인공위성 궤도역학 이물체 문제(Two-body problem)

소개

"인공위성 궤도역학 이물체 문제(Two-body problem)"에 대한 내용입니다.

목차

1. Introduction
2. The Two-Body Problem
3. Energy and Angular Momentum
4. The Orbit Equation
5. Conic-Section Geometry
6. Kepler's Equation
7. The Classical Orbital Elements
8. Position and Velocity
9. Orbit Determination and Satellite Tracking

본문내용

2.1 Introduction

Nicholas Copernicus (1473-1543) 지동설
Tycho Brache (1546-1601) 육분의, 천체 관측
Galilei Gaileo (1564-1642) 망원경 사용 천체관측, 지동설, 중력 실험
Johannes Kepler (1571-1630) 3법칙
Isaac Newton (1643-1727) 미적분학, 중력법칙, 운동법칙, Kepler의 법칙을 수식으로 유도

(http://www.gap-system.org/~history/BiogIndex.html)

2.2 The Two-Body Problem

그림 2.4에 있는 것 같은 두 개의 질점으로 이루어진 시스템을 생각하자. 각각의 질점은 서로 상대방의 질점에 인력을 미치고, 이 외에 다른 힘은 존재하지 않는다. 이 경우 이 두 질점의 운동방정식을 쓰면 다음과 같다.
m_1 {rm bold ddot R}_1 = {G m_1 m_2 } over { left| {rm bold R}_2 - {rm bold R}_1 right|}^2 { ( {rm bold R}_2 - {rm bold R}_1 ) } over {left| {rm bold R}_2 - {rm bold R}_1 right|} (2.1)
m_2 {rm bold ddot R}_2 = {G m_1 m_2 } over { left| {rm bold R}_1 - {rm bold R}_2 right|}^2 { ( {rm bold R}_1 - {rm bold R}_2 ) } over {left| {rm bold R}_1 - {rm bold R}_2 right|} (2.2)

<중 략>

2.7 The Classical Orbital Elements

앞에서 본 것처럼 two body problem은 원래 6자유도 시스템에서 무게중심의 등속운동조건이 적용됨으로 3자유도 시스템으로 바꾸어 생각할 수 있고, 시스템의 지배방정식에 초기 위치 및 속도를 적용하면 궤도를 예측할 수 있게 된다.

참고자료

· TLE (Two Line Element)
· http://www.celestrak.com/
· http://spaceflight.nasa.gov/realdata/sightings/SSapplications/Post/JavaSSOP/SSOP_Help/tle_def.html
· Definition of Two-line Element Set Coordinate System
· Name of Satellite
· (NOAA 6) This is simply the name associated with the satellite. Typical names you might be interested in might be "Mir" or "ISS".
· International Designator
· (84 123A) The 84 indicates launch year was in 1984, while the 123 tallies the 124th launch of the year, and "A" shows it was the first object resulting from this launch.
· Epoch Date and Day of Year Fraction
· The day of year fraction is just the number of days (in GMT) passed in the particular year. For example, the date above shows "86" as the epoch year (1986) and 50.28438588 as number of days after January 1, 1986. The resulting time of the vector would be 1986/050:06:49:30.94. Note that NASA SkyWatch will expect the time tag to be the same format as shown above when entering a TLE data.
· This was computed as follows:
· Start with 50.28438588 days (Days = 50)
· 50.28438588 days - 50 = 0.28438588 days
· 0.28438588 days x 24 hours/day = 6.8253 hours (Hours = 6)
· 6.8253 hours - 6 = 0.8253 hours
· 0.8253 hours x 60 minutes/hour = 49.5157 minutes (Minutes = 49)
· 49.5157 - 49 = 0.5157 minutes
· 0.5157 minutes x 60 seconds/minute = 30.94 seconds (Seconds = 30.94)
· Ballistic Coefficient
· (0.00000140) Also called the first derivative of mean motion, the ballistic coefficient is the daily rate of change in the number of revs the object completes each day, divided by 2. Units are revs/day. This is "catch all" drag term used in the Simplified General Perturbations (SGP4) USSPACECOM predictor.
· Second Derivative of Mean Motion
· (00000-0 = 0.00000) The second derivative of mean motion is a second order drag term in the SGP4 predictor used to model terminal orbit decay. It measures the second time derivative in daily mean motion, divided by 6. Units are revs/day^3. A leading decimal must be applied to this value. The last two characters define an applicable power of 10. (12345-5 = 0.0000012345).
· Drag Term
· (67960-4 = 0.000067960) Also called the radiation pressure coefficient (or BSTAR), the parameter is another drag term in the SGP4 predictor. Units are earth radii^-1. The last two characters define an applicable power of 10. Do not confuse this parameter with "B-Term", the USSPACECOM special perturbations factor of drag coefficient, multiplied by reference area, divided by weight.
· Element Set Number and Check Sum
· (5293) The element set number is a running count of all 2 line element sets generated by USSPACECOM for this object (in this example, 529). Since multiple agencies perform this function, numbers are skipped on occasion to avoid ambiguities. The counter should always increase with time until it exceeds 999, when it reverts to 1. The last number of the line is the check sum of line 1.
· Satellite Number
· (11416) This is the catalog number USSPACECOM has designated for this object. A "U" indicates an unclassified object.
· Inclination (degrees)
· The angle between the equator and the orbit plane. The value provided is the TEME mean inclination.
· Right Ascension of the Ascending Node (degrees)
· The angle between vernal equinox and the point where the orbit crosses the equatorial plane (going north). The value provided is the TEME mean right ascension of the ascending node.
· Eccentricity
· (0012788) A constant defining the shape of the orbit (0=circular, Less than 1=elliptical). The value provided is the mean eccentricity. A leading decimal must be applied to this value.
· Argument of Perigee (degrees)
· The angle between the ascending node and the orbit's point of closest approach to the earth (perigee). The value provided is the TEME mean argument of perigee.
· Mean Anomaly (degrees)
· The angle, measured from perigee, of the satellite location in the orbit referenced to a circular orbit with radius equal to the semi-major axis.
· Mean Motion
· (14.24899292) The value is the mean number of orbits per day the object completes. There are 8 digits after the decimal, leaving no trailing space(s) when the following element exceeds 9999.
· Revolution Number and Check Sum
· (346978) The orbit number at Epoch Time. This time is chosen very near the time of true ascending node passage as a matter of routine. The last digit is the check sum for line 2.
· http://www.celestrak.com/: 최신 TLE data
· SkyWatch (Java 필요)
· http://spaceflight.nasa.gov/realdata/sightings/SSapplications/Post/JavaSSOP/JavaSSOP.html
· (과제) 아리랑위성 1호(KOMPSAT)의 궤도 분석 (Earth Resource로 분류)
· (kompsat.kari.re.kr)
· keywords: MPC (minor planet center)