direction of the orbital plane, and the orbital inclination is from 0 ° to 180 °.If the inclination is less than 90 °, it is a forward orbit. The satellite always runs from west (southwest or northwest) to east (northeast or southeast).If the inclination is greater than 90 °, it is a retrograde orbit, and the satellite runs in the opposite direction to the forward orbit.Polar orbit is defined as an inclination equal to 90 °.
Right ascension of ascending node
(Ω）: It is an angular quantity.There are two intersections between the orbital plane and the earth's equator. The running arc from the southern hemisphere through the equator to the northern hemisphere is called the ascending segment. At this time, the point crossing the equator is called the ascending intersection.On the contrary, the operating arc from the northern hemisphere to the southern hemisphere is called the descending segment, and the corresponding intersection point on the equator is called the descending intersection point.In the revolution of the earth around the sun, the point where the sun crosses the equator from the southern hemisphere to the northern hemisphere is called the vernal equinox.The angle between the vernal equinox and the ascending node and the center of the earth is the right ascension of the ascending node, and it is specified to measure counterclockwise from the vernal equinox to the ascending node.The inclination of the orbit and the right ascension of the ascending node jointly determine the orientation of the orbit plane in space.
Perigee argument
(w）: It is the angle between perigee and ascending node and geocenter, measured from ascending node to perigee along the direction of satellite motion.The argument of perigee determines the orientation of the elliptical orbit in the orbital plane.
Time of passing perigee
(tp）: It is the time when the satellite passes the perigee, expressed in year, month, day, hour, minute and second, and is the starting point of the movement time.The actual operation orbit of artificial earth satellite is more complex than Kepler orbit.staySpacecraft orbit perturbationAlthough it is still based on orbital elements, it believes that orbital elements are no longer constants, but change with time.The orbital elements of a planetary probe orbiting a planet can be similarly determined by replacing the Earth's equator with the planet's equator and replacing the Earth's center with the planet's center of mass.The orbital elements of artificial planets can be determined by replacing the equatorial plane of the earth with the ecliptic plane, and also by replacing the geocenter with the heliocentric plane.[2]
computational procedure
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Given the position vector r and velocity vector v of the spacecraft at a certain time, the steps to calculate the orbital elements are as follows:
(1) Calculate the orbital elements determined by the momentum vector h.
According to the definition of h, there are
Calculate the inclination of the orbit i and the longitude of the ascending node Ω
Where:
；0≤i≤π；0≤Ω2π。
(2) Calculate the orbital elements determined by the eccentricity vector e.
According to the definition of e, there are
Eccentricity e is
(3) Calculate semi major axis a.
(4) Calculate the true near point angle f.
And
The calculation is similar. Let the longitude of the ascending intersection point be a, and the angular distance u of the ascending intersection point of the spacecraft be
Where: XYZ is the component of position vector r.Calculate from u f: f=u-
。[3]
Other common elements
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In the research, the close orbit elements and average orbit elements of satellites are also commonly used orbit elements.Because the satellite will be affected by various perturbation forces in actual operation, the satellite does not move according to the Kepler orbit. Its path is a complex space curve that is not closed, which will cause the satellite's orbit elements to change with time.When the satellite operates at any point in the orbit, the orbit elements at this point are called close orbit elements.When describing various attributes of satellite long-term movement, it is often necessary to use average orbital elements to reflect the long-term trend of satellite movement.In practical applications, close orbit elements are generally used in the process of simulation and numerical calculation to ensure the accuracy of calculation;The average orbit elements are used for satellite orbit design, space mission analysis and other work, which can simplify the analysis of orbit perturbation and reduce the amount of calculation.[1]
