Satellite orbit determination

first, Kepler's Law

The three Laws of planetary motion proposed by German astronomer J. Kepler. The first and second laws, published in 1609, were summed up in Kepler's data from the observation of the Martian position in the valley of astronomers; the third law was published in 1619. These three laws are called the Ellipse law, the area law and the harmonic law respectively.

The contents of the Three laws:

Kepler's First law (orbital law) all planets orbiting the Sun are elliptical, and the sun is in the center of the ellipse.

Significance: The basic morphology of satellite orbit and its relation to the inner Earth are clarified.

Kepler's second law ( area Law)　　 the lines of the planets and the sun sweep across equal areas within equal intervals.

　　Significance: It is shown that the speed of the satellite in elliptical orbits is changing, the maximum velocity at the perigee and the least at the apogee.

Kepler's third Law (periodic law) The square of the star Time (T) of all planets orbiting the sun is proportional to the cubic of their orbital long half axis (R), i.e.

Meaning: When the long radius of the Kepler ellipse is determined, the average angular velocity of the satellite operation is also determined and remains unchanged.

The role of Kepler's law in satellite orbit determination:

After the satellite launch has risen to a predetermined altitude, it begins to orbit the Earth. Assuming that the earth is a homogeneous sphere, according to the law of gravitation, the gravitational acceleration of the satellite is

G is the gravitational constant, M is the Earth mass, M is the satellite mass, and R is the geocentric path of the satellite. The problem of relative motion between Earth and satellites is studied according to the above formula, which is called the two-body problem in celestial mechanics. The gravitational acceleration determines the basic laws of the movement of satellites around the Earth. The non-perturbation motion of the satellite in the Earth's gravitational field, also called Kepler movement, can be described by Kepler's law.

iii. Description of the satellite orbit:

The passive motion of a satellite can be described by a set of appropriate parameters, but the selection of these parameters is not unique, and the most widely used set of parameters is called the Kepler orbit parameter or the Kepler orbital root number.

Kepler orbital parameters: A total of six parameters, three determine the shape and size of the satellite orbit, and the satellite's instantaneous position in orbit, three determine the satellite orbit relative to the celestial coordinate system position and direction.

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A is the long radius of the track, E is the orbital elliptical eccentricity, and these two parameters determine the shape and size of the Kepler ellipse.

I is the inclination angle of the orbital plane: the angle between the satellite orbital plane and the equatorial plane of the earth. These two parameters uniquely determine the relative orientation between the satellite orbital plane and the earth body.

is the angle of the center of gravity between the ascending intersection of the Earth's equatorial plane and the vernal equinox.

is the perigee angle: that is, in the orbital plane, the angle of the center of the earth between the ascending intersection and the perigee, which expresses the orientation of the Kepler ellipse on the orbital plane.

FS is the true near point angle of a satellite: the geocentric angular distance between the satellite and the perigee on the orbital plane. This parameter is a function of time, which determines the instantaneous position of the satellite in orbit.

Reference to the Baidu Library article "satellite orbit", the original author expressed thanks!

Satellite orbit determination