Orbits Definition and 498 Threads

Hi all, Only one is true at a time "general theory of relativity or Planetary orbits are elliptical...please clarify me I will thank full to you..

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?

<Moderator's note: Moved from General Math to Differential Geometry.> Let p:E→ B be a covering space with a group of Deck transformations Δ(p). Let b2 ∈ B be a basic point. Suppose that the action of Δ(p) on p-1(b0) is transitive. Show that for all b ∈ B the action of Δ(p)on p-1(b) is also...

If we take 1 high gravity object and 1 smaller object at a distance from the first object, the first is stationary in relation to the smaller object, and it is in orbit around the first. Will the orbit be circular the center of mass of the two? Now if we put an other object in a different orbit...

Hi, I am about to write a simple application, simulating in 3D current location of the planets in Solar system. Honestly, I do not know even how to start. Can you please guide me where could I find some good information on planet orbits, current locations and how to make all of the calculations...

In orbits it is said that ##\vec a \cdot \vec a' = |a||a'|## How is this possible? Two vectors multiply to get scalars, and yet we cannot do the dot product literally because we do not know either of the components of ##\vec a## or ##\vec a'##. Nor does the Angle Between Vectors Formula work...

In the following link, https://en.wikipedia.org/wiki/Geodesics_in_general_relativity they write:"the path of a planet orbiting around a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space." Is there anything wrong with the following circular...

Is it difficult to use Newton's theory of gravity for showing that planet's orbits must be elliptical?

This is a possible science-fiction scenario, and I'm wondering if it is scientifically plausible. If someone wanted to take a one-way trip into future, say 1000 years from now, then SR gives you a possible way to do it without dying of old age: Just hop in a rocket ship, accelerate to nearly...

Hello everyone! I'm trying to get a deeper understanding on how to determine those periodic orbits in the equal-mass three-body Newtonian gravitational problems. The most general idea I know is to confine the three bodies into a zero angular momentum space, which sounds vague to me. What is the...

Loosely speaking, we say that periodic orbits are 'dense' if given any $\epsilon$-neighborhood, there exists at least one periodic point in that neighborhood for any $\epsilon > 0$. Is there any requirement for these periodic points to be unique? For example, what if every neighborhood...

Homework Statement Run a numerical analysis on elliptical orbits using the standard Runka-Kutta method. I already have the equations from Euler-Lagrange method in cartesian x,y-coordinates. d2x/dt2 = -K x (x2 + y2 )-3/2 d2y/dt2 = -K y (x2 + y2 )-3/2 Homework Equations I find it a little to...

Homework Statement I'm rather confused as to where the orbited body is placed, and where the orbiting trajectory lies in this figure. Is it right for me to say that if I placed say, the Earth on the left hand focus, a comet with a hyperbolic trajectory will travel a path defined by the...

Homework Statement Why is the magnitude of Angular Momentum for an elliptical orbit as such? $$l = mr^2\dot{\phi}$$ where ##\dot{\phi}## represents angular momentum. I have always assumed that angular momentum was $$l = r \times P = mr \times V = mrVsin(\theta) = mr^2\dot{\phi} sin(\theta)$$...

Homework Statement The question is: A top secret spy satellite is designed to orbit the Earth twice each day (i.e, twice as fast as the Earth's rotation). What is the height of this orbit above the Earth's surface? Circumference of orbit not given. Mass not given. Centripetal force is not...

Homework Statement The orbits of the planets remains extremely stable over long times however this not always true for comets. Can you explain why not? What hazards might they encounter during their travels? Homework Equations None The Attempt at a Solution I think that due to the comet's not...

1. The problem statement, all variables, and given/known data Satellites orbiting the Earth are often put into orbit at different heights around the planet. What affect will this have on the motion of the satellite and how exactly would the motion of a very high orbit satellite differ from one...

1. The problem statement, all variables, and given/known data Venus is sometimes described as either the “Morning Star” or the “Evening Star”, since it can only be seen near sunrise and sunset, very close to the Sun in the sky. Why does Venus always appear close to the Sun in the sky for an...

Does anyone know where I can find information about how to calculate how much extra energy is required of a spaceship to try to thrust perpendicular (or at some angle) to the orbital plane verses flying completely/only in the orbital plane when moving outwards in our solar system? If the...

Do all stars orbit around the black hole in the same plane? Or some stars can have the same orbital radius but slightly different orbital inclinations?

Is there any evidence of the enlargement of planetary orbits over time? Are the planets moving further from the sun?

Hi! first time poster here. I'm making an orbital simulation and I am having a problem with one minor detail. The gravity is working great, and I've programmed it using this formula: A force vector is applied = DirectionOfCentralBodyNormalized * ((GravConstant * centralbodymass *...

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?

Homework Statement The problem is your typical N-body simulation, implemented using Python and Numpy. The implementation specifically calls for using the Euler-Cromer method. For this particular case I used the Sun and the first 4 planets of the solar system. Essentially the problem is I'm...

Context: In James Hartle's Gravity, pp. 318-319, Example 15.1, he considers the case of a particle that starts falling from infinity into a Kerr black hole, initially with no kinetic energy (e = 1) and initially moving radially (ℓ = 0). The particle's motion is constrained along the equatorial...

I have a satellite orbiting at a velocity of 3850Km/hr around planet Earth in a circular orbit, please help me in calculating it's height of orbit. I do know that the closer a satellite is, the faster it's orbital velocity, and the farther it is the slower it would be, and help me with the formulas?

How does the adiabatic invariance of actions J imply that closed orbits remain closed when the potential is deformed adiabatically? Is it because a closed orbit has commensurate angular frequencies $$\omega_i$$ defined by $$\omega_i = \frac{\partial H}{\partial J_i}$$ where H is the...

Homework Statement I'm trying to plot Newtonian orbits in Mathematica with the goal of extending this to orbits including GR after. I've derived equations for r(t) and ##\phi##(t) (see below) by integrating ##\dot{r}## and ## \dot{\phi} ## (see below also) from E = 1/2mv2 +V(r) with velocity...

Orbits of electrons around nucleus can never exist because it can lose energy as charges accelerate so there is never orbits of electrons. Why can't we treat gravity as forces in similar fashion.. as something that doesn't really exist. My point is. General Relativity and spacetime curvature...

We see in our solar system the planets orbiting the sun, but why doesn't with all of the other forces in play the perpendicular velocity seemingly not decrease(or does it?). And if the perpendicular velocity of the planets slow down would that result in static planets not moving around the sun?

First off, I'd like to note that I am by no means a physics expert. I am merely a high school student and a physics/maths enthusiast, nothing more, so if my thoughts are completely dysfunctional and downright incorrect, which is more than a distinct possibility, please tell me. I recently took...

So a light particle is orbiting a massive particle by gravity. We take both particles as spot particles. The light particle makes an eccentric orbit where maximum radius of the orbit equals 2 and minimum radius equals 1. I suppose the mass of the massive particle such that the speed of the...

Are there any stars in the solar neighborhood that orbit the galactic center in the opposite direction?

Homework Statement Hartle, Gravity, P9.8 A spaceship is moving without power in a circular orbit about a black hole of mass M, with Schwarzschild radius 7M. (a) What is the period as measured by an observer at infinity? (b) What is the period as measured by a clock on the spaceship...

How many orbits are in the hydrogen atom?

A smooth vector field on the phase plane is known to have exactly three closed orbit. Two of the cycles, C1 and C2 lie inside the third cycle C3. However C1 does not lie inside C2, nor vice-versa. What is the configuration of the orbits? Show that there must be at least one fixed point bounded...

Hello! I am a bit confused about Kepler 3rd law for circular orbits. So assume you have 2 bodies of masses M>m orbiting in circles around their center of mass. As the center of mass passes through the line connecting them, they must have the same period. But according to Kepler's 3rd law, this...

Homework Statement Hi! I am trying to solve a problem where I need to calculate a satellite's orbit, but first I would like to ask for some clarifications from someone here that might know this stuff. I need to design an orbit so that no maneuvers (one part of the problem) are necessary to...

Hi! This is a textbook problem that I need help with (I want to practice as much as I can before the exams) and I hope that there is someone who can guide me. The question is: You’re doing a first-order analysis on a new satellite in an elliptical (e = 0.2) orbit at 700 km altitude. Can you...

I was talking to someone online the other day, and they were claiming that general relativity must be wrong because it predicts that gravity must propagate at the speed of light, and he said this must be wrong, because if that were the case the Earth would be attracted to the place where the sun...

Hello everybody! Long-time lurker and second-time posting. I'm working on a project for my math class, and I'm trying to plot the orbits of the planets using vectors. I've chosen to use MATLAB because I am decently familiar with it. I've used the formulas described in this post here to get my...

All of the planets should have individual orbits, and should be between the mass of Mercury and Mars. What can their orbits be in AU's? Is there a way to find out how close they can be without destabilizing each other? If we assume the star is about the same size as Sol.

I'm trying to plot the solutions of the second order differential equation d^2R/dt^2 = GM/R^2 + Lz^2/R^3. I'm reducing this to a system of first order ODEs and then using RK4 to solve this system. My code is given by function RK4system() Tsim = 10...

Homework Statement A satellite moving in a highly elliptical orbit is given a retarded force concentrated at its perigee. This is modeled as an impulse I. By considering changes in energy and angular momentum, find the changes in a (semi major axis) and l (semi latus rectum). Show that \delta...

Homework Statement Show that Kepler's third law, \tau = a^{3/2}, implies that the force on a planet is proportional to its mass. Homework Equations 3. The Attempt at a Solution [/B] I haven't really attempted anything. I'm not sure what the question is going for. What can we assume and use?

Could we have a stable gravitational system with 2 Moons : * In the same orbit * In different orbits ? :wideeyed:

I entered in physicsforums archive search the wildcards "bohmian why electrons don't lose energy atom" but only got one hit that isn't related to it. In Bohmian mechanics, electron is localized and has trajectory.. why can't it lose energy as it rotates around the nucleus? What wildcard words...

There have been many questions on this forum about celestial mechanics in general, and concerning position and velocity in an orbit in particular. So I offer this post as a summary and reference. Here's a method for finding heliocentric position and sun-relative velocity in ecliptic coordinates...

Hello friends (I hope :biggrin:), For a maths project I am working on, I need to be able to prove the equation for an elliptical orbit, related to Kepler's first law: and p = a(1-e2) (or should be as p can be replaced by that value) Where: r = distance from sun to any point on the orbit p =...

Hi, my name is Andreas, and I am new to this forum. I had a couple of questions regarding orbital dynamics, since I am not very familiar with the field: Is tangential velocity in elliptical orbits stable like in circular orbits? If not, how exactly does it change? How do you calculate orbital...