# 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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### 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'...
44. ### 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 =...
45. ### 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)...
46. ### 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...
47. ### 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...
48. ### 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...
49. ### 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...
50. ### 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...