Orbits Definition and 498 Threads

How are orbits and cosets related? Are all orbits cosets? Are all cosets orbits? Also, what exactly are G-sets and G-equivariant sets?

doesn't that mean that one hemisphere would have a hotter summer than the other hemisphere and the opposite would have a colder winter? if so, which is which. I am willing to guess the northern hemisphere has the colder winter and southern has the hotter summer.

Homework Statement A satellite is in a circular orbit 655km above Earth's surface. Determine the magnitude of the gravitational acceleration at this height. Homework Equations Eg=mgh Eg=-GMm/r The Attempt at a Solution Would I just set the aforementioned eqations equal to each...

Hello, I have a couple of questions regarding the calculation of circular orbits in the Schwarzschild exterior spacetime and then the extension of these arguments to other (interior) metrics. First of all, in a few different books/sets of notes there seems to be a bit of 'drift' in the...

Hi all, As many of you have seen, I am thinking about spaceship trajectories. This next question falls under the same subject, but it is an entirely different question from the previous questions I have asked. Spaceships of the near future will fly in the plane of the solar system. Suppose if...

What is the relationship between the following in an elliptical orbit: -foci -geometric center -barycenter -the more massive body/the less massive body Also, what path does the larger mass take?

Homework Statement We have a homogenous toroidal planet. Its cross-section is half of a square, so that the hypotenuse is parallel to the z-axis. Find the orbits of constant (especially lowest) energy around that planet. Homework Equations 1) Homogenous planet: \rho=const. 2) Potential...

Homework Statement Two particles moving under the influence of their mutual gravitatonial force describe circular orbits about one another with period τ.if they are suddenly stopped in their orbits and allowed to gravitate toward each other. show that they will collide in a time τ/4√2...

I was reading an article and it said if we have a charged gas of particles and it is in a uniform B field, then at any point there will be Larmor orbits. I mean this seems correct. So the charged particles would start a circular orbit. F=q(vxB) I just want to make sure this is correct.

Hi there! I'm developing a game that involves simulating a star system. I'm using the Unity engine and its physics engine. I've got gravity working perfect. I've also developed an algorithm that works out how much force you would need to apply to a body to start it orbiting around another...

Hi there, First post, so be gentle. I'm currently doing a project on Kerr black holes, part of which is based on a project in Edwin F. Taylor's book "Exploring Black Holes" (the chapter is found here) as well as some of Hartle's book (chapter 15). Part of my project, and as a way of better...

Find the orbits for the m mass under the F(r)=-A/r^2+B/r^3 . Where A>0 and B is positive or negative. Friends, please help me for homework

So I saw a video on youtube: http://youtu.be/uhS8K4gFu4s And so I thought I'd try to understand the whole stable orbit thing. So first you have a simple energy equation of E = K + U. K = (1/2)mv^2 (kinetic energy) U = -GMm/r^2 (gravitational energy) r = radius of orbit v = velocity of...

Homework Statement The space shuttle makes 1 revolution around the Earth in 1.5 hours when it is in an orbit 200 km above the Earth’s surface. The radius of the Earth Re is 6.5 × 10^6m. If the shuttle moves to a new orbit such that it makes 1 revolution per day (24 hours), what is the radius...

Hi everyone, I was just wondering if you have an element of a G-set which has an orbit of only itself, Say Orbit(e) = {e}, in the set of permutations where G is the same order group of permutations and the operation is conjugation. This is an Orbit of size 1 correct? I was just...

Homework Statement Studies of the relationship of the Sun to our galaxy—the Milky Way—have revealed that the Sun is located near the outer edge of the galactic disc, about 30 000 ly (1 ly = 9.46 1015 m) from the center. The Sun has an orbital speed of approximately 250 km/s around the...

Came across some interesting animations here...test particle orbiting a black hole: Orbits in strongly curved spacetime http://www.fourmilab.ch/gravitation/orbits/ The precession advance of Mercury [which helped confirm Einstein's theory] is described under ... The Gravitational...

Hey all, this is my first post! (Although I've found a lot of useful answers here during the past). I have been trying to prove this fact, which is widely stated in literature and relatively well-known, about density of orbits of irrational n-tuples in the n-torus. My question is this: If...

Homework Statement We have proved that any Kepler orbit can be written in the form of r(\phi) = \frac{c}{1+\epsilon*cos(\phi)} where c>0 \epsilon\geq 0. for the case that 0 \leq \epsilon < 1, rewrite this equation in rectangular coordinates (x,y) and prove that the equation can be cast in...

hello. i recently came across this question in which a satellite is put into orbit at a point around a planet with velocity 1.2V, where V is the speed for a circular orbit at that point and they ask for ratio of max to min distance. [Ans. 2.57] what i want to know is how do we relate...

I was reading my textbook and was confused on the terminology, is an orbit each of those boxes that you fill up with the up and down arrow, and the subshell is like s, p, d, f, g, h? I was also confused about what the shielding effect is. If anyone can enlighten me that would be great, thanks

Hi, I know what geo stationary orbit is, my question is what does it mean when they say satellite is at "83.0°E", don't you need more coordinates to find it??

I have the folloring problem: Given the following flow on the torus (θ_1)' = ω_1 and (θ_2)' = ω_2, where ω_1 /ω_2 is irrational then I am asked to show that each trajectory is DENSE. So I need to prove that Given any point p on the torus, any initial condition q, and any ε > 0, then there...

I was wondering what the orbits of a Killing vector field are. Do you have any good sources or reading material for this?

http://t2.gstatic.com/images?q=tbn:ANd9GcT0sqrTGlvaB2RKBPMn759TUEtb-wfbrMz7OYYinYczpDndsVlt5Q MRI scanning create a hugh amount of magnetic field, does anyone have any suggestions how this strong magnetic field will affect the orbits of electrons within atom? Thanks in advance for any...

Hi all, first post, please bear with me! I am trying to understand Lagrange's Theorem by working through some exercises relating to the Orbit-Stabilizer Theorem (which I also do not fully understand.) I think essentially I'm needing to learn how to show cosets are equivalent to other things or...

Homework Statement An efficient way to reach the Moon is to first put the spacecraft in a low circular Earth orbit (radius r0, speed v0). The speed is then boosted to vp giving an elliptical orbit with apogee at the Moon’s orbit, ra, and perigee at r0. Show that: (vp/v0)^2=2ra/(r0+ra)...

Homework Statement A particle of mass m and charge e moves in a central field with potential V(r) = -\alpha r^{-3/2} and in a constant magnetic field \vec{B} = B_0 \hat{e}_z 1) Write the Lagrangian and the Hamiltonian 2) Write the first integral H_{orb} for the equation of the orbit u(\phi )...

Question is as follows: How much energy do i need when i move an object with a mass M from a circular orbit with a radius of R_1 to an ellipse orbit with aphelion radius of R_2. I'm assuming energy principle is the way to go here but it leads to a question i'd like someone to help me out...

Homework Statement For the finite group G and G-set X below, find the stabiliser \text{stab}_G(x) of the given element x \in X and describe the G-orbit of x. http://img36.imageshack.us/img36/1962/grouplg.jpg Homework Equations The stabiliser of x is defined: \text{stab}_G (x) = \{...

Homework Statement A particle moves in the central force field \overrightarrow{F}=-kr^{n}\hat{r} , where k is a constant, and r is the distance from the origin. For what values of n closed stable orbits are possible? Homework Equations The Attempt at a Solution I thought for...

There was one question i got in an interview, and I couldn't answer it at all: "There are 1 million stars, and 10 planets orbiting each star. Consider that the planets do not disturb each other, and the planet systems, including the stars, dont disturb each other. Then, how many of these...

THIS ISN'T THE SAME AS MY PREVIOUS QUESTION ALTHOUGH IT HAS THE SAME TITLE Homework Statement The Moon is satellite of Earth with a diameter equal to a quarter of Earth's diameter and a mass equal 1/81 of Earth's mass. The period of the moon's rotation about the Earth is 27d 7h 43.1 min...

Homework Statement An imaginary planet has a diameter twice that of our earth. The planet has one moon with an orbital radius of 5.0x10^7 km and orbital period of 10 Earth days. Determine the strength of the gravitational field at the surface of the planet. Radius of Earth = 6.38 x 10^6m...

As my state (Indiana) has removed Astronomy from the curriculum, my school no longer offers it. I have taken AP Physics B and that is my best knowledge provided by the modern school system, so I apologize ahead of time for any low-level or simple questions. I am wanting to know the equations...

This suddenly entered my mind while studying magnetic fields. I know of course that it is the gravitational force that holds the planets in orbit, but do their magnetic fields also have an effect, even by an infinitesimal amount? Do the magnetic fields of the planets have a small influence on...

Hello, I have the following problem where I have two groups of transformations R_\alpha (rotation) and S_\lambda (scaling) acting on the plane, so that the orbits of any arbitrary point x=(x0,y0) under the actions of S_\lambda and R_\alpha are known (in the former case they are straight lines...

I just started learning about group orbits, and wanted to look it up online, because I needed some more clarification. However, stumbling upon this Wolfram's Mathworld entry, I ended up even more confused, especially after reading that example for the permutation group G1. Could someone perhaps...

A ball of mass M attached to a string of length L moves in a circle in vertical plane. At the top of the circular path, the tension in the string is twice the weight of the ball. At the bottom, the ball just clears the ground. Air resistance is negligible. Express all answers in terms of M, L...

hi,can anyone solve this two problems?? these are from the "textbook on spherical astronomy" written by W.smart chapter five,problem number 18 and 19,Euler's theorem and Lambert's theorem thank you ;-)

Homework Statement A group G acts transitively on a non empty G-set S if, for all s1, s2 in S, there exists an element G in G such that g*s1 = s2. Characterize transitive G-set actions in terms of orbits. Prove your answer Homework Equations Transitive G-set Actions: for all s1, s2 in S...

what would happen if moon orbits around Earth were to be on the same plane as the earthe Earth's orbit around the sun?

Homework Statement A missile is launched upward with a speed that is half the escape speed. What height (in radii of Earth) will it reach? a. R/4 b. R/3 c. R/2 d. R e. 2R Homework Equations escape speed=√(2GM/r) The Attempt at a Solution r is inversely proportional to...

Homework Statement Find the linear velocity of a particle in a circular orbit of radius R in the Schwarzschild geometry as would be measured as by a stationary observer stationed at one point on the orbit. (It's problem 10 in chapter 9 of Hartle, if that helps) Homework Equations The...

Hi, I'm struggling with the following: I have a colored graph, and I used Bliss to find the generators group for the automorphisms. Finding the orbits given the generators is easy. What I'm trying to find now is dependence between orbits - for each orbit I want to know if it still exist if...

l don't quite understand the difference . as far as l see it , orbital was defined as a group of orbits so that one level of energy can contain many electrons without canceling each other . in other words one level can have exact similar electrons but in different orbits within the same...

Is the speed of different bodies in the same planetary orbit equal to each other? I think it should be the same because the acceleration is always the same in such a case. But it was not so when i compared the speed of moon per m/s with that of the international space station.

Homework Statement Assuming planar orbits, calculate the Hohmann ∆V required to transfer from a low-Earth circular orbit with radius of 1.03 Earth radii to the orbit of the Moon (assume 60 Earth radii). Compare this to the 3-maneuver strategy of (1) escaping to infinity on a parabolic orbit...

Hello everyone! After having being asked to help prepare a simulation(using computer programming), for the general(numerical) solution to Kepler's orbits(strictly speaking, for any central force, and for simplification, no other is acting here), I ran into a bit of a rut trying to resolve some...

Homework Statement Attached. A and D are circular. Find the orbit with largest angular momentum, largest total energy, and largest maximum speed. Homework Equations E is proportional to -1/a (elliptical; a is semimajor axis) U is proportional to -1/r K is proportional to 1/r...