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.
TL;DR Summary: What started as a neat idea for an RPG setting has become more intricate than expected. In a massive whirlpool there are several "orbiting" islands, and I would like an easier way to track sailing time between them.
I was so naive. A giant whirlpool with a bunch of islands that...
Orbits around the Lagrange point are not stable, and you need to tweak your trajectory every now and then to remain in that orbit. Simulations of a non-accelerated body give spectacularly weird results:
When the propellant runs out, is this what the JWST will do?
Hi,
If a 1000km space rock called Pluto can meaningfully perturb the orbit of Neptune - which is some 7,800 times more massive - at a distance of no less that 2.4AU, then surely the fact that gravity moves at the speed of light would produce significant effects too(?)
Is there any effect, for...
TL;DR Summary: Solar sytem forces on Unity
Hello !
For my last year in my school, I've got a project to do, and I wanted to recreate the Solar system with forces on Unity. My forces are Velocity and Acceleration (I'm using the Frenet's formulas).
I'm sorry I'm not a physicist and that's why...
I am struggling with Hamiltonian formulation of classical mechanics. I think I have grasped the idea of canonical transformations, including the idea of angle-action variables and invariant tori in phase space. Still, few points seem to elude my understanding...
Let's talk about a particle...
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...
As a retired physics professor with a long experience in complex simulation software for high energy physics experiments (e.g. the LHC) I revisited last July the n-body planetary simulations which I taught in an undergraduate physics course during the Spring 2017.
It was then that the...
I was running a simulation in Universe Sandbox where I placed a 10 million solar mass black hole about 10 light years from the Solar System, initially stationary relative to the Sun. I noticed once the Sun had reached about 70km/s relative to the black hole, all the orbits became wavelike rather...
Does anyone see a way I can find geodesics in the metric ##ds^2=-dt^2+dp^2+(5p^2+4t^2)d\phi^2## (ones with nonzero angular momentum)? I'm hoping it can be done analytically, but that may be wishful thinking. FYI, this is the metric listed at the bottom of the Wikipedia article about Ellis Wormholes.
I sometimes get surprised by things that do not seem to exist in this world. For example, as far as I know, nobody has ever, during the entire history of photography, made a photographic time-lapse of lunar libration. There are plenty of computer renderings, but no photographic time-lapse...
When we use the third Kepler law to calculate the period, distance and velocity of the Earth, we consider that the Sun is fixed. We know this is not true, because the Sun is also attracted by the Earth. I was wondering, how could we use Kepler laws to calculate the period, distance and velocity...
Hello everyone! So I have a fairly basic question about orbits, if I launch an object vertically from the surface of the earth, for most velocities it will come back to earth, if I launch at an angle it will have a velocity tangential to the vertical velocity, and this vertical velocity will...
Since hydrogen atom has only one orbit, how does the hydrogen line spectrum work? I saw somewhere, that infinite orbits(n) are possible, but wouldn't having too much energy end up causing the electron to break free from the nucleus and thus ending up as a free electron?
So when exactly does...
How does the Earth's reference frame "know" to experience the gravitational pull of where the sun/Earth barycenter will be in 8 minutes, rather than orbit around the spot where the barycenter was 8 minutes ago? The latter case seems required by the finite speed of gravitation, but coplanar...
For background, consider this paper, which describes circular orbits for the two-body problem in the presence of a cosmological constant:
https://arxiv.org/abs/1906.05861
What they describe is a system with three regimes of behavior: stable circular orbits below a certain radius, unstable...
Bertrand's Theorem says : the only forces whose bounded orbits imply closed orbits are the Hooke's law and the attractive inverse square force.
I'm looking at the hookes law ##f=-k r## and try to see explicitly that the orbit is indeed closed.
I use the orbit equation ##\frac{d^{2} u}{d...
I am looking for a Python Code/Package to calculate the orbits of the time-like and null-like particles in Schwarzschild metric (in spherical coordinates)
Does anyone know such package ?
Note: I am mostly looking for packages to calculate the RIGHT side of the given images (i.e the orbits...
I am thinking about an extraterrestrial object like Oumuamua but say volume 750 E+9 (=750,000,000,000 I think but not sure of density although not solid rock) that takes orbit near Space to Earth.
1. Would the magnetic field of this object disturb the balance of local orbits or operation of...
Hi
I am confused about certain aspects of deriving the planetary orbit equation by considering it as 2-body problem. I will ask my first question now before i get to my other questions. In the David Tong notes on "Dynamics & Relativity" he states that a particle in central force potential...
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...
I want to know what are generally the characteristics that can predict or things that could cause the orbit of an object to deviate from zero degrees relative to the equatorial plane of the object that it is orbiting?
After an impact, can a projection from the surface of a spinning planet obtain an orbit? I tried a three body simulation, but a two body works just fine.
"Newton cannon" is one Earth radius above the surface with different vt's. These are the types of orbits I am looking for.
"projected up"...
In this chapter, the stability of an object orbiting in a circular orbit of radius r_c in an arbitrary force field f is considered.
The author arrives at the equation of a harmonic oscillator, for small deviations x from the circular orbit:
\ddot{x} + \left[-3\frac{f(r_c)}{r_c} -...
I was recently working on the two body problem and what I can say about solutions without solving the differential equation. There I came across a problem:
Lets consider the Kepler problem (the two body problem with potential ~1/r^2). If I use lagrangian mechanics, I get two differential...
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?
From what I gather, there are S-type, P-type & T-type systems, but I'm having a hard time wrapping my mind around the orbital possibilities. Would it be theoretically possible to have a planet in a binary star system where there is a daily "pre-sunrise" and a "pre (or post) sunset" due to the...
Summary:: At what distance from the Sun will the speed of the planet be equal to the average orbital speed?
I'm not sure where to place this question, please move it in the right thread.
[Mentor Note -- thread moved from the technical forums, so no Homework Template is shown]
At what...
Just quick question: Could you put space stations (or even other small planets) at any aribitrary orbit or any radius in between Jupiter and Mars? Or, if something attempted to do so, would the orbit be unstable, and the object drift to either Mars or Jupiter?
I was reading about Lagrange...
I was thinking to myself, if it were ask to me why is the orbit of planets elliptic, how to justify?:
The bould phrases i just know to justify with collected dates.
IS this a reasonable justification?
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...
For a particle in a central potential, an orbital is the state determined by Energy, Angular Momentum, and Third Component of the Angular momentum, which constitute a maximal set of commuting operators, right?
Even in classical mechanics, this is not an orbit... it would be a set of orbits...
Tell me if I'm right:
A) Angular momentum is conserved because there are no external torques. Linear momentum isn't conserved because gravity is acting on the spacecraft . Mechanical energy isn't conserved because it has to change between different orbits.
B) Parabolic orbit...
Summary: (1) Would it be possible (relatively speaking) for a spaceship to "sit" stationary in space, i.e., not in orbit around a planet; and (2) if possible, how long would it take a planet, viewable from the spaceship's window (humor me) to pass through your field of vision?
Part One
I'm...
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...
Because of Zwicky'f findings back in 1933 on the Coma Cluster rotational curves there is something I was wondering about with regard to this cluster. Are the galaxies orbiting in generally the same direction? (like a spiral galaxy) or in completely random directions like an Elliptical, or...
What does it mean for an orbit to have a negative inclination? is it equivalent to an orbit with the same positive inclination but a shift in the node \Omega by \pi ?
Hi all,
I've been following the launch of the first commercial lunar lander, SpaceIL.
Because of its small size, there is not enough fuel for a more direct approach to the moon, so the path they are taking is multiple orbits around the Earth with impulses at the perigee, at each orbit.
As I...
Homework Statement
Consider an elliptical orbit of a satellite (of mass m)
around the Earth (of mass M >> m). The perigee is at ##r_A## and the apogee at ##r_B##, as measured
from the centre of the Earth, itself located at one of the focal points of the ellipse (see Fig. 1).
We work in an...
Is it difficult to show that planets follow elliptic orbits around the sun, using Newton's theory?
I have seen the equations showing it, but from General Relativity, considering the Newtonian limit.
How to arrive at them using only Newton?
Homework Statement
I have phase space coordinates (x0,y0,z0,vx,vy,vz)=(1,0,0,0,1,0). I need to analytically show that these phase space coordinates correspond to a circular orbit.
Homework Equations
r=sqrt(x^2+y^2+z^2) maybe?
The Attempt at a Solution
My core problem here is maybe that I...
A space vehicle enters the sensible atmosphere of the Earth (300,000 ft) with a velocity of 25,000 ft/sec at a flight-path angle of -60 degrees. What is its velocity and flight-path angle at an altitude of 100 nautical miles during descent?
(Assuming no drag or perturbations, two body orbital...
I have problem with an A2 physics question:
A planet is orbiting a star at an average distance of 10^9 km. The period of its orbit is 500 Earth days. The gravitational constant is 6.67x10^-11 Nm^2kg^2.
a) Calculation the mass of the star.
b)Explain why you cannot determine the mass of the...
I understand that Hypatia proposed elliptic orbits.
I also understand she studied conic sections.
And, of course, one of the intersections of an inclined plane through a cone is elliptical.
So now my question: if she did propose elliptic orbits (not interested in who may also have done it)...
Are there any good theories which can explain how the orbits of planets are not aligned with the rotation of the Sun?
I gather there is about 6 degrees of differance, which is not small.
I've been looking at the Kepler's problem, and it looks like your orbit (elliptic, parabolic or hyperbolic) are given in terms of energy and angular momentum. I was wondering: if I have a central attractive potential (such as the Sun) and a projectile starting from an infinite distance at a...
Would the velocity of a body which is orbiting another body change due to its radius to the center of gravity? If so, why? A body which moves passed a planet and starts orbiting it should have the same velocity it had before ,regarding the fact that it is orbiting a planet. Also, gravity isn’t...
Why is that?
It's easy to understand how planets and moons can become tidally locked.
but why do weird things like 3:5 Jupiter/Saturn stuff happen?
Or doesn't it?