DOCSLIB.ORG

On the Motion of Planets and the Determination of Orbits (An English Translation of De Motu Planetarum Et Orbitarum Determinatione)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Motion of Planets and the Determination of Orbits (An English Translation of De Motu Planetarum Et Orbitarum Determinatione) On the Motion of Planets and the Determination of Orbits (an English translation of De Motu Planetarum et Orbitarum Determinatione) Leonhard Euler All footnotes are comments by the translator, Patrick Headley1. 1. At this time it is agreed that planets move in ellipses, with the sun located at one of the foci, and that the motion is arranged so that times are proportional to areas described around the sun. Two questions about the motion of the planets arise, one asking for properties of the ellipse, namely, the position of an apsis and the eccentricity, and the other for the motion of the planet itself in its orbit. Both questions are studied here, and, as far as difficulties of calculation permit, I will try to resolve them. 2. In fact I will first take the orbit of the planet to be known, and I will direct Fig. 1 my attention to determining the motion of the planet in it. Therefore let ADB be half the orbit of a planet at P whose aphelion is at A and perihelion at B, with the sun at focus S of the ellipse (see footnote2). Furthermore, let C be the center of the orbit, and let the semiaxis AC or BC equal a, and the distance from focus S 3 to centerpC, or eccentricity CS (see footnote ), equal b, so that the minor semiaxis CD is a2 − b2. We now assume the planet has arrived at P from aphelion A, and then progressed in a brief interval of time to p. From P and p lines are 1Mathematics Department, Gannon University, 109 University Square, Erie, PA 16541, [email protected] 2The figures accompanying this article can be found on page 4 of eulerarchive.maa.org/publications/journals/figures CASP07.pdf 3In the modern definition, the eccentricity would be the ratio of CS to AC. 1 drawn top S, as well as perpendiculars to the axis AB. Letting CQ = r, then 2 2 2 2 (a −b )(a −r ) br PQ = a and PS = a + a . 3. In this situation, the angle ASP represents the true anomaly (see footnote4), which will be called z. The mean anomaly, however, is proportional to the time in which the planet moves from A to P , or to the area ASP . Therefore, the area ADB will be to the area ASP as two right angles are to the mean anomaly. We now consider a circle of radius 1, with an arc equal to the true anomaly z. If we wish to find the mean anomaly, equal to the arc x, the ratio of area ADB to two equal right angles, orp to twice the area of the semicircle,p will be the same as that of AC · CD to 2, or a a2 − b2 to 2. Therefore a a2 − b2 : 2 = Area ASP : x, so that x = 2 Areap ASP. a a2−b2 4. With the true anomaly equal to angle ASP , the differential dz will be equal to P Sp. The angle P Sp is equal to twice the area P Sp divided by the square of 2 Area PSp 2a2P Sp PS; that is to say, dz = br 2 = (a2+br)2 . But, from the equation shown ear- (a+ a ) lier, dx = p2 P Sp . It remains therefore to express the area P Sp in a convenient a a2−b2 form, and it will be done from considerationp of the entire area.p For, indeed, Area (b+r) (a2−b2)(a2−r2) dr (a2−b2)(a2−r2) ASP = PQ·QS + R PQ · Qq = − R , whose 2 p 2a a −dr(a2+br) a2−b2 differential is p , which therefore is equal to P Sp. From this there- 2a a2−r2 −dr(a2+br) p fore the differential of the mean anomaly is dx = 2 2 2 , and the differential p a a −r 2 2 of the true anomaly is dz = −a dr pa −b . (a2+br) a2−r2 5. A relation between the mean anomaly and the true anomaly is contained in these two equations. To express this it is necessary to integrate both equations so that in the end an equation between z and x can be derived. Concerning the p−dr pbr dr first equation, it transforms at once to dx = 2 2 − 2 2 2 , whose integral is p p a −r a a −r a2−r2 b 2 2 x = A: a + a2 a − r , where A signifies the arc of a circle whose sine is the subsequent quantity, the whole sine (see footnote5) being 1. Therefore let this 4In the modern definitions, the anomalies are measured from the perihelion and not the aphe- lion. 5The whole sine, or sinus totus, is a value chosen as a radius, so that Euler’s sine is what would now be considered the radius multiplied by the sine. The tables that Euler used had varying choices for the whole sine. The logarithms of sine values that Euler uses in this article assume a whole 2 p a2−r2 bs sine a equal s, so that x = A:s + a . p 2 2 6. The equation of the other differential is dz = −a dr pa −b , which is com- (a2+br) a2−r2 pletely integrable, but can also be integrated in several ways using series. The chosen method will be examined before proceeding. It yields a series in which the powers of b increase in the numerator, so that for small eccentricities it suf- fices to use two or three initial terms. p 2 2 1·b2 1·1·b4 7. Thus, I first convert a − b into a series, which will be a − 2a − 2·4·a3 − 1·1·3·b6 b2 b4 b6 a 1 br b2r2 b3r3 5 etc. = a− − 3 − 5 etc. Next, 2 = − 3 + 5 − 7 + etc. Thus, 2·4·6·a 2a 8a 16a a +br ap a a a a a2−b2 br b2(a2−2r2) these two series multiplied term-by-term will give a2+br = 1− a2 − 2a4 + b3r(a2−2r2) b4(a4+4a2r2−8r4) b5r(a4+4a2r2−8r4) 2a6 − 8a8 + 8a10 − etc. If now each of the terms of this series is preceded by p−dr , the differential dz of the true anomaly will be a2−r2 obtained. All of the terms after the first will be completely integrable, so it is found p p p p p a2−r2 b a2−r2 b2r a2−r2 b3(a2+2r2) a2−r2 b4r(a2+2r2) a2−r2 that z = A: a − a2 + 2a4 − 6a6 + 8a8 − etc. p a2−r2 8. The arc or angle whose sine is a will be called V . Then x = b V + a sin V , and z will be determined from V , its sine, and sines of multiples b b2 b3 of V as follows: z = V − a sin V + 4a2 sin 2V − 12a3 (sin 3V + 3 sin V ) + b4 b5 b6 32a4 (sin 4V + 4 sin 2V ) − 80a5 (sin 5V + 5 sin 3V + 10 sin V ) + 192a6 (sin 6V + b7 6 sin 4V + 15 sin 2V ) − 448a7 (sin 7V + 7 sin 5V + 21 sin 3V + 35 sin V ) + etc. (see footnote6) The rule for this series extends easily, for the denominators consist of the numbers in this series: 1 · 1, 2 · 2, 3 · 4, 4 · 8, 5 · 16, 6 · 32, etc. 9. Thus, the true anomaly z will be most conveniently determined from the value x of the mean anomaly if, first, the angle V is determined from angle x b through the equation x = V + a sin V , and this then is substituted into the other equation producing the true anomaly z. It is difficult, however, to see how to determine V from x with this equation, since the equation is transcendental, and sine of 1010, but the trigonometric values assume a whole sine of 107. As a result, Euler’s use of the decimal point (actually a comma in the original text) seems somewhat erratic to the modern reader. For more information on the sinus totus see Gonzalez-Velasco,´ Enrique A. Journey through Mathematics. New York, Springer, 2011. 6Euler actually uses the symbol R for sin in this and subsequent formulas, in spite of using it for integration earlier in the text. 3 therefore V cannot entirely be represented algebraically using x. It is therefore necessary, in order for V to be determined accurately and with as little work as possible, that it is presented in the following way which seems to me to be most b b b convenient, namely, that V = x− a sin(x− a sin(x− a sin(x− etc. It will be very a easy to find the angle V from this, since, after log sin x is found, from this log b is subtracted, and then from this the logarithm 6:4637261 is subtracted; this number is required for logarithms of natural numbers so that the corresponding number will give the angle in minutes (see footnote7). Then this angle is subtracted from the mean anomaly x, and the logarithm of the sine of the resulting angle is found, a from which log b and 6:4637261 are subtracted, and the number corresponding to the resulting logarithm will give the number of minutes to be subtracted from x. If the value is to be estimated correctly, the resulting angle is then treated in the same manner until at last it is neither increased nor decreased any further. Then that angle will be the true value of V itself. a 10. Angle V having been found in this way, both log b and 6:4637261 are subtracted from the logarithm of its sine.
Load more

Recommended publications
  • Appendix a Orbits
    Appendix A Orbits As discussed in the Introduction, a good ¯rst approximation for satellite motion is obtained by assuming the spacecraft is a point mass or spherical body moving in the gravitational ¯eld of a spherical planet. This leads to the classical two-body problem. Since we use the term body to refer to a spacecraft of ¯nite size (as in rigid body), it may be more appropriate to call this the two-particle problem, but I will use the term two-body problem in its classical sense. The basic elements of orbital dynamics are captured in Kepler's three laws which he published in the 17th century. His laws were for the orbital motion of the planets about the Sun, but are also applicable to the motion of satellites about planets. The three laws are: 1. The orbit of each planet is an ellipse with the Sun at one focus. 2. The line joining the planet to the Sun sweeps out equal areas in equal times. 3. The square of the period of a planet is proportional to the cube of its mean distance to the sun. The ¯rst law applies to most spacecraft, but it is also possible for spacecraft to travel in parabolic and hyperbolic orbits, in which case the period is in¯nite and the 3rd law does not apply. However, the 2nd law applies to all two-body motion. Newton's 2nd law and his law of universal gravitation provide the tools for generalizing Kepler's laws to non-elliptical orbits, as well as for proving Kepler's laws.
    [Show full text]
  • Astrodynamics
    Politecnico di Torino SEEDS SpacE Exploration and Development Systems Astrodynamics II Edition 2006 - 07 - Ver. 2.0.1 Author: Guido Colasurdo Dipartimento di Energetica Teacher: Giulio Avanzini Dipartimento di Ingegneria Aeronautica e Spaziale e-mail: [email protected] Contents 1 Two–Body Orbital Mechanics 1 1.1 BirthofAstrodynamics: Kepler’sLaws. ......... 1 1.2 Newton’sLawsofMotion ............................ ... 2 1.3 Newton’s Law of Universal Gravitation . ......... 3 1.4 The n–BodyProblem ................................. 4 1.5 Equation of Motion in the Two-Body Problem . ....... 5 1.6 PotentialEnergy ................................. ... 6 1.7 ConstantsoftheMotion . .. .. .. .. .. .. .. .. .... 7 1.8 TrajectoryEquation .............................. .... 8 1.9 ConicSections ................................... 8 1.10 Relating Energy and Semi-major Axis . ........ 9 2 Two-Dimensional Analysis of Motion 11 2.1 ReferenceFrames................................. 11 2.2 Velocity and acceleration components . ......... 12 2.3 First-Order Scalar Equations of Motion . ......... 12 2.4 PerifocalReferenceFrame . ...... 13 2.5 FlightPathAngle ................................. 14 2.6 EllipticalOrbits................................ ..... 15 2.6.1 Geometry of an Elliptical Orbit . ..... 15 2.6.2 Period of an Elliptical Orbit . ..... 16 2.7 Time–of–Flight on the Elliptical Orbit . .......... 16 2.8 Extensiontohyperbolaandparabola. ........ 18 2.9 Circular and Escape Velocity, Hyperbolic Excess Speed . .............. 18 2.10 CosmicVelocities
    [Show full text]
  • A Hot Subdwarf-White Dwarf Super-Chandrasekhar Candidate
    A hot subdwarf–white dwarf super-Chandrasekhar candidate supernova Ia progenitor Ingrid Pelisoli1,2*, P. Neunteufel3, S. Geier1, T. Kupfer4,5, U. Heber6, A. Irrgang6, D. Schneider6, A. Bastian1, J. van Roestel7, V. Schaffenroth1, and B. N. Barlow8 1Institut fur¨ Physik und Astronomie, Universitat¨ Potsdam, Haus 28, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany 2Department of Physics, University of Warwick, Coventry, CV4 7AL, UK 3Max Planck Institut fur¨ Astrophysik, Karl-Schwarzschild-Straße 1, 85748 Garching bei Munchen¨ 4Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA 5Texas Tech University, Department of Physics & Astronomy, Box 41051, 79409, Lubbock, TX, USA 6Dr. Karl Remeis-Observatory & ECAP, Astronomical Institute, Friedrich-Alexander University Erlangen-Nuremberg (FAU), Sternwartstr. 7, 96049 Bamberg, Germany 7Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA 8Department of Physics and Astronomy, High Point University, High Point, NC 27268, USA *[email protected] ABSTRACT Supernova Ia are bright explosive events that can be used to estimate cosmological distances, allowing us to study the expansion of the Universe. They are understood to result from a thermonuclear detonation in a white dwarf that formed from the exhausted core of a star more massive than the Sun. However, the possible progenitor channels leading to an explosion are a long-standing debate, limiting the precision and accuracy of supernova Ia as distance indicators. Here we present HD 265435, a binary system with an orbital period of less than a hundred minutes, consisting of a white dwarf and a hot subdwarf — a stripped core-helium burning star.
    [Show full text]
  • Electric Propulsion System Scaling for Asteroid Capture-And-Return Missions
    Electric propulsion system scaling for asteroid capture-and-return missions Justin M. Little⇤ and Edgar Y. Choueiri† Electric Propulsion and Plasma Dynamics Laboratory, Princeton University, Princeton, NJ, 08544 The requirements for an electric propulsion system needed to maximize the return mass of asteroid capture-and-return (ACR) missions are investigated in detail. An analytical model is presented for the mission time and mass balance of an ACR mission based on the propellant requirements of each mission phase. Edelbaum’s approximation is used for the Earth-escape phase. The asteroid rendezvous and return phases of the mission are modeled as a low-thrust optimal control problem with a lunar assist. The numerical solution to this problem is used to derive scaling laws for the propellant requirements based on the maneuver time, asteroid orbit, and propulsion system parameters. Constraining the rendezvous and return phases by the synodic period of the target asteroid, a semi- empirical equation is obtained for the optimum specific impulse and power supply. It was found analytically that the optimum power supply is one such that the mass of the propulsion system and power supply are approximately equal to the total mass of propellant used during the entire mission. Finally, it is shown that ACR missions, in general, are optimized using propulsion systems capable of processing 100 kW – 1 MW of power with specific impulses in the range 5,000 – 10,000 s, and have the potential to return asteroids on the order of 103 104 tons. − Nomenclature
    [Show full text]
  • AFSPC-CO TERMINOLOGY Revised: 12 Jan 2019
    AFSPC-CO TERMINOLOGY Revised: 12 Jan 2019 Term Description AEHF Advanced Extremely High Frequency AFB / AFS Air Force Base / Air Force Station AOC Air Operations Center AOI Area of Interest The point in the orbit of a heavenly body, specifically the moon, or of a man-made satellite Apogee at which it is farthest from the earth. Even CAP rockets experience apogee. Either of two points in an eccentric orbit, one (higher apsis) farthest from the center of Apsis attraction, the other (lower apsis) nearest to the center of attraction Argument of Perigee the angle in a satellites' orbit plane that is measured from the Ascending Node to the (ω) perigee along the satellite direction of travel CGO Company Grade Officer CLV Calculated Load Value, Crew Launch Vehicle COP Common Operating Picture DCO Defensive Cyber Operations DHS Department of Homeland Security DoD Department of Defense DOP Dilution of Precision Defense Satellite Communications Systems - wideband communications spacecraft for DSCS the USAF DSP Defense Satellite Program or Defense Support Program - "Eyes in the Sky" EHF Extremely High Frequency (30-300 GHz; 1mm-1cm) ELF Extremely Low Frequency (3-30 Hz; 100,000km-10,000km) EMS Electromagnetic Spectrum Equitorial Plane the plane passing through the equator EWR Early Warning Radar and Electromagnetic Wave Resistivity GBR Ground-Based Radar and Global Broadband Roaming GBS Global Broadcast Service GEO Geosynchronous Earth Orbit or Geostationary Orbit ( ~22,300 miles above Earth) GEODSS Ground-Based Electro-Optical Deep Space Surveillance
    [Show full text]
  • Use of MESSENGER Radioscience Data to Improve Planetary Ephemeris and to Test General Relativity
    A&A 561, A115 (2014) Astronomy DOI: 10.1051/0004-6361/201322124 & © ESO 2014 Astrophysics Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity A. K. Verma1;2, A. Fienga3;4, J. Laskar4, H. Manche4, and M. Gastineau4 1 Observatoire de Besançon, UTINAM-CNRS UMR6213, 41bis avenue de l’Observatoire, 25000 Besançon, France e-mail: [email protected] 2 Centre National d’Études Spatiales, 18 avenue Édouard Belin, 31400 Toulouse, France 3 Observatoire de la Côte d’Azur, GéoAzur-CNRS UMR7329, 250 avenue Albert Einstein, 06560 Valbonne, France 4 Astronomie et Systèmes Dynamiques, IMCCE-CNRS UMR8028, 77 Av. Denfert-Rochereau, 75014 Paris, France Received 24 June 2013 / Accepted 7 November 2013 ABSTRACT The current knowledge of Mercury’s orbit has mainly been gained by direct radar ranging obtained from the 60s to 1998 and by five Mercury flybys made with Mariner 10 in the 70s, and with MESSENGER made in 2008 and 2009. On March 18, 2011, MESSENGER became the first spacecraft to orbit Mercury. The radioscience observations acquired during the orbital phase of MESSENGER drastically improved our knowledge of the orbit of Mercury. An accurate MESSENGER orbit is obtained by fitting one-and-half years of tracking data using GINS orbit determination software. The systematic error in the Earth-Mercury geometric positions, also called range bias, obtained from GINS are then used to fit the INPOP dynamical modeling of the planet motions. An improved ephemeris of the planets is then obtained, INPOP13a, and used to perform general relativity tests of the parametrized post-Newtonian (PPN) formalism.
    [Show full text]
  • Orbit and Spin
    Orbit and Spin Overview: A whole-body activity that explores the relative sizes, distances, orbit, and spin of the Sun, Earth, and Moon. Target Grade Level: 3-5 Estimated Duration: 2 40-minute sessions Learning Goals: Students will be able to… • compare the relative sizes of the Earth, Moon, and Sun. • contrast the distance between the Earth and Moon to the distance between the Earth and Sun. • differentiate between the motions of orbit and spin. • demonstrate the spins of the Earth and the Moon, as well as the orbits of the Earth around the Sun, and the Moon around the Earth. Standards Addressed: Benchmarks (AAAS, 1993) The Physical Setting, 4A: The Universe, 4B: The Earth National Science Education Standards (NRC, 1996) Physical Science, Standard B: Position and motion of objects Earth and Space Science, Standard D: Objects in the sky, Changes in Earth and sky Table of Contents: Background Page 1 Materials and Procedure 5 What I Learned… Science Journal Page 14 Earth Picture 15 Sun Picture 16 Moon Picture 17 Earth Spin Demonstration 18 Moon Orbit Demonstration 19 Extensions and Adaptations 21 Standards Addressed, detailed 22 Background: Sun The Sun is the center of our Solar System, both literally—as all of the planets orbit around it, and figuratively—as its rays warm our planet and sustain life as we know it. The Sun is very hot compared to temperatures we usually encounter. Its mean surface temperature is about 9980° Fahrenheit (5800 Kelvin) and its interior temperature is as high as about 28 million° F (15,500,000 Kelvin).
    [Show full text]
  • Elliptical Orbits
    1 Ellipse-geometry 1.1 Parameterization • Functional characterization:(a: semi major axis, b ≤ a: semi minor axis) x2 y 2 b p + = 1 ⇐⇒ y(x) = · ± a2 − x2 (1) a b a • Parameterization in cartesian coordinates, which follows directly from Eq. (1): x a · cos t = with 0 ≤ t < 2π (2) y b · sin t – The origin (0, 0) is the center of the ellipse and the auxilliary circle with radius a. √ – The focal points are located at (±a · e, 0) with the eccentricity e = a2 − b2/a. • Parameterization in polar coordinates:(p: parameter, 0 ≤ < 1: eccentricity) p r(ϕ) = (3) 1 + e cos ϕ – The origin (0, 0) is the right focal point of the ellipse. – The major axis is given by 2a = r(0) − r(π), thus a = p/(1 − e2), the center is therefore at − pe/(1 − e2), 0. – ϕ = 0 corresponds to the periapsis (the point closest to the focal point; which is also called perigee/perihelion/periastron in case of an orbit around the Earth/sun/star). The relation between t and ϕ of the parameterizations in Eqs. (2) and (3) is the following: t r1 − e ϕ tan = · tan (4) 2 1 + e 2 1.2 Area of an elliptic sector As an ellipse is a circle with radius a scaled by a factor b/a in y-direction (Eq. 1), the area of an elliptic sector PFS (Fig. ??) is just this fraction of the area PFQ in the auxiliary circle. b t 2 1 APFS = · · πa − · ae · a sin t a 2π 2 (5) 1 = (t − e sin t) · a b 2 The area of the full ellipse (t = 2π) is then, of course, Aellipse = π a b (6) Figure 1: Ellipse and auxilliary circle.
    [Show full text]
  • Analysis of Transfer Maneuvers from Initial
    Revista Mexicana de Astronom´ıa y Astrof´ısica, 52, 283–295 (2016) ANALYSIS OF TRANSFER MANEUVERS FROM INITIAL CIRCULAR ORBIT TO A FINAL CIRCULAR OR ELLIPTIC ORBIT M. A. Sharaf1 and A. S. Saad2,3 Received March 14 2016; accepted May 16 2016 RESUMEN Presentamos un an´alisis de las maniobras de transferencia de una ´orbita circu- lar a una ´orbita final el´ıptica o circular. Desarrollamos este an´alisis para estudiar el problema de las transferencias impulsivas en las misiones espaciales. Consideramos maniobras planas usando ecuaciones reci´enobtenidas; con estas ecuaciones se com- paran las maniobras circulares y el´ıpticas. Esta comparaci´on es importante para el dise˜no´optimo de misiones espaciales, y permite obtener mapeos ´utiles para mostrar cu´al es la mejor maniobra. Al respecto, desarrollamos este tipo de comparaciones mediante 10 resultados, y los mostramos gr´aficamente. ABSTRACT In the present paper an analysis of the transfer maneuvers from initial circu- lar orbit to a final circular or elliptic orbit was developed to study the problem of impulsive transfers for space missions. It considers planar maneuvers using newly derived equations. With these equations, comparisons of circular and elliptic ma- neuvers are made. This comparison is important for the mission designers to obtain useful mappings showing where one maneuver is better than the other. In this as- pect, we developed this comparison throughout ten results, together with some graphs to show their meaning. Key Words: celestial mechanics — methods: analytical — space vehicles 1. INTRODUCTION The large amount of information from interplanetary missions, such as Pioneer (Dyer et al.
    [Show full text]
  • Perturbation Theory in Celestial Mechanics
    Perturbation Theory in Celestial Mechanics Alessandra Celletti Dipartimento di Matematica Universit`adi Roma Tor Vergata Via della Ricerca Scientifica 1, I-00133 Roma (Italy) ([email protected]) December 8, 2007 Contents 1 Glossary 2 2 Definition 2 3 Introduction 2 4 Classical perturbation theory 4 4.1 The classical theory . 4 4.2 The precession of the perihelion of Mercury . 6 4.2.1 Delaunay action–angle variables . 6 4.2.2 The restricted, planar, circular, three–body problem . 7 4.2.3 Expansion of the perturbing function . 7 4.2.4 Computation of the precession of the perihelion . 8 5 Resonant perturbation theory 9 5.1 The resonant theory . 9 5.2 Three–body resonance . 10 5.3 Degenerate perturbation theory . 11 5.4 The precession of the equinoxes . 12 6 Invariant tori 14 6.1 Invariant KAM surfaces . 14 6.2 Rotational tori for the spin–orbit problem . 15 6.3 Librational tori for the spin–orbit problem . 16 6.4 Rotational tori for the restricted three–body problem . 17 6.5 Planetary problem . 18 7 Periodic orbits 18 7.1 Construction of periodic orbits . 18 7.2 The libration in longitude of the Moon . 20 1 8 Future directions 20 9 Bibliography 21 9.1 Books and Reviews . 21 9.2 Primary Literature . 22 1 Glossary KAM theory: it provides the persistence of quasi–periodic motions under a small perturbation of an integrable system. KAM theory can be applied under quite general assumptions, i.e. a non– degeneracy of the integrable system and a diophantine condition of the frequency of motion.
    [Show full text]
  • Strategy for Human Spaceflight In
    Developing the sustainable foundations for returning Americans to the Moon and enabling a new era of commercial spaceflight in low Earth orbit (LEO) are the linchpins of our national human spaceflight policy. As we work to return Americans to the Moon, we plan to do so in partnership with other nations. We will therefore coordinate our lunar exploration strategy with our ISS partners while maintaining and expanding our partnerships in LEO. As we work to create a new set of commercial human spaceflight capabilities, we will enable U.S. commercial enterprises to develop and operate under principles of long-term sustainability for space activity and recognize that their success cannot depend on Federal funding and programs alone. The National Space Council recognized the need for such a national strategy for human spaceflight in LEO and economic growth in space, and in February of 2018, called on NASA, the Department of State, and the Department of Commerce to work together to develop one. This strategy follows the direction established by the Administration through Space Policy Directives 1, 2, and 3, which created an innovative new framework for American leadership by reinvigorating America’s human exploration of the Moon and Mars; streamlining regulations on the commercial use of space; and establishing the first national policy for space traffic management. Our strategy for the future of human spaceflight in LEO and for economic growth in space will operate within the context of these directives. Through interagency dialogue, and in coordination with the Executive Office of the President, we have further defined our overarching goals for human spaceflight in LEO as follows: 1.
    [Show full text]
  • Sun-Synchronous Satellites
    Topic: Sun-synchronous Satellites Course: Remote Sensing and GIS (CC-11) M.A. Geography (Sem.-3) By Dr. Md. Nazim Professor, Department of Geography Patna College, Patna University Lecture-3 Concept: Orbits and their Types: Any object that moves around the Earth has an orbit. An orbit is the path that a satellite follows as it revolves round the Earth. The plane in which a satellite always moves is called the orbital plane and the time taken for completing one orbit is called orbital period. Orbit is defined by the following three factors: 1. Shape of the orbit, which can be either circular or elliptical depending upon the eccentricity that gives the shape of the orbit, 2. Altitude of the orbit which remains constant for a circular orbit but changes continuously for an elliptical orbit, and 3. Angle that an orbital plane makes with the equator. Depending upon the angle between the orbital plane and equator, orbits can be categorised into three types - equatorial, inclined and polar orbits. Different orbits serve different purposes. Each has its own advantages and disadvantages. There are several types of orbits: 1. Polar 2. Sunsynchronous and 3. Geosynchronous Field of View (FOV) is the total view angle of the camera, which defines the swath. When a satellite revolves around the Earth, the sensor observes a certain portion of the Earth’s surface. Swath or swath width is the area (strip of land of Earth surface) which a sensor observes during its orbital motion. Swaths vary from one sensor to another but are generally higher for space borne sensors (ranging between tens and hundreds of kilometers wide) in comparison to airborne sensors.
    [Show full text]