What is Orbits: Definition and 497 Discussions

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. K

    Path of a ball thrown radially from a satellite orbiting Earth

    Homework Statement A satellite has a circular orbit 500 km above earth. A ball is thrown directly downwards radially at 20 m/s. Find the path of the ball relative to the satellite. Homework Equations mv^2/r=GMm/r^2 The Attempt at a Solution From the height of the orbit you can easily solve...
  2. ideasrule

    Celestial mechanics, particularly as it relates to spacecraft navigation

    I'm trying to teach myself celestial mechanics, particularly as it relates to spacecraft navigation. Essentially I'm interested in how spacecraft can get from A to B with the lowest delta-V (or whatever the criteria are), and how mission planners figure this out. Can anyone recommend a...
  3. kirinmew

    Exploring Habitability of a Planet with Two Suns

    I apologize in advance for my low understanding, but please play along if you can. I'm working on a story and in the story I want to toy with the idea of the solar system containing two suns and one planet. The story will be fantasy so it doesn't need to follow our laws of physics totally, but...
  4. F

    Orbits around a Schwarzschild/Kerr black hole

    Hi everybody, Around a black hole, a test particle can experience two types precession: of its pericenter and of its angular momentum vector. I would like to know if there exist an EXACT expression for the rate at which these two precession occurs both for a Schwarzschild and a Kerr black hole...
  5. PhysicsStudnt

    About satellite launching and satellites in orbits

    Dear Experts, When we launch a satellite, we launch it from Earth which is spinning, so the tangential velocity component of the point on the surface where the rocket is launched from will be acquired by it. Is that the only horizontal velocity or is the rocket accelerated at an angle upward...
  6. G

    Low-eccentricity orbits and the Plane of the Elliptic

    So I've been playing some Kerbal Space Program, and it's taught me a couple things. Primarily, that circularizing an orbit (bringing its eccentricity down to near 0) is a matter of extremely precise engineering, and that matching planes with another satellite's orbit is also extremely...
  7. cbram

    Why Electrons Don't Radiate in h/2π Orbits

    Why is electron rotating in h/2pi orbit does not radiate energy
  8. D

    How do we know the orbits of the planets?

    What exactly does it take to figure out the orbital parameters or planets and what's the Math behind it? Can it be done using only a telescope or is it necessary to send a probe?
  9. F

    Can a satellite be raised to a new orbit with two impulses in this scenario?

    Homework Statement A satellite of mass m is in circular orbit about a planet of mass M, with orbital radius r. Show that with two appropriately located impulses, each directed along the satellite's instantaneous velocity at the moment of the impulse, it can be raised to a new circular orbit of...
  10. S

    Are Flat, Coplanar Orbits Only Found in Spiral Galaxies?

    Hey PF! Have two questions here for everyone. Recently had a professor define the The Big Bang as "the expansion and cooling of the universe from an originally hot and dense state", but is this correct? To me it sounded more like the description of cosmic inflation...thoughts? Additionally...
  11. leviterande

    Do orbits in diamagnetic materials align to external magnetic fields?

    Hi, I am having a question about diamagnetism. I understand that ferromagnets realign with external magnetic fields. I know that besides diamagnets like copper, bismuth, that all matter exhibit some diamagnetism to some degree. I wonder though if these paired electron filled orbits of...
  12. B

    Elliptical orbits double velocity

    Homework Statement A rocket ship is in circular orbit of radius R around a planet. Its velocity is doubled by a sudden engine burst. Calculate the furthest distance from the planet on the new trajectory. Homework Equations Elliptical energy equation: E = Ek +Ep = -GMm/2a (a=semi major axis)...
  13. D

    The elliptical orbits and inverse-square law forces.

    Greetings, I read a chapter in the book College Physics by Vuille and Serway explaining the laws of planetary motion in terms of the universal law of gravitation. The first law stated that planets move in an elliptical orbit and the book's explanation was that all objects bound by an...
  14. C

    Solve Orbital Period for Two Identical Planets Around Star

    Homework Statement Two identical planets (equal masses, m) move in identical circular orbits around a star (mass M) diametrically opposed to each other (opposite sides of the planet). Find an expression in terms of m, r, M and G for the orbital period T. Homework Equations...
  15. W

    General Quantization of Motion in Circular Orbits

    For this question, I have to obtain a general quantization of motion in circular orbits by combining the equations (Where U(r) is potential energy): (mv2)/r= |(dU(r))/dr| With the angular momentum quantization of: mvr= nℏ Then use this to calculate the spectrum for circular motion in a...
  16. M

    What is the equation of the orbits of things in space?

    I appologize for any grammar or spelling errors. English is not my first language. I do my best. Given 2 objects in space, is there an equation that explains that one will, naturally and without any interference other than gravity, assume an orbital movement around the other? And does the...
  17. I

    Elliptical Orbits and Resonance of Eccentricities

    Hi, Dumb Question #1251: What I understand so far (which maybe incomplete or wrong): in any system with multiple objects orbiting a larger body (either star+planets or planet+moons) each body can have an influence on the others, such that large bodies such as stars and big gas giants have...
  18. Y

    Rotational speed due to gravitational pull in earth's orbits

    Hi All, Assume we have a package that we want it in an orbit with highest possible speed. In which orbit (low,mid,high) the package will rotate faster ? Due to smaller distance, low Earth orbit should allow more speed but there is also more air friction there. What would be the mathematical...
  19. O

    Questions About Things in Orbit and Why They Don't Descend

    Hello. I asked a question a couple of weeks back about things in orbit. Now, I am watching a video on youtube about when mankind disappears, and they mentioned that the artificial satellites in space will 'run out of batteries and plummet to earth'. So, I am curious again. Why will these...
  20. O

    Satellites in various orbits above the earth exploded?

    1) What would happen if artificial satellites in various orbits above the Earth exploded? Where would the fragments go? 2) How do constituents of asteroid belts stay in their orbit? Why don't they change orbits? Why that particular distance? Thanks
  21. T

    Deteriorating Orbits of Satellites and Objects

    Assuming that an object in orbit has no means of propulsion (dead satellites, NEOs, etc.) and it remains aloft long enough, will it tend to specific areas of orbit or inclination? Do these unnatended objects tend to the poles? to the equator? etc. (I understand that it can be dependent on...
  22. E

    Orbits of objects of equal mass

    What basic types of stable orbits are there for sets of objects of equal mass? For example, with one object it would just be stationary, with two objects they would rotate at equal speed around a common centre with a constant distance between them (and more complicated stable orbits where...
  23. R

    Classical mechanics: orbits, force, potential

    Homework Statement a particle of mass m moves on the orbit r= a cos(θ), a>0. Find the force acting on the particleThe Attempt at a Solution I had this formula in my notebook:U(r)= E-(L^2/2mr^2)(1+(1/r^2)(dr/dθ)^2) Using it I got U(r)=E-L^2a^2/2mr^4 and F(r)=-dU/dr= (-5L^2a^2/2mr^5)...
  24. E

    How Do You Derive the Axes of a Kepler Orbit from Its Equation?

    Homework Statement I am trying to see if I am on the right track with this. The problem: A kepler orbit (an ellipse) in Cartesian coordinates is: $$(1−\epsilon^2)x^2 + 2\alpha \epsilon x + y^2 = \alpha^2$$. The task is to show that the major and minor axes are: $$a =...
  25. P

    How Do Lorentz Transformations Relate Time-like Four-Momenta in SO^{+}(1,3)?

    I want to determine the orbits of the proper orthochronous Lorentz group SO^{+}(1,3) . If I start with a time-like four-momentum p = (m, 0, 0, 0) with positive time-component p^{0} = m > 0 , the orbit of SO^{+}(1,3) in p is given by: \mathcal{O}(p) \equiv \lbrace \Lambda p...
  26. A

    Calculating elliptic orbits in Cartesian coordinates

    I have a function to plot the orbits of planets based on their orbital elements (Semi-major Axis, Eccentricity, Argument of periapsis, Inclination, and longitude of ascending node). I have the x and y coordinates working great using only the semi-major axis, eccentricity, and argument of...
  27. K

    Optimal Distance for Collision-Free Earth Orbit

    IN a relatively circular Earth orbit, how far away from Earth would you have to be in order to avoid collisions?
  28. D

    This description of orbits seems wrong to me

    and I would be grateful if those who understand classical mechanics, in particular the physics of orbital motion, could visit this link -- https://earthkam.ucsd.edu/resources/students_orbital_mechanics#shuttle_stays_in_orbit -- and read the description of the 'four cases' by which a spacecraft...
  29. T

    Stationary Orbits, Are they Real or just Idilization?

    Hi, I raised this question in another forum but get no satisfactory answer, so hope will get something new here... Stationary orbits of atoms are based on variable separation (time and spatial) of usual Schrodinger equation when Hamiltonian is time independent, and we get eigenvalues for...
  30. M

    Using Index Theory to show a system has no closed orbits

    Homework Statement I'm doing a course in nonlinear dynamics using Strogatz. One of the exercises in the book is "Using index theory show that the system has no closed orbits" Homework Equations \dot{x} = x(4-y-x^{2}) , \dot{y} = y(x-1) The Attempt at a Solution Turns out there...
  31. U

    Orbits: Firing satellite to Moon

    Homework Statement Homework Equations The Attempt at a Solution Parts I'm unsure of: Sketching of graphs in (a) and (b). I know increasing its energy will shift the entire graph upwards. But does it shift it rightwards if the angular momentum is increased? Last part, they said to ignore the...
  32. D

    Mean anomaly as a function of the true anomaly elliptical orbits

    The book Orbital mechanics by Curtis says that the function (I labeled M2evals) is monotonically increasing. However, at pi, I have a discontinuity and the graph jumps below the negative axis when it should continue on; that is, the e = 0 should be the line y = x. import pylab import...
  33. P

    AP Physics MC Questions: Orbits, Momentum

    Homework Statement Answer is D. Answer is E. Homework Equations 14. v=√(Gm/r) 17. p=mv τ=rxF L=Iω The Attempt at a Solution Number 14 made perfect sense until I saw the answer, which is D. If the velocity of the spacecraft increases, according to v=√(Gm/r), the radius...
  34. L

    Two Satellites in Parallel Orbits

    Homework Statement Two Earth satellites are in parallel orbits with radii 6700 km and 6701 km. One day they pass each other, 1 km apart, along a line radially outward from the earth. How long will it be until they are again 1 km apart? Homework Equations s=r*θ The Attempt at a...
  35. Monsterboy

    Why are all the orbits elliptical and not circular?

    In high school whenever i asked questions about planets and their orbits around their star or the orbits of satellites around their planets ,i always got the answers with the terms centrifugal ,centripetal force and an example of a stone tied to a thread and how it behaves when you hold the...
  36. Ackbach

    MHB Exploring the Relationship Between Conic Sections & Orbits

    If you think about a double-napped cone, and the various non-degenerate sections you can get with it: 1. Circle 2. Ellipse 3. Parabola 4. Hyperbola, you can see that there is a progression here: increasing angle $\alpha$ that the intersecting plane makes with the horizontal. To be clear about...
  37. C

    Comet Elliptical Orbits Question

    Homework Statement Comets move around the sun in very elliptical orbits. At its closet approach, in 1986, Comet Halley was 8.79 x 10^7 km from the sun and moving with a speed of 54.6 km/s. What was the comet's speed when it crossed Neptune's orbit in 2006? Homework Equations Mv1r1=Mv2r2...
  38. P

    Some general formulae for circular orbits in symmetric spacetimes

    Consider the equatorial plane of a spherically symmetric space-time. Then we can write the metric in the equatorial plane (theta=pi/2) in terms of three coordinates - [t, r, phi] ds^2 = -f(r) dt^2 + g(r) dr^2 + h(r) dphi^2 For the Schwarzschild metric we can write: f = c^2(1 -\frac{2 G...
  39. U

    Geostationary satellite collision - Orbits

    Homework Statement A geostationary satellite of mass m, speed v orbits earth. (a) Find expressions for (i) Radius of the orbit, r0. (ii) Satellite's Speed (b) A meteorite with mass m and speed v approaches in the direction towards the centre of the Earth and collides with the satellite...
  40. C

    Stability of Orbits Homework: Analyzing Central Force Motion

    Homework Statement A particle of mass m moves under a central force ##\mathbf{F}(\mathbf{r}) = -\frac{\mu}{r^2} e^{-kr} \hat{r}##. The particle undergoes motion in a circle if ##h^2 = (a\mu/m)e^{-ka}##. I have shown that if ##u(\theta) = 1/r,## then the orbit eqn for ##u(\theta)## becomes...
  41. W

    Question on Elliptic Orbits. Difficult.

    A satellite undergoes an elliptic orbit about the Earth of mass M, with maximum distance 6R and minimum distance 3R from the Earth's centre. (a) Show that twice the minimum velocity v(min) = the maximum velocity v(max) = (2/3)*sqrt(GM/R) (b) Show eccentricity = 1/3 We are told that we...
  42. K

    Do planets wave in their orbits?

    Do planets "wave" in their orbits? Hi, I was wondering if a planet moves up and down as they orbit the Sun due to the differing inclinations of the other planets? In other words do the planets move in a wave like motion in their orbits or is it smooth? Thanks in advance.
  43. E

    How do Trojan Asteroids effect a planets' orbits

    Question: What would happen if a planet's trojans were removed or added to? And I don't mean "very little" please. What exactly would happen, for example, if a planet's huge trojan asteroids were pushed out of orbit into the Sun? What would happen if L4 and L5 had asteroids as big as the planet?
  44. F

    Conservation of Energy in Orbits

    Homework Statement 1.A rocket at the surface of the Earth is launched with a speed of 2500m/s. What is the orbit that the rocket will achieve? 2.A meteorite traveling at 3500m/s approaches Earth from outer space. With what speed will the meteorite hit the surface of Earth? 3.Also, in...
  45. J

    Show that the system has no closed orbits by finding a Lyapunov

    Show that the system has no closed orbits by finding a Lyapunov ... Homework Statement I'm at the point in the problem where I need constants a and b satisfying ax2(y-x3) + by2(-x-y3) < 0 and ax2+bx2 > 0 for all (x,y)≠(0,0). Homework Equations Just in case you're wondering...
  46. W

    Could this solar system have stable orbits.

    The will be a G2v star with the sam mass, radius and luminousity of our sun Planet 1: 0.5 Earth masses orbiting at 0.51 au Planet 2: 1 Earth masses orbiting at 0.63 au planet 3: 2 Earth masses orbiting at 0.78 au planet 4: 0.2 Earth masses orbiting at 0.85 au planet 5: 4 Earth masses...
  47. C

    Atomic excitation and electron orbits

    hi guys, i have a basic question over the atomic excitation and it's relationship with the hydrogen like atoms. we know while excitation the electron in the ground state jump to the higher orbits. but when hydrogen or atoms containing little principal quantum numbered orbits get excited , then...
  48. S

    Gravitation: Satellite Orbits

    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...
  49. P

    Gravitation and Orbits help

    Homework Statement A spacecraft orbiting the Sun uses its jet engine for slowing down its orbital rotation and changing the direction of its velocity. At the moment when the velocity is directed away from the Sun and has a magnitude of v = 30 km/s, the jet engine is switched off. At the same...
  50. P

    Relationship between orbits and cosets

    How are orbits and cosets related? Are all orbits cosets? Are all cosets orbits? Also, what exactly are G-sets and G-equivariant sets?
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