Orbit Definition and 1000 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. Shadow236

    Magnitude of acceleration given the orbit

    Homework Statement A satellites are placed in a circular orbit that is 3.22 × 105 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?Homework Equations a = MG/R^2The Attempt at a Solution For the above formula I have trouble because I do...
  2. S

    Relativistic effects of a low orbit around supermassive objects

    Hi everyone, first post here. Lurking for a while but it was time to register.. I'm trying to conceptualize an idea in which humans are sent to orbit a very massive object, like a neutron star, a magnetar or even possibly a black hole. I would like the ship to be relatively close to the surface...
  3. C

    Understanding Gravity & Orbit in Our Solar System

    Keeping in mind I am a person that did not go to school...This must be a common question. Can be maddening for you guys to keep reading it over and over. Would be happy to read any links you want to post. I did a search on Gravity and Orbit, and did not see this topic. But those words garner a...
  4. S

    Hydrogen atom: potential well and orbit radii

    Hello, I happened to open up an old book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level E_n" The orbit radius is r_n=\frac{4*\pi*ε_0*\hbar^2*n^2}{mq^2} and the potential well...
  5. A

    Why don't electron go into the next orbit during stimulated emission?

    Why don't electrons go into the next orbit during stimulated emission? Hey all, I was studying stimulated emission in lasers and I had a doubt regarding the same. When the electron collides with another which is in an excited state, why doesn't the electron, which gets collided, move into the...
  6. Z

    How to Launch a Satellite with Apogee 2.5 Times the Planet's Radius?

    Homework Statement It is required to put a satellite of mass m into orbit with apogee 2.5 times the radius of the planet of mass M. The satellite is to be launched from the surface with speed v0 at an angle of 30° to the local vertical. Use conservation of energy and angular momentum to...
  7. V

    Spin orbit and double group representations

    I am reading a text about the splitting of the energy levels in crystals caused by the spin orbit interaction. In particular, the argument is treated from the point of view of the group theory. The text starts saying that a representation (TxD) for the double group can be obtained from the...
  8. M

    Find eccentricity of orbit given position and velocity

    Homework Statement Hey, I need to find whether an asteroid is in a "bound orbit" around the Sun. Furthermore, describe the shape of the orbit (elliptical or circular). The only information I have been given is its velocity and position at a random point. v_o=61m/s r_o=13.75AU=2.06E12m I also...
  9. Jorrie

    Orbit eq. holds inside BH? - MTW sec. 25

    MTW section 25, from eq. 25.16 onwards, derives an orbital equation (with G=c=1, u = M/r, E and L Schwarzschild constants for energy and angular momentum respectively): \left(\frac{du}{d\phi}\right)^2 = \frac{M^2}{L^2}(E^2-1) + \frac{2M^2}{L^2}u - u^2 + 2u^3 This equation is readily...
  10. T

    What Speed Must an Electron Achieve to Orbit a Charged Glass Sphere?

    Homework Statement A 2.70-mm-diameter glass sphere has a charge of + 1.10 nC. What speed does an electron need to orbit the sphere 1.50mm above the surface? Homework Equations a = v^2/r -> force = m*v^2/r electrostatic force = K*Q1*Q2/distance^2 therefore...
  11. D

    Change in orbit due to moment of inertia change?

    Hi, So recently I read about the massive 3 gorges dam changing the mass moment of inertia of the Earth to such an extent that the days will now be 60ns longer. Then I thought, how will this effect the orbit of the Earth about the Sun? Any thoughts?
  12. AwesomeTrains

    Solving a Satellite Orbit Problem: Help Appreciated!

    Warning read on your own risk: This is my first post here. I'm new to english, sorry for my bad grammar. Homework Statement A satellite is launched one time Earth radius straight above the northpole (two times radius from center), with an angle of 60° to vertical. Find the launch velocity...
  13. K

    Simulated gravity-satellites in orbit

    Homework Statement Ringworld is an artificial world constructed in the shape of a giant ring that rotates around a star similar to our sun. The radius of the ring is 1.53x10^11m (from the sun to the ring). The mass of ringworld is 2.1x10^27kg and its simulated gravitational acceleration is...
  14. O

    Angular Momentum and Energy from parametric orbit equations

    Homework Statement Given the parametric equations for a satellite in orbit around a spherical mass find angular momentum L in terms of ε, a, k, m, where k=GMm. Also, find the energy E in the same terms. Lastly, I can only use the equations provided and "fundamental definitions." Homework...
  15. R

    Orbit of figure eight 3 or more bodies

    If I wanted to set up some initial conditions for a 3 body figure eight orbit, what would I have to set the position and velocity vectors? Say I have three vector inputs: initial position <x,y> initial velocity <x,y> mass of bodies <m1,m2,m3> The solutions for position use f=mi*x''...
  16. E

    How Is Work Done by Gravitational Force Calculated in Satellite Orbits?

    [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...
  17. P

    Tidal forces,moons & changing orbit in solar system.

    Ok I know our moon is getting farther away due to gravity (tidal force indirect), basically giving it kinetic energy and exchanging that for orbital energy. If the moon was in retrograde orbit, i.e. Triton around Neptune, it would work the opposite way and pull the moon closer to the...
  18. O

    Find delta-v; Hohmann transfer orbit

    Homework Statement A space vehicle is in circular orbit about the earth. The mass of the vehicle is 3300 kg. The radius of the orbit is 2RE. It is desired to transfer the vehicle to a circular orbit of radius 4RE. An efficient way to accomplish the transfer is to use a semielliptical orbit...
  19. S

    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...
  20. O

    Mass shot into orbit; find max distance from Earth

    Homework Statement A projectile of mass m is fired from the surface of the Earth at an angle α from the vertical, where α = 0.46 radians. The initial speed v0 is equal to √{GM/Rearth}. Calculate the maximum height that the projectile will reach. Neglect air resistance and the Earth's rotation...
  21. P

    Interruption of solar observation on a sun-synchronous orbit

    Homework Statement Analyse the interruption of solar observation of a satellite on a sun-synchronous orbit (altitude 900km above Earth's surface). The orbit crosses the equatorial plane at the day/night border and the orbital plane should follow this border as close as possible. a) Draw the...
  22. P

    Sun-synchronous orbit: Implication on the orbit's inclination

    Homework Statement A satellite is launched into a circular sun-synchronous orbit at a height of 900km above Earth's surface. What is the implication on the orbit's inclination (in deg) and on the change of the position of the right ascension of the ascending node per day.Homework Equations The...
  23. H

    Mechanical Energy- Geosynchronous Orbit

    Homework Statement What is the total mechanical energy of a 290 kg satellite in a geosynchronous orbit around the Earth? Homework Equations W= K + UG where K= 1/2 (mv2) and UG= -(GmM)/r Fc= mac where ac= v2/r The Attempt at a Solution I think the geosynchronous part is what is...
  24. P

    Molniya Orbit: calc angular displacement of ascending node

    Hello there :), Homework Statement We have a molniya orbit with an eccentricity of e = 0.72 and a semi-major axis a = 26554 [km]. The task: Calculate the angular displacement of the ascending node Ω after 100 sidereal days Homework Equations Moreover I know from Wikipedia that a...
  25. H

    E= 2.377074x1010 J * 380 kgE= 9.038314x1012 J

    Homework Statement What is the total mechanical energy of a 380kg satellite in a circular orbit 3.0 Earth radii above the surface? Homework Equations W= E2- E1 E= 1/2 mv2- \frac{GmM}{r} The Attempt at a Solution I'm not sure if the equations above are suitable to solve this or...
  26. A

    Achievable orbit from launch location

    Hi Astro gurus, Is there any limitation on the inclination of the achievable orbit because of the latitude of the launch location? For example, latitude of Baikonur is roughly 46° E. Does that limit somehow the inclinations of the orbits that can be achieved from Baikonur? I think there...
  27. S

    Typical energy ratios to get into orbit? (height, friction, velocity)

    I realize the answer depends how where in the atmosphere speed is increased more, and whether a higher orbit or lower orbit is desired, and the shape size and weight of the craft. But I'm just curious about typical ratios. About what fraction of the fuel goes to lifting the weight of the...
  28. A

    Is it possible for the earth to come off orbit and crash into the sun?

    Or get so close that human life will be destroyed
  29. S

    Deriving formula for surface velocity of a satellite in orbit.

    I may be being stupid here... But I'm trying to derive such an equation to no avail. Maybe such a formula requires more than one variable - but I would like to easily display this graphically. To start out the derivation I stated that the Surface Velocity = (2pi/T)-(v/r) where v/r=angular...
  30. B

    The Magic of Light: Trapping Light in Orbit

    Can light be bend in such a way that it is essentially trapped in an orbit?
  31. B

    Hohmann Transfer Orbit (Simple)

    Homework Statement I've been stuck on this problem forever, any help is greatly appreciated. A satellite is in a LEO at h=300km and it is sent to a geosynchronous orbit at 4.224x10^4 km. Calculate velocity at pericenter i.e v_pe Homework Equations v_pe = (2πa_to)/p_to[2a_to/a_leo -1...
  32. E

    Circular prograde orbit homework

    Homework Statement Hi! I have a problem with an assignment and need som help. The question is: You’ve just completed an analysis of where the Space Shuttle must be when it performs a critical maneuver. You know the shuttle is in a circular prograde orbit and has a position vector of: ro=...
  33. P

    Exploring the Effect of Lower Moon Mass on Orbit Distance

    Hi everybody, I've registered to PF because after searching the web and this forum too, I couldn't find a clear answer to my dilemma. I've read this article but something seems wrong: http://www.scientificamerican.com/article.cfm?id=half-mass-moon What if the mass of the Moon would be...
  34. Philosophaie

    Turn a sinusoid into a elliptic orbit

    I am trying to get my head around these equations. I am not sure they are correct. My logic is an orbit exists at a starting point (x0,y0,z0) with a starting velocity at time zero (vx0,vy0,vz0) changing with time (dx/dt, dy/dt, dz/dt). The gravity is (d^2x/dt^2, d^2y/dt^2, d^2z/dt^2). How do...
  35. D

    Finding the Orbit of a Particle with Varying Position Vector

    I'm given the position vector as a function of time for a particle (b, c and ω are constants): \vec{r(t)} = \hat{x} b \cos(ωt) + \hat{y} c \sin(ωt) To obtain it's velocity i differentiate \vec{r(t)} with respect to time and i obtain: \vec{v(t)} = -\hat{x} ωb \sin(ωt) + \hat{y} ωc...
  36. B

    Can Conservation of Angular Momentum Help Estimate the Mass of Binary Asteroids?

    Homework Statement Two asteroids (approximately the same size and mass) are orbiting each other at a given radius a. The center of mass is orbiting the sun at a distance (semimajor axis) b with an orbital period of P. I would like to estimate the mass/size of each of the asteroids. By...
  37. D

    MHB Hyperbolic trajectories from a parking orbit

    This is a fun TikZ picture to play with. \documentclass[convert = false]{standalone} \usepackage[utf8]{inputenc} % Euler for math | Palatino for rm | Helvetica for ss | Courier for tt \renewcommand{\rmdefault}{ppl} % rm...
  38. E

    How can a particle coming from infinity get on bound orbit around BH?

    Studying the movement of a particle on bound orbits around a black hole I found a fact that seemed a little strange for me -- that on these orbits particle's total energy on infinity must be less than unit (E<1). As far as I understrand, it is not so horrible, since here we deal with an...
  39. K

    Can the earth loose its orbit and regain its orbit again

    lets say a rogue star or black hole pass by our solar system and disrupt the orbits of the planets and pull the Earth away from the sun, can it regain or get back to its original orbit if the black hole is gone? some people say the chances of a black hole passing by our solar system is slim but...
  40. S

    Do a comet's tails ever point in the same direction when in an orbit?

    Homework Statement The problem and its solution are attached as TheProblemAndSolution.jpg. Homework Equations *The (“instantaneous”) dust tail is opposite the direction of motion. *The plasma tail is oppositely directed to the star in question (at all times). The Attempt at a Solution...
  41. A

    Angular momentum and orientation of electron orbit with l = 0

    Let an electron is orbiting in a orbit with the principal quantum number n =1. According to wave mechanics its angular momentum is √ l(l+1) h/2∏ and angle : cosθ = ml/ √ l(l+1) How one can explain the electron angular momentum and its possible orientations for l =0? Off course for n =2, l...
  42. B

    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...
  43. J

    How Can I Accurately Simulate the Earth-Apophis Encounter on April 13, 2029?

    I would like to have a nice picture/simulation of the Earth - Apophis encounter on April 13th 2029. I found this applet http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=aPOPHIS;orb=1;cov=0;log=0;cad=0#orb but it seems to produce too great error for the time of encounter - the minimal distance much...
  44. J

    Circular Orbit Four-Velocity and Schwarzschild Metric

    If an object is orbiting on a circular time-like geodesic path around a mass then the Wikipedia claims that the first component of its four-velocity is given by \frac{dt}{d\tau} = \frac{1}{\sqrt{1-\frac{3}{2}\cdot \frac{r_0}{r}}} where r_0 is the Schwarzschild radius. Is this right and how...
  45. B

    Radius of a photon's circular orbit around a mass

    What is the radius of a photon's circular orbit around a mass M? My guess would be the Scharzschild radius. Is that true?
  46. Q

    Why do geosynchronous satellites have to orbit above the Equator?

    I get that they have to be at the same position relative to the earth but why is it that they have to be specifically above the equator? thats the sense I get from the textbooks, they all seem to emphasize the satellite being above the Equator can't you have a geosynchronous satellite...
  47. U

    Orbit about star, emission spectrum of light

    Homework Statement Show that in the Bohr model, the frequency of revolution of an electron in its nth In classical physics, the frequency of revolution of the electron is equal to the frequency of radiation it emits. Show that when n is very large, the frequency of revolution is equal...
  48. maverick280857

    Is the Spin Orbit Hamiltonian really Hermitian?

    The regular spin orbit Hamiltonian is H_{SO} = \frac{q\hbar}{4 m^2 c^2}\sigma\cdot(\textbf{E}\times \textbf{p}) If I consider a 2D system where E = E(x,y) and p is treated as an operator, i.e. \hat{p} = \hat{i}p_x + \hat{j}p_y then, clearly E and p do not commute, so this doesn't look like...
  49. B

    Satellite Low-Earth Orbit: Does Air Friction Slow It?

    Homework Statement A satellite in low-Earth orbit is not truly traveling through a vacuum. Rather, it moves through very thin air. Does the resulting air friction cause the satellite to slow down? Homework Equations The Attempt at a Solution Evidently, the answer is, "Air...
  50. G

    What keeps the planets in orbit

    If the reason why the planets orbit around the sun is the deviations in the fabric of spacetime,what keeps the planets from crashing into each other? Like if I put a boulder on a trampoline and then I put a baseball next, the baseball would go toward the boulder. I think it could be dark matter...
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