What is Eccentricity: Definition and 61 Discussions

In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy.

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  1. Sciencemaster

    I Database of binary star data info within 10 PC of Earth

    I'm looking for a database of binary stars within 10 PC of Earth, including information such as eccentricity of orbits, their distance from one another, etc. I'm hoping to find a list with this information, or just a collection of pages with this information. I've tried Simbad but I can't find...
  2. O

    I Is the eccentricity of the lunar orbit constant?

    The wikipedia article on Lunar distance contains a confusing graph. The graph seems to suggest that the eccentricity of the lunar orbit is maximal in january and ~july, and minimal in april and ~october. I think the eccentricity should be constant. Is wikipedia right or wrong, or is there some...
  3. C

    What is the eccentricity of an orbit such that Vp = 2Va?

    Summary:: A question on a recent exam was, "At what eccentricity does an orbit experience a velocity at periapsis that is twice the velocity an apoapsis?" I don't know why the provided solution is correct. On a recent exam, one of the questions was "At what eccentricity does an orbit...
  4. DnA 9413

    Writing: Input Wanted How to model Eccentricity, Obliquity and Recession in Excel

    Hi Everyone, I'm writing a sci-fi book that looks at humanity's response to the end of life on Earth and their voyage to a new home. The first part of the book is how a large mass of dark matter in the relative vicinity of Earth (50 light years?) starts the process of extending the...
  5. QuarkDecay

    I Understanding the Impact of Solar Radiation and Eccentricity on Earth's Climate

    I have two questions (1) If we have two areas, for example one in America and the other on Asia, both with the same latitude φ, which one of the areas will receive more Solar Radiation? Or will it be the same? (2) If Earth's eccentricity graph for the past 750k years is this...
  6. D

    I Moon's eccentricity, apogee and perigee

    Why do these properties each have a range each instead of a fixed value? Is it because of the 8 year precession? I'm writing a graphical software that will illustrate the lunar orbit. I planned to show the precession too but am unsure what values of apogee and perigee and even eccentricity...
  7. M

    B Celestial Mechanics: Eccentricity of Orbits

    a simple question about celestial mechanics...will the orbit of an object in an eccentric orbit become more circular over time, irrespective of impacts with other debris?
  8. sempiternum

    Vibration in "cantilever" rotating bar

    Hi. I'm working in the design of an auotomatic bar feeder for a CNC lathe. I've established that the bars will not be longer than 1.2 m and will not have a diameter of more than 75 mm. Suppose they are steel bars, which would make them have a mass of about 80 kg So, bars are tightly held in one...
  9. Vanessa Avila

    Finding the speed of the comet

    Homework Statement Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.2×10^4 m/s when at a distance of 2.6×10^11 m from the center of the sun, what is its speed when at a distance of 4.2×10^10 m Homework Equations L = rp = r(mv) The Attempt at...
  10. Clive Redwood

    I Physical Significance of Eccentricity & Semi-Latus Rectum of Orbital Ellipse

    What are the physical significances of the eccentricity and of the semi-latus rectum of the orbital ellipse?
  11. A

    How to add eccentricity to Kepler's Laws in cartesian

    Hi, I'm currently making a three-body simulator and I'm trying to add the eccentricity to Kepler's Law to turn the circular orbits to more of a elliptical orbit? I'm using Newton's Law of Gravitational to plot the new positions. How would I add in the eccentricity to this equation? I'm...
  12. F

    What is the cause of variations in lunar eccentricity?

    I'm still working on understanding some of the subtleties of the lunar orbit. We know that the lunar nodes ( where the lunar orbit crosses the plane of the ecliptic ( a cryptic term for the plane of the Earth's orbit.)) shift progressively and complete a cycle in 18.61 years: the period of...
  13. C

    Correlation between orbit eccentricity and mechanical energy

    Homework Statement I have been tasked with showing "how the mechanical energy of a planet determines the shape of its orbit", and I cannot for the life of me make sense of it. I've run into a formula, see below, but I'm not sure how to interpret it nor if it even applies in my case at all (as E...
  14. C

    Quick question on orbital eccentricity and mechanical energy

    Hi I'm really at a loss: How should this formula be interpreted? Is e simply dependent on the specific mechanical energy of, say, a planet in orbit around the Sun as well as its angular momentum?
  15. C

    Calculating albedo and eccentricity

    I have a three part question: Background: For a planet on an orbit with semi-major axis a and eccentricity e, the distance of closest approach to the Sun is r = a(1 − e) and the farthest approach is r = a(1 + e). (1) Assuming an albedo A = 0.2, estimate the temperature on Earth in equilibrium...
  16. Drakkith

    Exoplanet Eccentricity vs Orbital Period

    I have a question concerning the eccentricity vs orbital period of observed exoplanets. Going to this link let's you plot different exoplanet properties on each axis of a graph. Plugging in Orbital Period for the X-axis and Eccentricity for the Y-axis shows that a trend towards decreasing...
  17. Greg Bernhardt

    What is the Mathematical Definition of Orbital Eccentricity?

    Definition/Summary Eccentricity is the measure of the 'roundness' of the orbit. For circular orbits: e=0 For elliptical orbits: 0<e<1 For parabolic trajectories: e=1 For hyperbolic Trajectories: e>1 Equations e= \frac{c}{a} For ellipses: e = \frac{r_A-r_P}{r_a+r_P} e = \sqrt{...
  18. Greg Bernhardt

    Eccentricity: Definition, Summary & Equations

    Definition/Summary The eccentricity e of a conic section (other than a parabola or a pair of crossed lines) is its focal length divided by its major axis: e = f/a The eccentricity of a conic section (other than a pair of crossed lines) is the distance from any point P on the conic section...
  19. M

    Find eccentricity of orbit given position and velocity

    Homework Statement Hey, I need to find whether an asteroid is in a "bound orbit" around the Sun. Furthermore, describe the shape of the orbit (elliptical or circular). The only information I have been given is its velocity and position at a random point. v_o=61m/s r_o=13.75AU=2.06E12m I also...
  20. O

    Find mass of black hole in center of galaxy given eccentricity+

    Homework Statement Astronomers believe that there is a massive black hole at the center of the Milky Way galaxy. What evidence is there for that? A group of astronomers have observed a star "S2" in a 15.2-year orbit around the center of the galaxy. They measured the period of revolution T =...
  21. R

    Find eccentricity of orbit after star has lost mass

    Homework Statement Initially, a planet with mass m moves on a circular orbit (r = R) around a star with mass M. Now M is instantaneously decreased to M'. Find the eccentricity e of the elliptical orbit the planet now follows. Homework Equations specific angular momentum l = L/m...
  22. D

    Eccentricity elliptical orbit

    ##\mu_{sun} = 132712000000## ##\mu_{earth} = 398600## ##\mu_{mars} = 42828## ##R_{earth} = 149.6\times 10^6## ##R_{mars} = 227.9\times 10^6## ##r_{earth} = 6378## ##r_{mars} = 3396## The spacecraft will make 3 rev in 2 Earth years. I found the semi-major axis of the ellipse which is...
  23. B

    Equation of an ellipse given c and eccentricity.

    Homework Statement Write the equation of the conic that meets the conditions: An ellipse that has the centre at (0, 0), has a horizontal major axis, the eccentricity is 1/2 and 2c = 1.Homework Equations \frac{(x - h)^2} {a^2} + \frac{(y - k)^2}{b^2} = 1 The Attempt at a Solution 2c =...
  24. U

    Find the eccentricity of this ellipse

    Homework Statement The tangent at any point P of a circle meets the tangent at a fixed point A in T, and T is joined to B, the other end of diameter through A. Prove that the locus of point of intersection of AP and BT is an ellipse whose eccentricity is 1/ \sqrt{2} Homework Equations...
  25. T

    Eccentricity of projectile in Newtonian gravitational model

    When we were taught gravitation, we were taught that if a projectile (with mass very less compared to that of the Earth) is projected from the Earth, its path is: 1. Ellipse, if the velocity is less than critical (orbital) velocity. 2. Circle, if the velocity is exactly equal to critical...
  26. A

    Angular momentum and eccentricity

    I'm trying to find the relationship between angular momentum and orbital eccentricity but so far I haven't really found anything. I did find an indirect relationship, though, which looked like it should come out to,L=\sqrt{\frac{a(1-e^{2})}{m_{1}+m_{2}}}, but I may be completely wrong. Anyone...
  27. J

    Finding Eccentricity of Orbit Given Masses, Positions, and Velocities

    Homework Statement Find the eccentricity of an orbit given the masses, cartesian position components, and cartesian velocity components for particles 1 and 2. The case is reduced to the xy plane. Homework Equations I am attempting this problem using reduced mass from the center of mass...
  28. B

    Measuring eccentricity of the ends of a shaft

    Hi! My name is Daniel and I'm new to this forum. I work as a mechanical engineer at a machining workshop in Norway. We are currently producing some steel shafts that require a high level of accuracy. The shafts are about 1500mm long, and has a diameter of 40mm h6 (+0,000mm, -0,011mm) all...
  29. S

    Eccentricity of orbits and gravitational energy

    hello. i recently came across this question in which a satellite is put into orbit at a point around a planet with velocity 1.2V, where V is the speed for a circular orbit at that point and they ask for ratio of max to min distance. [Ans. 2.57] what i want to know is how do we relate...
  30. P

    Apocentre and Eccentricity of a Comet's Orbit

    Homework Statement If a comet passes close to the Earth with a velocity of 38km/s, how far is the apocentre of its orbit from the Sun? What is the eccentricity of its orbit? Homework Equations Vis-Viva Equation: (V)_{ecc}^{2} = GM [ \frac{2}{R} - \frac{1}{a} ] Apocentre distance...
  31. J

    Mechanics: Manual Drill Eccentricity

    Homework Statement In order to manually drill a hole, as shown below, it is important to keep the drill perpendicular to the surface. The drill is spun by a 30-lbf force applied downward at the handle at B, while pressure on the bit at A is obtained by applying a 10-lbf force along the x-axis...
  32. Dotini

    El Bosque UFO Incident: Real or Hoax?

    http://www.nbcdfw.com/news/local/Lightning-Storm-Leads-to-Rare-Light-Show-121648069.html The video is from an unusual electrical storm today in Ft Worth, Texas. It is showing fairly odd electrical explosions. Are we really seeing transformers exploding, or what? For comparison, known...
  33. B

    The orbital eccentricity change of the Earth ?

    Can someone answer one, some or all these questions; Is the orbit of the Earth right now getting more circular or more elliptical? How much? How can we be sure?
  34. R

    Expression for orbital eccentricity

    Homework Statement From Prussing and Conway (Q1.11): derive an expression for the eccentricity e in terms of the initial speed v, radius r, and flight path angle x (they use gamma). Homework Equations (1) h^2 = mu*a*(1-e^2) [a is semimajor axis, mu is gravitational parameter] (2) h =...
  35. S

    The eccentricity of binary stars' orbits

    Hi As two stars orbit their mutual center of mass in elliptical orbits, why are their eccentricity the same? And why is it the same as the one of reduced mass around center of mass? Thanks
  36. M

    Find eccentricity of orbit of comet

    Homework Statement Find eccentricity for: a comet with mass 1.2x1010kg moves in an elliptical orbit around the sun. Its distance from the Sun ranges between .5AU and 50 AU. Homework Equations The Attempt at a Solution I drew it out to try and viualize it and i know eccentricity...
  37. E

    Speed of orbiting planet given eccentricity of orbit

    Homework Statement If the eccentricity of a planet's orbit about the sun is 0.4, find (a) the ratio of the lengths of the major to minor axes of the planet's orbit, and (b) the ratio of the speeds of the planet when it is at the ends of the major axis of its elliptical orbit. Homework...
  38. Rasalhague

    Eccentricity and specific mechanical energy

    Bate, Mueller, White: Fundamentals of Astrodynamics (Dover 1971), p. 29, equation 1.6-4 for the eccentricity of a satellite's orbit: e=\sqrt{1+\frac{2\mathcal{E}h^2}{\mu^2}} e \text{, eccentricity} \mathcal{E} \text{, specific mechanical energy} h \text{, magnitude of specific...
  39. amarante

    Orbital Angular Momentum with eccentricity

    Homework Statement Considering a two-body problem, star-planet, prove that the angular momentum of the planet is given by: \begin{equation} {\cal L}_{e} = {\mu}\sqrt{GMa(1-e^2)}, \end{equation} $\mu$ is the reduced mass M is the star mass a and e are the semi-major axis and...
  40. G

    Eccentricity of a compressed circular ring

    If an initially circular ring is made out of round by cutting out a section of the ring (delta g) and compressing the ring till the gap is approx zero is there an equation to describe the eccentricity of the circle? Cheers Gordon
  41. F

    Possible webpage title: What is Mass Eccentricity and Its Role in Biomechanics?

    Mass Eccentricity <-- What?! Hi everyone! Can someone define "Mass Eccentricity" for me? I looked it up in a few online dictionaries, and didn't get a definition I understood in relation to its use: and I'm reading an interesting bio-mechanic-type paper, and got lost with this term...
  42. T

    Calculation of orbital speed for given eccentricity

    Hi, I am trying to work out, for a given eccentricity,a known planet mass and a known value for the semi major axis is there a formula to work out the orbital speed of a planet around a central star? I have looked around online with not much success and was wondering if anyone could point me...
  43. J

    Comet with eccentricity of 0.7 and 200 year period

    Homework Statement A comet of the star Sol has an eccentricity of .7. It takes 200 yrs to complete on orbit 1)find the average distance of the comet from Sol. 2) Find the perihelion and aphelion distances from Sol 3)find the velocity of the comet at perihelion Homework Equations...
  44. O

    What is the Equation for Calculating Halley's Comet Eccentricity?

    Homework Statement I am given Rp=.6AU and need to find the eccentricity. Homework Equations Rp=a(1-e) The Attempt at a Solution I can find what Halley's comet eccentricity is (0.967) but I need to actually calculate it. What is the equation I need? I know I need to know Ra, or a...
  45. DaveC426913

    Does Earth's eccentricity change?

    I've just been asked of the Earth's eccentricity or orbit changes over time. The idea is that, over a period of 100,000 years or so, the Earth's orbit changes from nearly circular to more elliptical. I have never heard of such a thing. Can anyone confirm or refute?
  46. F

    Eliptical Orbit and Eccentricity

    1. Problem statement The space shuttle is in circular orbit of radius R around the earth. The pilot triggers a brief burn that imparts a forward impulse 'p' to the shuttle. After the burn, the shuttle is in an elliptical orbit which passes back through the point where the burn took place once...
  47. S

    [spacefight mechanics]how to find true anomaly and eccentricity?

    Homework Statement An Earth satellite has a speed of 7km/s and a flight path angle of 15 degree when its radius is 9000km calculate the true anomaly and eccentricity of the orbit. Homework Equations r=h^2/u(1+ecostheta) The Attempt at a Solution The problem statement just doesn't...
  48. K

    Exploring Comet's Aphelion: Limiting Eccentricity and Closest Approach

    Homework Statement Consider a comet which passes through its aphelion at a distance rmax from the sun. Imagine that, keeping rmax fixed, we somehow make the angular momentum l smaller and smaller though not actually zero; that is we let l\rightarrow0. Use equations c=l2/\gamma\ mu and...
  49. R

    Eccentricity & GR precession; Mercury vs. GPB

    Eccentricity & GR precession; Mercury vs. GP-B How big a factor is the Eccentricity of Mercury orbit in contributing to its precession? GR precession has been confirmed in the Gravity Probe B orbit even though it has an eccentricity of zero. The GP-B used a gyroscope to take the place of a...
  50. B

    What are causing the Eccentricity of the planets?

    What are causing the Eccentricity of the planets? When reaching Neptune we have nearly a completely circular orbit. Why ? It seems not to be any logic in this ! Mercury 0,20563069 Venus 0,00677323 Earth 0,01670900 Mars 0,09340100 Jupiter 0,04849500 Saturn...