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. J

    Find at what rate the orbit radius will grow

    In order to change the radius, additional energy is required, the total energy of mass m on a circular orbit is given by: $$E_{total} = - \frac {GMm} {2R},$$ The change in energy between orbits ##R## and ##R_{0}## is: $$\Delta E_{total} = \frac {GMm} {2} \cdot \left( \frac 1 R_{0} - \frac 1 R...
  2. M

    Mechanical energy in an orbit

    Obviously the mechanical energy of the total system remains the same. But I'm having a hard time determining of the ME of the planet is constant or if it is changing.
  3. M

    Two stars orbit their common center of mass

    Why do we add the two masses (3M+M=4M) and use that for M in the equation of kepler's 3rd law? Namely why is it T^2=4pi^2R^3/G(3M+M)
  4. cianfa72

    I Integral curves of (timelike) smooth vector field

    Hi, suppose you have a non-zero smooth vector field ##X## defined on a manifold (i.e. it does not vanish at any point on it). Can its integral curves cross at any point ? Thanks. Edit: I was thinking about the sphere where any smooth vector field must have at least one pole (i.e. at least a...
  5. DaveC426913

    NASA ISS orientation over its orbit

    Does the ISS remain oriented with the Earth? I.e. it rotates 360 degrees every 24 hours, or is it fixed with the stars? If the latter, there should be a time when it's visible end-on. I looked it up but did not find the deets. I guess that what the gyros are for.
  6. J

    Creating a Habitable Planet with 3 Moons

    TL;DR Summary: I’m worldbuilding for a novel I’d like to write. I’d like my planet to have 3 moons, and I’m curious how to develop the planet and moons in a scientifically sound way. I apologize in advance if any of this doesn’t make sense or if terminology is way off or misused. This stuff is...
  7. M

    Where (what) is an orbit? Where is Space?

    As background, I grew up in a working class neighborhood where few parents went to school. In 1962, John Glenn came back from space. I was told this. I am not sure what the adults believed back them. "Space" was new. It would be 4 years before star trek, and even then,Space was labeled the...
  8. A

    I Using the orbit-stabilizer theorem to identify groups

    I want to identify: ##S^n## with the quotient of ##O(n + 1,R)## by ##O(n,R)##. ##S^{2n+1}## with the quotient of ##U(n + 1)## by ##U(n)##. The orbit-stabilizer theorem would give us the result, but my problem is to apply it. My problem is how to find the stabilizer. In 1 how to define the...
  9. R

    Where in orbit should a rocket fire to escape with minimum ΔV

    I am really lost on how to deal with this. Since this is an elliptic orbit, the mechanical energy is negative. For the rocket to escape orbit, we have to get the mechanical energy to be equal to or greater than zero. I thought at first that it would escape in the perigee, since that's where the...
  10. D

    I Estimating Mass of Central Object Using S2's Orbit Motion and Kepler's 3rd Law

    During one of my class lectures, we were shown a graph of star S2's orbit motion (shown at the bottom of this post) and was told to try and figure out how to find the mass of the central object using Kepler’s 3rd law in solar units, as shown below: We were also given a hint to use the arcsec...
  11. E

    I Circular Orbit in Schwarzschild: Orbital Period

    Schutz finds that the orbital period for a circular orbit in Schwarzschild is $$ P = 2 \pi \sqrt {\frac { r^3} {M} }$$ He gets this from $$ \frac {dt} {d\phi} = \frac {dt / d\tau} {d\phi/d\tau} $$ Where previously he had ## \frac {d\phi}{d\tau} = \tilde L / r^2## and ## \frac {dt}{d\tau} =...
  12. Muu9

    I Change in orbit when mass is doubled

    A satellite is orbiting a planet in a circular orbit. The planet's mass doubles instantly. What happens to the orbit of the satellite? I think it would move to an elliptical orbit with major axis equal to the old radius and a minor axis equal to either 1/2 or sqrt(2)/2 times the old radius. I'm...
  13. James1238765

    I Modeling the Earth and Sun (2 body orbits) using general relativity?

    Modeling the time evolution of the sun and earth orbiting each other using ##F = \frac{GMm}{r^2}## is straightforward. However, it appears that modeling the time evolution of the same 2 body system using general relativity seems to be a hard/intractable problem? There was in depth discussion by...
  14. A

    A MOND: Two Small Masses at Great Distance - Orbit Speed

    In MOND should two small masses placed at a great distance orbit faster than in Newtonian dynamics? Would it be theoretically possible to do this experiment in the solar system, or would the presence of the sun and earth be a problem?
  15. Z

    I Can a Gyroscope on a Satellite Detect Orbit?

    Einstein said, when describing someone falling off a building, that the Earth accelerating up to meet him/her. Without the Earth getting larger in all directions as the paradox goes, it curvature of space-time which is why you can have the acceleration up without the surface moving up as you...
  16. slogals

    Two black holes moving in a circular orbit around a point

    I tried solving it and i was able to do a) and b) here is what i did on c), but its not correct according to the solution
  17. Sciencemaster

    I Database of binary star data info within 10 PC of Earth

    I'm looking for a database of binary stars within 10 PC of Earth, including information such as eccentricity of orbits, their distance from one another, etc. I'm hoping to find a list with this information, or just a collection of pages with this information. I've tried Simbad but I can't find...
  18. O

    I Is the eccentricity of the lunar orbit constant?

    The wikipedia article on Lunar distance contains a confusing graph. The graph seems to suggest that the eccentricity of the lunar orbit is maximal in january and ~july, and minimal in april and ~october. I think the eccentricity should be constant. Is wikipedia right or wrong, or is there some...
  19. Delta2

    I Earth's orbit not perfect ellipse

    Listen to the following arguments: Earth's orbit isn't perfect ellipse because classically there is the gravitational field of moon and possibly of Mars and Venus which affect it According to general relativity isn't perfect ellipse because there is the curvature of space time which doesn't...
  20. Graham87

    Comp Sci Orbit of the Earth - numerical methods leapfrog

    I am attempting this homework exercise part b). I've modified my code but I get error overflow message. My goal is to modify my code so it returns kinetic and potential energy of Earth's orbit. I made a new f(z,t) and modified the rows 99 and 100 with dz[2]=-G*M*m/r, and dz[3]=0.5*m*y**2 but...
  21. Graham87

    Comp Sci Orbit of Earth: Plotting Trajectory

    I am attempting this homework exercise but my plot does not show the whole trajectory. I don't know if it is something wrong with my equations or if it is a plotting matter. Cheers!This is my code:import matplotlib.pyplot as plt import numpy as np import scipy.integrate as spi G =...
  22. physicsnmathstudent0

    From circular orbit to elliptical orbit

    Problem: a particle of mass m is in a circular orbit around a planet at a distance R from the center. The planet mass is M and it's radius is R_0. What is the tangential impulse that will cause the particle to brush against the back of the planet? Describe the orbit. The attempt at solution...
  23. M

    I Is a horseshoe orbit a hyperbolic orbit?

    Epimetheus and Janus switch places periodically, because they follow a horseshoe orbit around Saturn, which is considered a "pseudo-orbit" around each other. I'm thinking that if you look at the conic sections - taking an elliptical orbit of two moons to greater and greater extremes until they...
  24. rudransh verma

    B To displace the Earth from its orbit

    We know that the centripetal force and the tangential velocity is responsible for the motion of Earth around sun. Newton’s second law says F=ma. If we all get together(whole population) in one place like parallel to the tangent to orbit and jump can we displace Earth from its orbit?
  25. dirb

    Calculating Angle & Speed to Reach Planet's Moon from Station Orbit

    A station is orbiting a planet at a distance R1, a moon is orbiting the planet at distance R2 with the period T. The planet itself has a radius rp and a mass mp. We know that when an object adds its velocity at a point in the orbit, the height of the opposite orbit will increase. Determine the...
  26. L

    A satellite in orbit in a system with one planet and two moons

    1) Considering the forces on one of the moons, I have: ##\frac{GMm}{(10R)^2}+\frac{Gm^2}{(20R)^2}=m\frac{v^2}{10R}\Leftrightarrow v=\sqrt{\frac{G}{10R}(M+\frac{m}{4})}.## 2) Considering the initial situation in which the satellite is at rest on the surface of the planet...
  27. R

    B Earth's orbit and the expansion of the Universe

    Does the Earth's orbit get very slightly larger over long periods of time due to the expansion of the universe? If so does it stay at the slightly larger distance or somehow does the energy to go back to the earlier orbit go somewhere else and if so where? If the orbit does not get slightly...
  28. bland

    I Why does Webb orbit L2, is it because of the Moon?

    I was already puzzled by the concept of orbiting a Lagrange point and then I find out it's about the same size orbit as the Moon. I am thinking that if there was no Moon that the Earth and the Sun are far enough away to be treated as points and so that there would be an exact distance further...
  29. X

    B Could satellite be geo-stationary away from equatorial plane?

    I hope this is okay to ask here. I'm working on a sci-fi short story, and for the purposes of the story I want to have a small ship that maintains its position over a specific location on the Earth's surface. Originally, I thought this would be easy. After all, that's what geostationary...
  30. stephenklein

    Conservation of the Laplace-Runge-Lenz vector in a Central Field

    I actually have worked through the solution just fine by taking the derivative of \vec{L}: \frac{d \vec{L}}{dt} = \dot{\vec{v}} \times \vec{M} - \alpha \left(\frac{\vec{v}}{r} - \frac{\left(\vec{v} \cdot \vec{r}\right)\vec{r}}{r^{3}}\right) I permuted the double cross product: \dot{\vec{v}}...
  31. gromit

    Using Lagrangian to show a particle has a circular orbit

    Hi :) This is a problem from David Tong's Classical Dynamics course, found here: http://www.damtp.cam.ac.uk/user/tong/dynamics.html. In particular it is problem 6ii in the first problem sheet. Firstly we can see the lagrangian is ##L = \frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+\dot{z}^2) -...
  32. C

    What is the eccentricity of an orbit such that Vp = 2Va?

    Summary:: A question on a recent exam was, "At what eccentricity does an orbit experience a velocity at periapsis that is twice the velocity an apoapsis?" I don't know why the provided solution is correct. On a recent exam, one of the questions was "At what eccentricity does an orbit...
  33. L

    Stargazing Does an Analemma visualize the Earth's actual orbit around the sun?

    An Analemma is the shape that arises from taking a picture of the sun everyday at the same time of the day. This shape also have depth to it since Earth's orbit is elliptical, showing what looks like an wobbly orbit. Isn't this the "real" orbit of Earth around the sun?
  34. C

    Maximum safe mass of an asteroid in geostationary orbit

    Summary:: What is the maximum safe mass of an asteroid in geostationary orbit before it causes problems? Hello everyone, If there was an asteroid in geostationary orbit around the Earth, over the Pacific Ocean, what would be the highest mass it could have before it would start having...
  35. D

    B Observing Orbital Mechanics from the 2nd Focus of Earth's Orbit

    If a hypothetical spacecraft could keep station at the 2nd focus of Earth's orbit, what useful observations could be made? Each minute sees a new solar triangle Earth Sun Craft (ESC). Swept area remains constant, as should length SC, and length CE + ES. With the Sun as our point source...
  36. A

    I Atomic Structure: Why Does Energy Decrease with Orbit Number?

    I have read that an electron requires certain minimum energy of threshold frequency to move an orbit However the energy needed decreases with increase in shell number The transition energy is reduced with each orbit For example The energy to shift an electron from 1st to 2nd orbit is much...
  37. Andy Resnick

    I Apparent angular velocity (inclined orbit)?

    Here's the problem setup, my student and I are stuck. A disk is rotating at constant angular velocity ω, and we are watching a point on the rim, parameterized by the angular position θ, move. Because we are observing the motion from an inclination angle Ψ, we do not always observe the...
  38. Buzz Bloom

    I Find GR Equation: Collapsing Orbit & Gravitational Wave

    I recall some time ago seeing a GR equation describing the rate of orbital energy loss from the moving objects in orbit generating gravitational waves. I can no longer find this equation again. I am hoping someone can help me.
  39. greg_rack

    Hohmann Orbit Transfer: Minimize Delta V for Bigger Orbit

    Hi guys, just a short question of Hohmann transfer. I got the derivation for the required ##\Delta v##, composed by the sum of two impulses, for establishing on a larger orbit... but how do we demonstrate it's actually the transfer which requires the smallest ##\Delta v##?
  40. Arman777

    A Obtaining the Orbit equation (Effective Potential) from the Newtonian metric

    We can write the Newtonian metric in the form of $$ds^2 = -(1 - 2M/r)dt^2 + (1+2M/r)[dr^2 + r^2d\Omega^2]$$ In order to obtain the orbit equation I have written the constant of motion, $$e = (1 - 2M/r)(\frac{dt}{d\tau})$$ and $$l = r^2sin^2(\theta)(\frac{d\phi}{d\tau})$$ I can divide the...
  41. E

    I Precession of a spherical top in orbit around a rotating star

    Looking at L&L's solution to problem four of section §106. Lagrangian for a system of particles:\begin{align*} L = &\sum_a \frac{m_a' v_a^2}{2} \left( 1 + 3\sum_{b}' \frac{km_b}{c^2 r_{ab}} \right) + \sum_a \frac{m_a v_a^4}{8c^2} + \sum_a \sum_b' \frac{km_a m_b}{2r_{ab}} \\ &- \sum_a \sum_b'...
  42. S

    MATLAB How can I plot a Hohmann Transfer Orbit in MATLAB using ode45?

    function Asteroid_Mining clc %Initial conditions g0 = 9.81; %gravity (m/s^2) p = 1.225; %atmospheric density at sea level (kg/m3) Re = 6378; %radius of Earth (km) Ra = 7.431e7; %distance of Bennu from Earth in (km) [August 2023] G = 6.674e-11/1e9; % Gravitational constant (km3/kg.s2) mu =...
  43. S

    MATLAB How to plot an orbit around the Earth in MATLAB

    Hi. can you help me to plot orbit around Earth with sphere in MATLAB? I wrote the code that plot 3D orbit but without earth. the code: clear all close all clc R=6371e+3; r0=3e+5; p0=[R+r0;0;0;0;10000;0]; [t,p]=ode45(@sattelite,[0,12000],p0); xout=p(:,1); yout=p(:,2); zout=p(:,3); vx=p(:,4)...
  44. S

    MATLAB Question about how solve 2 body problem in orbit using MATLAB ode45

    hi guys, I'm trying to write a program in MATLAB to solve and plot equation of motion of 2 body problem but it errors as i don't know what it says! do you know how to help me? please! The main equation is r(double dot)=-(mu)*r(hat)/r^3 The code that i wrote is: clear all close all clc...
  45. D

    Finding the period of an orbit ##r=a(1+\cos\theta)##

    I've already found the potential and force that produce the given orbit. my results were: ##V=-\frac{al^2}{mr^3}## ##\vec{F}=-\frac{-3al^2}{mr^4}\hat{r}## Now, I've been trying to find the period using the equation ##t=\sqrt{\frac{m}{2}}\int_{r_0}^{r}\frac{dr'}{\sqrt{E-V_{eff}}}## Using...
  46. matteo446

    Time that a comet spends inside Earth's orbit

    I tried in the first place to use the effective potential of a parabolic orbit which is 0 to get the angular momentum L. Evaluating the function U(r) at r = rP i get U(rP) = L^2/(2m(rP)^2) - GmM/rP = 0. Here I get L = m√(2GMrP). Now the relationship between angular momentum L and areal...
  47. H

    B Explaining Perihelion Shift of Mercury in GR Theory

    Recently, when reading an entry about Mercury's perihelion shift, someone mentioned a "hand-wavy" explanation as to why GR predicts the orbit so precisely. I was wondering if there was some elementary way to expound on what he was saying. Fundamentally, the comment said something to the effect...
  48. duchuy

    Altitude of Geostationary Orbit

    Hi, They gave me this formula T = 2piR / v, with T the revolution period of the satellite, R the distance between the center of masses and v the velocity. They gave me the value of G and the eath's mass and asked to determine the value of R. I don't even see fromwhere I should start... Thank...