Orbits Definition and 498 Threads

In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.

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  1. Sai Siddhartha k

    B General theory of relativity&Planet orbits

    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..
  2. A

    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?
  3. A

    I Proving that an action is transitive in the orbits

    <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...
  4. Simon Peach

    B Can Friction Create Preferentially Circular Orbits?

    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...
  5. Toreno

    Calculating orbits of planets in Solar System

    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...
  6. A

    I Questions About Acceleration and Jerk in Orbits

    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...
  7. Z

    B Understanding Orbital Geodesics in General Relativity

    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...
  8. K

    I Can Newton's Theory of Gravity Explain Planetary Elliptical Orbits?

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

    I Using Black Holes to Time Travel Into the Future

    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...
  10. P

    A The method of finding periodic three-body orbits

    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...
  11. Joppy

    MHB You're welcome, happy to help!

    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...
  12. D

    Runge-Kutta on Elliptical Orbits

    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...
  13. W

    Understanding Hyperbolic Orbits: The Relationship Between Foci and Trajectory

    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...
  14. W

    Elliptical Orbits and Angular Momentum

    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 $$l = r \times P = mr \times V = mrVsin(\theta) = mr^2\dot{\phi} sin(\theta)$$...
  15. S

    Calculating Height of a Twice-Daily Orbit Above Earth's Surface

    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...
  16. R

    Why are orbits of Comets unstable?

    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...
  17. R

    Effects of Varying Satellite Heights on Orbit Motion

    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...
  18. R

    Why does Venus always appear close to the Sun in the sky?

    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...
  19. A

    I Orbits -- radial verses perpendicular orbits & energy

    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...
  20. V

    B Inclinations of star orbits in the Milky Way

    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?
  21. Sanborn Chase

    B Enlarging Planetary Orbits: Evidence of the Solar System's Evolution?

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

    I Planetary Orbits: Force needed for circular orbit

    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 *...
  23. M

    B Celestial Mechanics: Eccentricity of Orbits

    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?
  24. X

    N-body simulation - straight line orbits

    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...
  25. Conclaude

    Numerical Plot of Particle Orbits in Kerr Equatorial Plane

    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...
  26. J

    I Help in calculating the orbiting height of a satellite?

    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?
  27. K

    A Adiabatic Invariance: Why Do Closed Orbits Remain Closed?

    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...
  28. P

    Finding r(ϕ) from r(t) and ϕ(t) to plot Newtonian orbits

    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...
  29. M

    B Rethinking Gravity: The Reality of General Relativity and Spacetime Curvature

    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...
  30. micropulsar

    B Can Orbiting Bodies Slow Down Over Time?

    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?
  31. Unteroffizier

    Centripetal Force - same thing as gravitational force?

    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...
  32. farolero

    How is Angular Momentum conserved in orbits?

    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...
  33. L

    B Retrograde star orbits in the Milky Way

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

    Circular orbits in Schwarzschild geometry

    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...
  35. L

    I How many orbits are in the hydrogen atom?

    How many orbits are in the hydrogen atom?
  36. I

    Proving that three closed orbits must contain a fixed point

    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...
  37. S

    I Kepler 3rd law for circular orbits

    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...
  38. I

    What are J2 perturbations and how do they affect satellite orbits?

    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...
  39. I

    Orbit that does not need maneuvering

    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...
  40. Platonist

    Speed of gravity and planetry orbits

    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...
  41. A

    I Plotting the orbits of the planets

    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...
  42. Q

    I Planetary Orbits in AU - Stability & Mass Limits

    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.
  43. J

    MATLAB Solving Orbital Motion Equations with RK4 Using MATLAB

    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...
  44. H

    Orbit: impulse making orbit spherical

    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...
  45. D

    Kepler's third law implies force proportional to mass

    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?
  46. petrushkagoogol

    A Could Earth Support Two Moons in Different Orbits?

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

    Quantized electron orbits in Bohmian mechanics

    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...
  48. Jenab2

    I Position and Velocity in Heliocentric Ecliptic Coordinates

    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...
  49. Memocyl

    Mathematical Proof of Kepler's First Law of Orbits

    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 =...
  50. Andreas C

    I Is tangential velocity in elliptical orbits stable?

    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...
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