Eccentricity Definition and 61 Threads

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. S

    Eccentricity of orbit. Apogee and perigee positions and distances

    Homework Statement A satellite is in an elliptical orbit about the Earth. The center of the Earth is a focus of the elliptical orbit. The perigee (C) is the point in the orbit where the satellite is closest to the Earth's center (F). The perigee distance (P) is the distance from the perigee...
  2. C

    Eccentricity of Elliptical Orbit

    A particle moves in an elliptical orbit in an inverse-square law central force field. If the ratio of the maximum angular velocity to the minimum angular velocity of the particle in its orbit is n, then show that the eccentricity of the orbit is \epsilon = \frac{\sqrt{n}-1}{\sqrt{n}+1}...
  3. R

    Semimajor Axis and Eccentricity after increased velocity

    Question: A space shuttle is in an orbit about the Earth. At its apogee, it uses thrusters and increases its velocity by 400 m/sec. What is the new orbit semimajor axis, eccentricity and how much will the next perigee altitude be increased? Known: Original semimajor axis: 7000 km -> a...
  4. R

    Orbit Semimajor Axis and Eccentricity after increasing V

    Question: A space shuttle is in an orbit about the Earth. At its apogee, it uses thrusters and increases its velocity by 400 m/sec. What is the new orbit semimajor axis, eccentricity and how much will the next perigee altitude be increased? Known: Original semimajor axis: 7000 km -> a...
  5. C

    How Do You Calculate the Square of Eccentricity for a Rotated Ellipse?

    This one question has me totally beaten. And I thought I was pretty good in co-ordinate geometry. Here it is: If the equation ax^2 + 2hxy + by^2 =1 represents an ellipse, find the square of the eccentricity of the ellipse. I know that the ratio of the distance from the directrix to the...
  6. Amith2006

    Eccentricity of elliptical path of earth

    Sir, The eccentricity of Earth's orbit is 0.0167. What is the ratio of its maximum speed to its minimum speed in its orbit? I solved it in the following way: Let its maximum and minimum speed be v1 and v2 respectively. Let a and b be the semi length of the major and minor axis...
  7. G

    How to Derive Eccentricity in the Kepler Problem?

    For a planet moving in an elliptical orbit, fraction of maximum and minumum angular is given to be n \frac{\dot{\theta}_{max}}{\dot{\theta}_{min}} = n Show that \varepsilon = \frac{\sqrt{n}-1}{\sqrt{n}+1}. I keep finding \varepsilon = -\frac{n^2-1}{n^2+1} Can someone show a path to correct...
  8. L

    Orbit of almost 1 eccentricity

    You make a 100 m diameter tunnel that goes from the north pole to the south one. You put into orbit a tennisball by dropping it in the tunnel from the north hemisphere Supposing it makes an ellipse 99 m the minor axe and the Earth radius the bigger axe wouldn't the ball get into an orbit...
  9. D

    Finding the eccentricity of Earth's orbit

    Given the mass of the sun, the gravitational constant, the period of Earth's orbit, and the semi-major axis of Earth's orbit, is it possible to find the eccentricity of the orbit? If yes, how?
  10. T

    How Do You Calculate the Eccentricity of an Ellipse Given x^2/49 + y^2/64 = 1?

    How would I find the eccentricity of the ellipse: x^2/49 + y^2/64 = 1 :confused:
  11. S

    Angular momentum, torque and eccentricity

    How is eccentricity of an orbit affected by the angular momentum of the orbiting body (mathematically, that is)? How does torque affect angular momentum? How is a torque exerted? What is a torque?
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