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.
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...
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...
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?
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.
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...
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...
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 =...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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:
$$ A = \pi a b $$...
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...
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?
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...
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=...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
[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...
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...
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...
##\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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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.
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...
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...