What is Elliptical orbit: Definition and 84 Discussions

In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit). In a wider sense, it is a Kepler's orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1.
In a gravitational two-body problem with negative energy, both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit.
Examples of elliptic orbits include: Hohmann transfer orbit, Molniya orbit, and tundra orbit.

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  1. K

    Astrophysics - elliptical orbit proof help.

    A.) Assume a rectangular coord system has its origin at the center of an elliptical planetary orbit and that the coord system x-axis lies along the major axis of the ellipse. Show that the equation for the ellipse is given by x^2/a^2 + y^2/b^2 =1. where a and b are the lengths if the...
  2. Philosophaie

    Tracking Unstable Elliptical Orbits for College-Educated Scientists

    A satellite is in an unstable elliptical orbit around the earth. Is there a way of tracking each satellite's orbit till it reaches the critical stage then follows it's reentry path? V<Vescape r=a*(1-e^2)/(1+e*cos(True Anomaly)) Book recommendations welcome. College educated.
  3. M

    Object in elliptical orbit around another object

    Homework Statement In a science fiction story, humans have built a large spherical spaceship for an interstellar journey of many generations; they have christened their ship Big Bird. The mass of Big Bird is 7.496×1011 kg (the mass of an aircraft carrier is about 10^8 kg). Most of Big...
  4. S

    How Does Orbital Eccentricity Affect Satellite Calculations?

    elliptical orbit question please help Homework Statement see attachmentHomework Equations 2a (average distance of satellite from central body) = A (aphelium) + P (perihelium) ME = KE + PE ME = -GMm/24 KE = .5mv^2 PE = -GMm/r ME orignall = ME final The Attempt at a Solution I tried to put ME =...
  5. S

    Calculating Eccentricity for an Elliptical Orbit

    Homework Statement a satellite is set to orbit a planet of mass 4X 10^20 kg . It is placed at a distance of separation of 10^7m with a velocity of 30 degrees to the line connecting the center of the planet and the satellite. What will be its eccentrity fo orbit? (Answer is .89) Homework...
  6. S

    Speed update of a comet in an ELLIPTICAL orbit

    A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 5e10 m (inside the orbit of Mercury), at which point its speed is 9e4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6e12 m from the Sun...
  7. S

    Change in speed around elliptical orbit

    A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 5e10 m (inside the orbit of Mercury), at which point its speed is 9e4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6e12 m from the Sun...
  8. K

    Putting a satellite into an elliptical orbit

    Homework Statement It is required to put a satellite into an orbit with apogee of 5R/2, where R is the radius of the planet. The satellite is to be launched from the surface with a speed Vo at 30degrees to the local vertical. If M is the mass of the planet, show that (Vo)^2 = 5GM/4R. Assume...
  9. C

    Elliptical Orbit Homework: Calculate r1/r0

    Homework Statement The equation of the elliptical orbit of Earth around the sun in polar coordinates is given by r =ep/1 − e cosa where p is some positive constant and e = 1/60. Let r0 and r1 denote the nearest and the furthest distance of the Earth from the sun. Calculate r1/r0...
  10. E

    Velocity of a satellite in an elliptical orbit

    Homework Statement see attachment #12.106 Homework Equations V=R\sqrt{}(g/r) (for a circular orbit) where R is the radius of the Earth and r is the radius of the orbit from the center of the earth conservation of momentum for elliptical orbits: Vara=Vbrb The Attempt at a Solution...
  11. O

    Impulsive delta v hyperbolic and elliptical orbit

    Homework Statement On July 1, 2004, the Cassini spacecraft approached Saturn with hyperbolic excess velocity 5.5 km/s to swing by the planet at the closest approach distance rp = 80,680 km. Compute the impulsive ΔV required for a maneuver performed at the closest approach to Saturn to...
  12. E

    Total energy of elliptical orbit

    Why is the total energy of an elliptical orbit given by: E_{tot}=\frac{-GMm}{2a} Where a=semi major axis. I agree for a circular orbit I can do the following: F_c=F_g ma_c=\frac{GMm}{r^2} \frac{v^2}{r}=\frac{GM}{r^2} v^2=\frac{GM}{r} Since the total energy also equal to the kinetic plus...
  13. G

    Circular orbit VS Elliptical orbit? Differences?

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  14. P

    Earth's Elliptical Orbit around the Sun

    By just knowing the clues like the force of attraction between two masses and angular momentum conservation principle , linear momentum conservation principle and geometry..can we derive the trajectory of the Earth around the sun is ellipse..if so please tell me your ideas..
  15. K

    How Do You Calculate the Period of a Spacecraft's Elliptical Orbit?

    Homework Statement Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the Earth's surface; at the high point, or apogee, it is 4000 km above the Earth's surface. 1. What is the period of the spacecraft 's...
  16. H

    The Mystery of Satellite Speed: Solving an Elliptical Orbit

    Homework Statement A satellite is in an elliptical orbit at altitudes ranging from 230 to 890 km. At the high point it's moving at 7.23 km/s. How fast is it moving at the low point? I would think i would have to use some sort of energy conservation equations. but i really don't know where...
  17. V

    Elliptical Orbit Question with no numbers

    Homework Statement A satellite of mass m is in an elliptical orbit around the Earth, which has mass M and radius R. The orbit varies from closest approach of 'a' at point A to maximum distance of 'b' from the center of Earth at point B. At point a the speed of the satellite is vo. Assume Ug...
  18. Philosophaie

    Elliptical orbit around the Sun

    Why do the planets travel in elliptical orbit around the Sun?
  19. P

    Derive Angular Momentum in Elliptical Orbit

    Homework Statement A planet with mass m is orbiting about the Sun (mass m(s)) with elliptical orbit such that the maximum and minimum distance is r1 and r2 respectively. What is its angular momentum, L, of the planet relative to the centre of the Sun? Homework Equations...
  20. P

    Derive angular momentum of planet with elliptical orbit

    Homework Statement A planet of mass m orbiting the Sun(mass=m_s along an elliptical orbit, with aphelion r1 and perihelion r2. Find the angular momentum of the planet relative to the centre of the Sun. Homework Equations Angular momentum, M=m(R\times v)=mvR sin\theta Distance from Sun...
  21. M

    Solving Elliptical Orbit Homework: Comet's Semi-Major Axis & Sun Distance

    Homework Statement The period of a comet orbit is 100 years. As its closests approach is 0.37 AU from the sun. What is the semi-major axis of the comet's orbit? How far does it get from the sun? Homework Equations (T1/T2)^2 = (s1/s2)^3 The Attempt at a Solution I don't even know...
  22. Philosophaie

    Calculating the Earth's Elliptical Orbit around the Sun

    To help me you will need tho know Excel VBA very well. Earth has an elliptical orbit around the sun. JPL's website has the data to calculate this orbit: http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt In the spreadsheet the parameters are calculated from widely used equations and some of my...
  23. S

    Help deriving this elliptical orbit equation?

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  24. N

    Elliptical orbit around a massive spherical planet

    Homework Statement The path of a very small satellite S in an elliptical orbit around a massive spherical planet P is shown in the figure. The distance from 3 to 4 is the same as from 4 to 5, 9 to 10, and 10 to 11. (Select T-True, F-False, G-Greater than, L-Less than, E-Equal to, If the first...
  25. N

    Help Needed: Solving Kepler's Third Law for a Solar Elliptical Orbit

    Homework Statement I have this problem for homework and I don't know how to even start. Can someone help? Thanks in advance.A neat and exploitive use of the sun would be to put a space probe into a solar elliptical orbit from the Earth on one side of the sun headed towards a rendezvous with...
  26. K

    What is the speed of the comet when it crosses the Earth's orbit?

    Homework Statement There is a system of 3 bodies, consisting of the sun, the Earth and a comet. When the comet is at perihelion it is at a distance half that of the Earth's orbital radius. At this point it has a speed twice that of the earth's. Ignore the gravitational forces between the...
  27. L

    How Does Comet Speed Change at Aphelion Compared to Perihelion?

    Homework Statement A particular comet has an elliptical orbit. When closest to the Sun (perihelion) it is at a distance of 8.823 1010 m and moves with a speed of 54.6 km/s. The greatest distance between this comet and the Sun (aphelion) is 6.106 1012 m. (a) Is the speed of the comet greater...
  28. C

    Solving for the Speed of a Comet in an Elliptical Orbit

    Homework Statement Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.3×10^4 m/s when at a distance of 2.7×10^11 m from the center of the sun, what is its speed when at a distance of 4.3×10^10 m. Homework Equations I tried using v =...
  29. A

    What Causes Earth's Elliptical Orbit?

    Why is the Earth's orbit elliptical? That is, what force acts on the Earth perpendicular to the force of the sun, that causes the tangential accelerations characteristic of an ellipse?
  30. B

    Calculate Tangential & Normal Acceleration of Particle in Elliptical Orbit

    A particle is moving in a elliptical orbit with uniform speed. How can I tell whether there are tangential and normal acceleration or not on the particle? (At A B and C ) thanks for help!
  31. vincentm

    Lower mass = more elliptical orbit?

    Does it? :confused:
  32. X

    Elliptical Orbit Greetings: Exploring Gravitational Force

    greetings If we throw an object in straight line this objects travels in parabolic path until it hits the ground. But in fact this parabola is only a part of an ellipse that object would travel in and center of the Earth is one of the foci points I understand that object can circle around...
  33. C

    Hyperbolic, Parabolic or Elliptical Orbit?

    A comet is first seen at a distance of d AUs from the Sun and is traveling with a speed of q times the Earth's speed. Apparently it can be shown that if q2·d is greater than, equal to, or less than 2, then the comet's orbit will be hyperbolic, parabolic or elliptical respectively. Any idea...
  34. M

    Calculate Velocity of Object in Elliptical Orbit

    i was wondering, is there a particular formula to calculate the velocity of a object in an elliptical orbit. Let's say a satellite orbiting around the earth, and the orbit is elliptical, so how do u calculate the velocity at a certain distance from earth. I tried using the v^2=GM/r, but that's...
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