Satellite orbit and two rows of data tle

Recently, because of the relationship between Sino-2 and Beidou, many netizens posted the Tle data indicating the orbit of the satellite. Here is a brief introduction to the satellite orbital parameters and the format of the tle. Although no one actually reads the TLE data directly, it is the use of software to obtain satellite orbit and location information, but it is hoped that these introductions can be useful for understanding the concept of satellite orbits. As hastily written, there may be some errors, if seen also please point out.
Earlier on the track part was written earlier, and later found similar to the corresponding part of an article in the magazine about China's anti-health. Estimates refer to similar materials, and the thing itself is a mature theory.
First, take a look at satellite orbits. Satellites in space do periodic motions under the influence of forces such as the Earth's gravity, and the first-order approximation is a Kepler elliptical orbit. Due to the existence of other forces (such as the shape of the earth, atmospheric resistance, gravitational attraction of other planets, etc.), the actual orbit deviates from the ideal Kepler orbit, which is called "orbital perturbation" in space. Here we do not look at the perturbation, first talk about the ideal Kepler orbit situation.
For the sole purpose of determining the orbit of a satellite, we need 6 parameters, see below:

1. Track half-length axis, half the length of the elliptical axis. For a circle, that is, the radius
2. Orbital eccentricity, which is the distance between the two focal points of the ellipse and the ratio of the long axis. For a circle, it is 0.
These two elements determine the shape of the track
3. Orbital inclination, this is the angle between the orbital plane and the Earth's equatorial plane. For geosynchronous geostationary satellites over the equator, the dip is 0.
4. Ascending intersection red: The point at which a satellite travels from the southern hemisphere to the northern hemisphere through the equator is called the ascending intersection. This point and the vernal equinox for the center of the earth are called ascending intersections of the red meridian.
These two quantities determine the position of the satellite orbital plane in space.
5. Perigee amplitude angle: This is the angle of the perigee and ascending intersection to the center of the Earth.
While the front determines the position of the orbital plane in space, the orbit itself can be rotated in the orbital plane. This value determines the position of the track in the orbital plane.
6. The significance of this is obvious at the time of the perigee. The change of satellite position over time requires an initial value.
One thing to point out is that the 6 parameters above are not the only ones that describe the orbit of a satellite, and can select other parameters, such as orbital periods. However, since the complete description also requires only 6 parameters, there is a fixed conversion relationship between them. For example, the orbital period can be determined only by the half-length axis (which is also covered by the tle below), and vice versa. The group selected above is a more natural group.
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Let's talk about two rows of data from the Tle (Two-line Element). Examples of recent data from the North bucket
Beidou 2A
1 30323U 07003A 07067.68277059.00069181 13771-5 44016-2 0 587
2 30323 025.0330 358.9828 7594216 197.8808 102.7839 01.92847527 650
The real data is actually the following 2 lines, but there is a line of information about other things about the space object (the space object can be a satellite, can be an end-stage rocket, can be a fragment.) For simplicity here, it's called a satellite). The first one is the satellite name. Note that this is going to change and not necessarily accurate. In the first few tle data after the launch of the satellite, it is often called object A, B, C ... Slowly you will figure out which is the satellite, which is the last rocket, which is the fragment of the separation, and give the corresponding name. But if this is another country's secret satellite, then the satellite name is purely American speculation, such as our Beidou. In some cases, the name of the line contains some numbers, about the size of the satellite, brightness and so on.
Tle first row of data
1 30323U 07003A 07067.68277059.00069181 13771-5 44016-2 0 587
30323U 30323 is the satellite number given by the North American Air Defense Command (NORAD). U stands for non-secrecy. All we see is u, otherwise we won't see this set of tle.
07003A International number, 07 means 2007 (2 digits indicate that the year will have a problem after 50, because humans fired the first orbital object in 1957) and 003 indicated that it was the 3rd launch of the year. A means the object with the number a in the launch, and the other b,c,d and so on. The international number is 2007-003a.
07067.68277059 this represents the point in time for this set of track data. 07 or 2007, 067 means the 67th day, that is, March 8.
68277059 means that the moment of the day is about 16:22.
.000069181 the time first derivative of the average movement is in addition to 2. Note that this is not instantaneous angular velocity.
13771-5 the second derivative of the average motion to time is in addition to 6.
44016-2 Bstar resistance coefficient. These 3 quantities are used in the orbital perturbation model. In fact, the first 2 has not really been adopted.
0 orbital model. They have different numbers representing different models, but they're all 0, which is using the SGP4/SDP4 orbital model.
58 means this is the 58th set of tle for this space object.
7 The last one is the check digit
tle second row of data
2 30323 025.0330 358.9828 7594216 197.8808 102.7839 01.92847527 650
30323 NORAD satellite number.
025.0191 orbital inclination. This corresponds exactly to the previous orbital inclination.
The Red meridian of the 358.9828-liter intersection, which corresponds to the red meridian of the ascending node above.
7594216 orbital eccentricity, 0.7597678, indicates that this is an ellipse
197.8808 perigee amplitude angle, and this is the same as before.
102.7839 Close Point angle. This represents the time when the group of tle corresponds to the location of the satellite in orbit, the details are a little complicated, not to repeat. This and the previous "perigee moment" can be deduced from each other.
01.92847527 laps around the Earth each day. The countdown to this is the cycle. It can be seen that the current period of Beidou is about 12 hours. And the cycle and the half-length axis of the track have a simple conversion relationship. So the 6 elements of Tle's orbit, and the 6 elements we said earlier, can be deduced entirely from one another.
65 number of laps flown since launch
0 Check Digit

the above is Shh original. --darklighter

conversion of orbital period and half-length axes

The relationship between the artificial Earth satellite operating cycle T (seconds) and the circular orbital radius or the half-length axis R (m) of the elliptical orbit can be calculated using the following formula:
R= (GM t^2/4π^2) ^ (1/3)
Among them, gm=398.60047x10^12,
After substituting the constants, we know that R=21613.546XT^2/3
It is known that the Earth's rotation period is 86164.09053 seconds,
The satellite orbits the Earth 16 times a day, with a period of one-sixteenth (about 1.5 hours) of the Earth's rotation, and a half-length axis of 6640.441 kilometres. The orbit is suitable for near-earth reconnaissance satellites.
The satellite orbits the Earth 12 times a day, with a period of one-twelveth (about 2 hours) of the Earth's rotation, and a half-length axis of 8044.321 kilometres.
The satellite orbits the Earth 8 times a day, with a period of one-eighth (about 3 hours) of the Earth's rotation, and a half-length axis of 10541.043 kilometres.
The satellite orbits the Earth 6 times a day, with a period of one-sixth (about 4 hours) of the Earth's rotation, and a half-length axis of 12769.564 kilometres.
The satellite orbits the Earth 4 times a day, with a period of One-fourth (about 6 hours) of the Earth's rotation, and a half-length axis of 16732.862 kilometres.
The satellite orbits the Earth 3 times a day, with a period of one-third (about 8 hours) of the Earth's rotation, and a half-length axis of 20270.419 kilometres.
The satellite orbits the Earth 2 times a day, with a period of one-second (about 12 hours) of the Earth's rotation, and a half-length axis of 26561.763 kilometres. This track is suitable for global positioning systems.
The satellite orbits around the Earth 1 times a day, with the same cycle as the Earth's rotation, with a radius of 42164.171 km in the Earth's orbit and 35786.031 kilometres above the equator (6378.140 km). The orbit is suitable for communications satellites.

It is very complicated to calculate and determine the orbit of artificial Earth satellites in actual work, so many factors should be taken into account to solve them with advanced mathematics. The above is simply calculated with elementary mathematics, is really swim, right when the science bar.

The following is a supplement to Darklighter:

calculation of orbital velocity

Elliptical orbital Velocity formula:
v = (GM (2/r-1/a)) ^0.5
G: Gravitational constant
M: Center Celestial Mass
R: The distance between the satellite and the heart of the central Sky
A: half-length shaft

Special conditions for circular orbits:
v = (gm/(H + R)) ^0.5
H: Track Height
R: Radius of the center celestial body

Special case of far and near Arch point:
VA = (GM (ha + R)/(HP + R)/a) ^0.5
VP = (GM (HP + R)/(HA + R)/a) ^0.5
VA: Far arch point speed
VP: Near-Arch point speed
Ha: Far arch point height
HP: Near Arch point height

Instance:
(km) LEO:
h = km
v = 7785/s

The SSO:
h = km
v = 7452/s

GEO:
H = 35786 km
v = 3075/s

Lunar Circular orbit:
h = (km)
M = 7.3477 x 10^22 kg
R = 1738 km
v = 1633/s

Standard GTO:
Ha = 35786 km
HP = km
VA = 1598/s
VP = 10240/S

The orbit of a farming month is transferred:
Ha = 380000 km
HP = km
VP = 10917/S

Reference documents:

1. Orbital elements (http://baike.baidu.com/link?url=87mNHh7IDMNN7v1wjDWk-BN5r8MjjFuUK7vbKN_ 1jxawoct1jpwp75ukdp0zvx9niudhxbul_oadwsgua-bo0k)

2. The concept and calculation method of TLE data and satellite orbits (http://www.shenkong.net/Explore/1207/TLESJHWXGDDGNHJSFF09081535.htm)

3. Tbus,agros and Tle Rail (http://blog.sina.com.cn/s/blog_764f855d0100rgw1.html)

4, [Science]tle satellite orbital parameters detailed, and perigee calculation (http://lt.cjdby.net/thread-332217-1-1.html)

Satellite orbit and two rows of data tle