What is Orbit: Definition and 1000 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. E

    I Spin orbit coupling/Filling order/Nucleus

    Which tends to fill first: p3/2 or p1/2? d5/2 or d3/2? And why is there no spin orbit coupling in the nucleus?
  2. Kaguro

    Angular momentum of orbit from orbit parameters and mass of sun

    L = mvr = mr (dr/dt) = 2m*r*(dr/dt)/2 = 2m*(dA/dt) So, A = (L/2m)T so, ## L = \frac{2 \pi a b m}{T}## Now, ##T^2 = \frac{4 \pi^2}{GM} a^3## So from all these, I get ##L = \sqrt{ \frac{GM m^2 b^2}{a}}## But answer given is ##L = \sqrt{ \frac{2GM m^2 ab}{a+b}}## (This, they have derived from...
  3. B

    Orbit determination from radar readings of a satellite in orbit

    Hello everyone! This is from The Fundamentals of Astrodynamics Chapter 2 Questions. I'm doing this as a self-study (and never took Linear Algebra) so my "technique" might be a little sloppy 😖😖 Finding specific angular momentum Finding the orbital parameter Finding Eccentricity Vector...
  4. J

    Using Orbital Energy to Calculate Velocity

    So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m. Then I found change in potential energy, -5.597*10^11 m. Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial...
  5. S

    Converting State Vectors to Keplerian Orbital Elements for Binary Objects

    Homework Statement:: I'm working on a personal project to convert objects from a simulation using state vectors for position and velocity to Keplerian orbital elements (semimajor axis, eccentricity, argument of periapsis, etc.). However, the equations I am using do not calculate the...
  6. Py3_3

    I Determining Relative Position of Space Object to Earth

    Hello, i'm doing a project where the goal is to get the relative position of a space object to the earth, roughly. Basically, i want to say that this object is currently e.g. above New York. The data for any given space object that i have is (It's sourced from an NASA API). The specific...
  7. T

    I Earth's Rotation & Orbit: Effects on Space Objects?

    Hi. I don't know what prefix this question belongs in so I just chose advanced at random. What's the physical effect called when the Earth orbits around the sun at extremely fast speeds and also rotates around itself every 24 hours at the same time? Does that force cause anything in space...
  8. AN630078

    Potential Energy and raising a satellite from Earth into a Circular Orbit

    a. V=-GM/r V=-6.67*10^-11*6.0 x 10^24/6.4 x 10^6 V grav = -62531250 ~ -62.5M Jkg^-1 b. To find the gravitational potential 200 km above the surface of the Earth; r=6.4 x 10^6 +2*10^5 m=6.6*10^6 V grav=-6.67*10^-11*6.0 x 10^24/6.6*10^6 V grav= -60636363 ~ -60.6 M Jkg^-1 Can I check that it is...
  9. AN630078

    Finding r of a Jovian-synchronous orbit and escape velocity

    1. The satellite would be in a jovian-synchronous orbit, Rearranging the formula for the orbital period in terms of r, since T^2 is proportional to r^3: T^2=4π^2r^3/GM which becomes r^3=(GM/4π^2) T^2 M(mass of Jupiter)=1.89 x 10^27 G=6.67*10^-11 m^3kg^-1s^-2 T=9 hours and 55 minutes =...
  10. thaiqi

    I Can we imagine that an electron moves on an orbit of chaos?

    Bohr's hydrogen atom model is outdated facing Schrodinger's wave equation. Now that wave mechanics doesn't use a concept of orbit for the electron in hydrogen atom. But can we suppose the electron is still circling around the atom core, not necessarily in circles or ellipses, but in chaos like a...
  11. Sabertooth

    Expressing Elliptic Orbitals As Speed Functions.

    Hi everyone:) I have spend a couple of days trying to teach myself the math of orbital mechanics and have been able to generate a model of the orbital path of Haley's Comet, incorporating realistic distances and periods using Kepler's second law & ellipsoid functions. This is a GIF of the motion...
  12. T

    How Do You Calculate a Hohmann Transfer Orbit for a Mars Mission?

    I cannot understand the solution at https://www.aapt.org/physicsteam/2015/upload/E3-2-5-solutions.pdf, because the solution is terse and skip steps (at least i think so). I figured out that the name of this transfer is "Hohmann-Transfer Orbit". A detailed walkthrough would be appreciated. If I...
  13. 1977ub

    B Largest Moon With A Concave Orbit

    Asimov pointed out that Earth's Moon is nowhere concave (looped) in its motion with regard to the Sun. What about Pluto and Charon - are both concave w.r.t. the Sun at certain times? Moreover, what is the largest body in the solar system which is sometimes concave w.r.t. The Sun? Thank you...
  14. S

    I Orbits of Photons Around a Massball: Explained

    I am reading MWT gravitation and on page 676, they are talking about orbits of photon, and I don't understand it very well. Energy and angular momentum of the photon are important as a ratio when calculating the orbit. But not energy alone or angular momentum alone. Why is that, and the energy...
  15. J

    Stargazing Planetary orbits -- Why do planets orbit at same “level”?

    Why is it that all of the planets in our solar system (to our knowledge) orbit the sun in such a way that they all go around the sun in roughly similar orbital planes? Why don’t we have planets with orbital planes at significantly different angles?
  16. T

    Orbital equations in polar coordinates

    The equations of motion are: \ddot{r}-r{\dot{\theta}} ^{2} = -\frac{1}{r^{2}} for the radial acceleration and r\ddot{\theta} + 2\dot{r}\dot{\theta}= 0 for the transverse acceleration When I integrate these equations I get only circles. The energy of the system is constant and the angular...
  17. Buzz Bloom

    I How does the perihelion passage affect the orbital period of comet Neowise?

    The orbit diagram https://en.wikipedia.org/wiki/C/2020_F3_(NEOWISE)#/media/File:Comet_2020_F3-skyview.png' in the Wikipedia article https://en.wikipedia.org/wiki/C/2020_F3_(NEOWISE) shows some very odd spirals. My first guess is the picture shows what Neowise does in one Earth year (mostly...
  18. K

    Calculating Angular Diameter of an Orbit Using Kepler's Law

    I am confused because the question implies that I need to do some sort of calculation with Kepler's law. I got ##r+d = \sqrt[3]{\frac{T^2 GM}{4 \pi^2} } ## But don't understand why I need this, since I already have the distance and the angular diameter should be ##\arctan (2R/d)## I think I...
  19. Buzz Bloom

    I Formula: velocity of circular orbit wrt Schwartzschild metric

    Below are equations/formulas/text from https://en.wikipedia.org/wiki/Schwarzschild_geodesics https://hepweb.ucsd.edu/ph110b/110b_notes/node75.html I apologize for not remembering the source for the "v=" equation, or for my inability to find it again. For a circular orbit, the distance r and...
  20. LCSphysicist

    Prove the symmetry of an orbit from the given equation

    How can i know the resulting orbit of is symmetric about two turning points? Where m, l is constant. V is function of r u = 1/r and It is in polar coordinates. We could show that varying theta from 0 to -θ will be the same if we vary 0 to Θ, but i don't know where to start
  21. T

    What is the Correct Radius and Mass of Earth for Satellite Orbit Calculations?

    I just have a question on the problem itself. If I am putting the satellite into orbit 450,000 m above the surface, then would r=6,371,000 m(earth's radius)+450,000 m? And what mass of Earth should I be using, in kg of course.
  22. J

    I The effect of Faraday braking on the Earth’s orbit

    If you let a magnet free-fall down a copper or aluminum tube, the induced magnetic field in the surrounding conductive medium imposes a braking effect on the magnet, reducing its speed (explained by Lenz’s law). The earth, being a large magnet, is essentially free-falling around the sun. The...
  23. cwill53

    Calculating Orbital Velocity and Radius Using Energy Conservation

    I know this problem can be solved using energy conservation, but I tried another method that I don't know is correct or not, but yielded a similar result to what my classmates got: $$F_{C}=F_{G}\Rightarrow \frac{mv^{2}}{r}=\frac{GMm}{r^2}$$ $$\frac{v^2}{r}=\frac{Gm}{r^2}\Rightarrow...
  24. DuckAmuck

    I Elliptical Orbit and Kepler's equation

    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...
  25. DuckAmuck

    A Elliptical orbit parameterized by time

    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?
  26. B

    Radius of the electron orbit in a Hydrogen atom

    I am really stuck on what to do here in this question I have arrived at forming an equation to work out the radius of electron orbit from doing the following However I do not know what to do next as I don't know what the value of n (quantum number) must be? :oldconfused: Any help would be...
  27. C

    A Elliptical orbit and how seasons would be affected

    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.
  28. PainterGuy

    B The precession of Mercury's orbit

    Hi, I was reading about the general relativity to get some basic understanding and it was said that the proper answer to problem of precession of Mercury was provided by the general relativity. Then, I started reading about the precession of Mercury orbit. "Mercury deviates from the precession...
  29. K

    I Vector addition in spin orbit coupling

    Hello! I am reading about spin-orbit coupling in Griffiths book, and at a point he shows an image (section 6.4.1) of the vectors L and S coupled together to give J (figure 6.10) and he says that L and S precess rapidly around J. I am not totally sure I understand this. I know that in the...
  30. Saptarshi Sarkar

    Time period of an object traveling in an elliptical orbit

    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...
  31. cemtu

    Classical Mechanics: Finding the centripetal force acting on an object that moves within a spiral orbit.

    I believe I solved this. Is this solution true? Can please anyone just check?
  32. BiggestAfrica

    Gravity problem: determining the period of a satellite in Earth orbit

    Hi! This is a problem from my physics 1 high school course. I've tried using the first and third equations to determine period (answer of 8326.9544s.), however that was incorrect and I never even touched G. I'm not sure where to go from here at all. Any help is appreciated!
  33. T

    Spin Orbit Coupling + Magnetic Field

    I am pretty confused where to even start with this question, which is not a good thing less than a week before the final :(. One thing in particular that I don't get is that I thought we were using the Clebsch-Gordon coefficients for ##\vert jm \rangle ## states, not for ##\vert J, J_z \rangle...
  34. B

    Height and Acceleration of a Satellite in Orbit

    a) Eg = Gme/r^2 r = √Gme/Eg r = √[(6.67x10^-11 N*m^2*kg^2)(5.98x10^24 kg)]/(4.5 N/kg) r = 9.41x10^6 m h = r2 - r1 h = 9.41x10^6 m - 6.38x10^6 m h = 3.03x10^6 m that's over 3000 km. Did I not use for right equation? Is Eg not 4.5 N/kg? Also for b), isn't the force of gravity the centripetal...
  35. Gumbrain

    I Help With Simple Orbital Modeling

    I have yet to decide on values for the mass of the fixed object, M, the mass of the moving celestial body, m, the initial velocity, v, and the distance between the two objects, r. I will most definitely decide on a larger mass M because I would like the celestial body to spiral in towards the...
  36. WaiYan

    The Conservation of Angular Momentum in Polar Coordinates

  37. N

    Analytic solution of the Earth's orbit around the Sun

    The exercise is to compare numerical and analytical solution. I have worked out the code from earlier exercise (see code under this text), but I don't understand how the analytical solution works. I have tried to use the equation r(theta) = a(1-e^2)/(1+e*cos(theta)), which is OK but I don't...
  38. Zala Jaydevsinh

    I About L-S interaction or spin orbit coupling

    I want to understand this topic but I can not understand very well so please suggest any reading for good conceptual grasp of this topic.
  39. Evenlander

    B What is the shape of an asteroid impact on Earth?

    The Earth's orbit around the Sun is an elliptical orbit. Why is that so? Does that mean Sun, much like Earth bulged at some points which makes the gravitational force between Earth and Sun stronger at some points and weaker at some comparatively?
  40. G

    Any plausible non-rocket based method to reach orbit?

    Recently i read, that GEO orbit actually isn't enough for a space elevator, since its weight would pull it down, either it needs constant thrust, or build it much taller than 33.000 km, so upper GEO parts pull it up. That further lowers its plausibility level. Any other methods? Build a tall...
  41. P

    MHB Geostationary Orbits: Benefits & Challenges

    Hi, everyone can you help me with this question, please?
  42. D

    I A "space elevator" extended to Neptune's orbit

    Summary: Achieving speed of light with Earth's rotation Excuse my ignorance, but I think of dumb things. If you theoretically built a strong, lightweight cable that traversed over 2.5 billion miles attached to the rotating Earth, the tip would be traveling at or greater than the speed of...
  43. Andres Padilla

    Problem about orbital mechanics

    I tried it, but I am not getting no of the given answers According to the statement, it is saying that 3 KE (in the orbit ) = ΔUg So, beeing R the radius of the Earth and R2 the radius of the orbit: 3 (1/2)(GMm/r2) = -GMm/r2 - (-GMm/R) Canceling out the GMm: (3/2)(1/r2)= (-1/r2) + (1/R)...
  44. W

    B Why do oceans look blue from orbit?

    This is something that one seldom stops to think about, but I suddenly thought of it myself: Why do oceans look deep blue when photographed from orbit? Oceans look blue when looked from the shore because they are reflecting the sky... But the atmosphere doesn't look deep blue when photographed...
  45. T

    4-acceleration in a circular orbit around a black hole

    In a circular orbit, the 4-velocity is given by (I have already normalized it) $$ u^{\mu} = \left(1-\frac{3M}{r}\right)^{-\frac{1}{2}} (1,0,0,\Omega) $$Now, taking the covariant derivative, the only non vanishing term will be $$ a^{1} = \Gamma^{1}_{00}u^{0}u^{0} + \Gamma^{1}_{33}u^{3}u^{3} $$...
  46. diogenesNY

    Stargazing Two White Dwarfs in a seven minute mutual orbit

    From CNN: These two dead stars zip around each other every seven minutes https://www.cnn.com/profiles/ashley-strickland-profile By Ashley Strickland, CNN Updated 2:48 PM ET, Wed July 24, 2019 (CNN)While searching the skies for brightness and blinking, the California Institute of Technology's...
  47. P

    I Free Orbit Insertion: Is it Possible?

    Good evening, This week I had a discussion/conversation with one of my coworkers about the posibility of a mass from outer spate that could start orbiting the earth. The issue is, I believe you cannot, whithout a proper change of energy (velocity) start orbiting a celestial body just by coming...
  48. amjad-sh

    Band structure of a 2deg including spin orbit coupling

    first of all, I tried to obtain the energy eigenvalues of the Hamiltonian, by using the equation ##det(\hat H -\lambda \hat I)=0## ##\gamma V\delta(z)(\hat z \times \mathbf{p}) \cdot \sigma=\gamma V\delta(z)(p_x\hat j-p_y\hat i)\cdot(\sigma_x\hat i + \sigma _y \hat j)=\gamma...
  49. caters

    What is the period of this binary orbit?

    Okay, so let's simplify things and look at the ideal case, where the 2 masses are the same. Well, this gives us a sine wave pattern to the orbital velocity. Consequently, the acceleration would follow a cosine wave since the derivative of velocity is acceleration and the derivative of sine is...
  50. S

    I Can Satellites in Frozen Orbits of the Moon Study Different Ground Areas?

    Quick question for the people to better understand orbital mechanics. Due to large mass concentrations on the moon's surface, there are only four orbital inclinations that a satellite can be at to maintain an indefinite orbit: 27°, 50°, 76°, and 86°. My question is this: If a satellite was...
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