# 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. ### From circular orbit to elliptical orbit

Problem: a particle of mass m is in a circular orbit around a planet at a distance R from the center. The planet mass is M and it's radius is R_0. What is the tangential impulse that will cause the particle to brush against the back of the planet? Describe the orbit. The attempt at solution...
2. ### I Elliptical Orbit and Kepler's equation

It is easy to find that the equation for an ellipse is: $$1 = x^2/a^2 + y^2/b^2$$ Then according to Kepler's equation: $$x = a(\cos(E)-e)$$ $$y = b\sin(E)$$ where E is the eccentric anomaly and e is the eccentricity. If you plug the Kepler's equations' x and y into the equation for the ellipse...
3. ### A Elliptical orbit parameterized by time

It is fairly trivial to do this with a circular orbit: $$(x,y) = (cos(\omega t),sin(\omega t))$$ where t is time, and $$\omega = \sqrt{GM/r^3}$$ How this parametric equation look for an elliptical orbit?
4. ### A Elliptical orbit and how seasons would be affected

Trying to establish the conditions needed in order for a planet to have more than the standard 4 seasons. I may be wrong for assuming an elliptical orbit is required, but could make sense in order for there to be two winters for example.
5. ### Time period of an object traveling in an elliptical orbit

I know that the angular momentum of the particle orbiting in an elliptical path is constant and due to which the particle speeds up near the foci when r is small. But, I cannot figure out how to calculate the time period of rotation. I can do the same for an ellipse by taking mv²/r = central...

7. ### I Typo in elliptical orbit energy derivation?

I'm reading through a derivation for the energy of a satellite in an elliptical orbit. Shouldn't EO-2 read as: ... and not as shown in the following?
8. ### Is the Circular to Elliptical Orbit Calculator Accurate?

I have an object in a 500,000 km circular orbit around earth. I want to change it into an elliptical orbit with a perigee of 500 km. I found this cool site and put those numbers in the calculator. The ”Injection into elliptical transfer orbit delta V” answer is -741.97 m/s. Does that mean to...
9. ### Elliptical orbit centered at the origin

Homework Statement Under the influence of a central force F(r), a particle of mass m is observed to move in an elliptical orbit centered at the origin (the force center is not at one of the foci, as would be the case for a gravitational orbit) a.) Show that the polar equation has the form 1/r =...
10. ### Elliptical orbit/ determine speed & potential energy

Homework Statement True statements about Jupiter as it moves in its elliptical orbit around the Sun include which o the following? I. It has its greatest speed when closest to the Sun. II. It has its greatest potential energy when farthest from the Sun. III. The magnitude of its...
11. ### Increasing the speed of a circular orbit

What If the velocity of particle moving in a circular orbit has increased , would the particle be no longer in circular orbit or it would go in an orbit with bigger radius?
12. ### Why is the specific angular momentum equal to this?

From a wiki's vis-viva equation page, it is given that the specific angular momentum h is also equal to the following: h = wr^2 = ab * n How can ab * n be derived to be equal to the angular momentum using elliptical orbit energy/momentum/other equations without having to use calculus or...
13. ### How to get tangential velocity

I am in the process of making a program that visually shows an elliptical orbit over time. I wish to find the tangential velocity of the satellite in the elliptical orbit based on the variables that I know. Here is what I know: a) The angle relative to the right focus with 0 radians being the...
14. ### Mechanical energy for planet in elliptical orbit around star

Homework Statement A planet is in an elliptical orbit around a star. Which of the following best represents the mechanical energy E_planet of just the planet and the mechanical energy Es_tar-planet of the star-planet system as functions of time for one complete orbit? Homework Equations...
15. ### I "Unexpected" Symmetry in Elliptical Orbit

Hello everyone :) Not too long ago, I was thinking about planetary motion around a sun, both with circular orbits and elliptic orbits. However, when thinking a little longer about these two cases in a broader sense, I spotted a big difference which I found quite odd (assume purely classical...
16. ### Doubling speed in circular orbit to attain elliptical orbit

Homework Statement A satellite is in a circular orbit (radius R) around a planet of mass M. To change the satellite's orbit the engines fire and its speed is suddenly doubled. The engines fire for a very short time. Determine the length of the semi-major axis of the new orbit. Homework...
17. ### Points on an elliptical orbit where V(radia) is zero.

Homework Statement Points on an elliptical orbit where the speed is equal to that on a circular orbit? Homework EquationsThe Attempt at a Solution I have attempted this question and my calculations show that at points on minor and major axes, the radial component of velocity is zero. Hence at...
18. ### I Will an elliptical orbit self-correct into a circular one?

I know that moons tend to orbit their planets in a slightly elliptical orbit rather than a perfectly circular orbit. But for the purpose of this thread, let's assume that moons effectively orbit their planet in a circular orbit. So here is the question... If our moon was struck by an object...
19. ### I Is a 2-body elliptical orbit stable in GR?

I understand that in a 2-body system a circular orbit is gravitationally stable in General Relativity. In Newtonian dynamics, an elliptical orbit is also stable, but is this also true in GR? I understand that the orbit precesses, but I do not intend that to change my meaning regarding stability...
20. ### Time-weighted average distance in an elliptical orbit

Homework Statement Using the polar formula for an ellipse, and Kepler's second law, find the time-weighted average distance in an elliptical orbit. Homework Equations The polar formula for an ellipse: $$r = \frac { a(1-e^2)} {1 \pm e cos \theta},$$ Area of an ellipse: $$A = \pi a b$$...
21. ### Satellite Orbit Trajectory and Velocity Doubling: Parabolic or Hyperbolic?

Homework Statement A satellite moves in an elliptic orbit with eccentricity e=1/2 around a planet which it was launched. When it arrives at an apsis( a radial turning point), its velocity is suddenly doubled. Show that the new orbit will be either parabolic or hyperbolic depending on which of...
22. ### I Focus of Earth's elliptical orbit

If the orbit of the Earth has only one focus which is the Sun then why can't it move in a circular path. Since a circle has only one focus and that is at the centre. Why is the sun the only focus when the path of Earth is an ellipse?
23. ### B Calculating distances with an elliptical orbit

Wasn't sure exactly what the title of this post should be. Working on a side project using machine learning and the solar system (using n-body simulator). Let's say I have two bodies with coordinates: Body1: x=-1.42790218981 y=1.4003882805 z=0.0 Body2: x=0.983274588755 y=0.0477301860159 z=0.0...
24. ### Tangential acceleration in elliptical orbit?

Homework Statement A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Choose the correct statement. Ans: (A) the acceleration of S is always directed towards the centre of the earth Homework Equations F=...
25. ### Acceleration in an Elliptical Orbit

So let's say you are on an orbital satellite in an elliptical orbit around our planet Earth, meaning that the at one point in the orbit you are going faster, due to the gravitational pull of the planet. Would you feel the acceleration in space due to the shape of the orbit?
26. ### Ptolemy's Theory of the Empty Focus of an Elliptical Orbit

An ellipse has two foci. For a planet in such an orbit, the star is at one of the foci. The other is empty. According to Ptolemy, if we draw a line connecting the planet and the empty focus, we will find that the line moves at a constant angular velocity. Is this true, or is it a crude...
27. ### Heliocentric polar orbit crossing the Earth's orbit twice

Sorry, the title's length didn't allow me to explain this better and I need it for a story that I'm writing, if you're so kind to help me. I've been trying it hard to solve it myself but I've been unable to. The problem looks simple but it isn't (for me): Please assume we have a space probe of...
28. ### Why does Mercury have an elliptical orbit?

Why is mercury obit elliptical? Is it because of the curvature of spacetime caused by the presence of sun such that the mercury moves in that orbit otherwise known as geodesics? However what about the other planets like Earth that orbits in a circular orbit? Is is just that that is their...
29. ### Time dilation in an elliptical orbit

The formula for time dilation in a circular orbit is readily available but the literature seems to indicate it would not be so simple in the case of an elliptical orbit, and no simple formula seems to be available. Given that time dilation in a circular orbit adds the velocity effect (GM/r) to...
30. ### Elliptical Orbit of Sun Around Milky Way

Hi, I'm new to this forums (and please forgive my grammer and sentence structure as my first language is not English and I'm trying my best :) I'm just a teenager who has great interest in these types of stuff, never did any proper education relating to this, just some research out of curiosity...
31. ### Investigating Comet 67P's Elliptical Orbit

Homework Statement Currently, I am trying to prove the "conservation of energy" concept within a comet's elliptical orbit by finding the mechanical energy of the aphelion and perihelion point to see if they're equal. However, they don't equal each other when I calculate both points. (aphelion...
32. ### Calculate elliptical orbit using attitude and velocity

Hi. I'm just a hobbier of astronomy and have a question about elliptical orbit. I wonder that can calculate elliptical orbit using just atitude(location) and velocity(vector). Please look at my picture. The blue dot is central body and green dot is my interesting body. Let me assume mass of...
33. ### Seasons due to Earth's elliptical orbit

Hello there! What I have never understood is that our seasons are the result of the tilt of the Earth's axis, and I've always interpreted that to mean that the northern hemisphere is closer to the sun in June, July, and August, and the southern in December, January, and February. If that is the...
34. ### Gravity and velocity of a body in an elliptical orbit

consider a body revolving around a star and having a velocity v when closest to the star ( distance r) then the velocity of the body at a point farthest ( distance R) is? 1)by angular momentum conservation :: r × mv = R× mV »V = (r/R).v...
35. ### Satellite in elliptical orbit

[b]1. Homework Statement A 7655 kg satellite has an elliptical orbit. The point on the orbit that is farthest from the Earth is called the apogee and is at the far right side of the drawing. The point on the orbit that is closest to the Earth is called the perigee and is at the far left side...
36. ### Constant energy in an elliptical orbit

Homework Statement There's no specific question, but mostly a theory I wanted clarified. According to my textbook, the measurement of the total mechanical energy E of a mass orbiting a much larger mass in an ellipse is: E = radial (change in radius) kinetic energy + rotational kinetic energy...
37. ### Tangetial acceleration in elliptical orbit

Homework Statement Is there any position in an elliptical orbit where the tangential component of the acceleration is greater than the component perpendicular to the tangential component? If so, what conditions on the orbit must there be for such a position to exist? Homework Equations...
38. ### 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...
39. ### MHB Calculating Elliptical Orbit Points & Flight Path Angle

Determine the location of the point(s) on an elliptical orbit at which the speed is equal to the (local) circular orbital speed. Determine the flight path angle at this location. What equation(s) should I be using or thinking about for this?
40. ### Total mechanical energy of a point mass in an elliptical orbit

Hey, I was trying to prove to myself an expression for the total energy, and I got stuck Here is the picture (it's transparent, so I won't embed it here). The problem I seem to be having is when I observe these two points where the speed is in its highest and its lowest. Since in these...
41. ### Charge moving in elliptical orbit under Coulomb field.

Under the influence of the coulomb field of charge +Q, a charge −q is moving around it in an elliptical orbit. Find out the correct statement(s). (A) The angular momentum of the charge −q is constant (B) The linear momentum of the charge −q is constant (C) The angular velocity of the charge...
42. ### Integrating the generator lines of an elliptical orbit

Hi, I am having difficulty understanding the following: \int^{2π}_{0}(x+y)\,dθ = \int^{2π}_{0} 2a\,dθ = \textbf{4}πa where x and y are the generator lines of an elipse, a is the semimajor axis and θ is the angle formed by x and the major axis. I understand that x+y = 2a. However I...
43. ### Proving a particle is moving in an elliptical orbit.

Homework Statement A particle of mass m is acted upon by two forces. P(t) in the x direction with magnitude p(sinkt) and Q(t) acting on the line y=x with magnitude qsinkt. At t=0 it starts at (b,0,0) and velocity p/(mk) moving toward the origin. Prove the particle is in an elliptical orbit...
44. ### Find Aphelion of an elliptical orbit given Perihelion and Orbital Period

Homework Statement Comet Halley approaches the Sun to within 0.570 AU, and its orbital period is 75.6 years. (AU is the symbol for astronomical unit, where 1 AU = 1.50 x 1011 m is the mean Earth‐Sun distance.) How far from the Sun will Halleyʹs comet travel before it starts its return...
45. ### Elliptical Orbit Homework: Momentum, Direction & d/dt

Homework Statement Based on your observations of the behavior of your computer model of a planet orbiting a star, and on your reading in the textbook, which of the following statements about an elliptical orbit are true? At any instant the momentum of the planet is tangent to the planet's...
46. ### Longest and shortest distance in an elliptical orbit

Homework Statement Two satellites are launched at a distance R from a planet of negligible radius. Both satellites are launched in the tangential direction. The first satellite launches correctly at a speed v0 and enters a circular orbit. The second satellite, however, is launched at a speed...
47. ### Elliptical orbit, velocity at aphelion

Hello everyone! Should be obvious it's my first time here. I'm looking for assistance not for myself, but for my girlfriend. She's got a college science class that up until now I was able to help her with, but unfortunately my physics knowledge (one year in high school, eight years ago now) did...
48. ### How Can I Calculate the Distance of an Object in an Elliptical Orbit Over Time?

What would the equation be for the distance of an object orbiting another object in an elliptical orbit with time as the variable? How would I derive this equation? A comet would be an example. I am looking for the equation that would plot the distance from the sun at any given time.
49. ### Elliptical Orbit Homework: Find Angular Momentum

Homework Statement A comet of mass 5x10^16 kg moves in an elliptical orbit around the sun, with the sun at one focus. At the perihelion, 10^6 m, the comet has a linear velocity of 1.5x10^7 m/s. Find the angular momentum of the comet with respect to a focus at the sun. Homework Equations...
50. ### Equation of an Elliptical Orbit for a Moon around a Planet

I am kind of new to astronomy and I have a few questions.. I need to be able to determine an equation expressing the elliptical orbit of Oberon around Uranus. I have four nights of data showing Oberon in different positions relative to Uranus. I am able to calculate the RA and Dec for both...