Perigee meansspacecraftOrbiting the earthElliptical orbitThe point closest to the center of the earth.Astronomically, perigee meansMoonThe point closest to the earth in orbit around the earth.The perigee distance of the moon is 363300km, and the perigee movement cycle is 8.85 years.The earth is located at one of the two focal points of the ellipse.Taking the two focus points of the ellipse as the horizontal axis, a straight line can be drawn. This straight line will produce two intersections with the satellite orbit. We call the point closest to the earth perigee, and the point farthest from the earth apogee;Usually, at perigee, the angular velocity of the satellite is the fastest.
Spacecraft orbiting the earthEllipses of rowsOn circular trackFrom the groundHeart nearestOne ofPoint.near-earthPoint to groundSphericDistance scaleIs near the groundPoint heightDegrees.In order to avoid the spacecraft falling prematurely, the orbit is near the groundPoint heightUsually more than 180 km.The spacecraft has the smallest potential energy and the largest kinetic energy at perigee.
The earth is located in two ellipsesfocusOne of the positions.Draw a straight line with the two focus points of the ellipse as the horizontal axis, which will produce two intersections with the satellite orbit. The closest one is called perigee, and the farthest one is called perigeeApogee；Usually at perigeeangular velocityFastest.
Perigee argument
It is the angle between the perigee and the ascending node and the geocenter, measured from the ascending node to the 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
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.Artificial earth satelliteThe actual operation orbit of 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.
kinetic analysis
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Schematic diagram of satellite orbit change
Synchronous satellite launch is usually launched to the parking orbit, adjusted and stabilized into a circular orbit, and then launched at a predetermined locationBooster engineTo accelerate the satellite.This process takes a short time. When the speed increases to a preset value, the engine will be shut down.The satellite will make centrifugal motion, and the orbit radius will become larger and larger.Due to the gravitational nature, the moving orbit behind the satellite will be an ellipse, called the transfer orbit. The satellite position after the engine is turned off will be the perigee of the elliptical orbit, and the apogee will be in the circular orbit of the designed satellite operation. The preset value of the satellite speed when the engine is turned off is to meet the requirements of the apogee.After regulation and stabilization, start the engine again at the apogee to accelerate the satellite to the speed required by the operating orbit, as shown in the Schematic Diagram of Satellite Orbit Change:
The speed of the satellite at the perigee and apogee of the elliptical orbit is determined by the parking orbit and the operating orbit.[1]
Energy balance
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After the earth satellite enters orbit, it is in the conservative field of the earth, and the total energy of the satellite is conserved without considering the drag loss.Thus, an energy balance formula for satellite orbit can be established.
The potential energy of the satellite position is
, the kinetic energy of the satellite is
, the total energy of the satellite is:
The total energy is the same at any point in the orbit.
The total energies of the perigee and apogee of the satellite are:
Where, GM is the earth constant, GM=gRtwo，roneIs the perigee geocentric distance, rtwoIs the apogee geocentric distance, voneIs the perigee speed, vtwoIs the apogee speed.
Because Eperigee=Eapogee, with:
That is:
fromKepler's lawIt can be seen that the ratio of perigee to apogee velocity is equal to the inverse ratio of its geocentric distance, that is
, substituted into the above formula, including:
After sorting out, we can get:
order
, with:
The above equation is called the perigee energy balance equation of satellite orbit, which means that the kinetic energy at perigee is equal to k times its potential energy.
If ordered
, there are:
This is the satellite orbit perigee energy balance formula.[2]
