Orbit Definition and 1000 Threads

Homework Statement Hey, I need to find whether an asteroid is in a "bound orbit" around the Sun. Furthermore, describe the shape of the orbit (elliptical or circular). The only information I have been given is its velocity and position at a random point. v_o=61m/s r_o=13.75AU=2.06E12m I also...

MTW section 25, from eq. 25.16 onwards, derives an orbital equation (with G=c=1, u = M/r, E and L Schwarzschild constants for energy and angular momentum respectively): \left(\frac{du}{d\phi}\right)^2 = \frac{M^2}{L^2}(E^2-1) + \frac{2M^2}{L^2}u - u^2 + 2u^3 This equation is readily...

Homework Statement A 2.70-mm-diameter glass sphere has a charge of + 1.10 nC. What speed does an electron need to orbit the sphere 1.50mm above the surface? Homework Equations a = v^2/r -> force = m*v^2/r electrostatic force = K*Q1*Q2/distance^2 therefore...

Hi, So recently I read about the massive 3 gorges dam changing the mass moment of inertia of the Earth to such an extent that the days will now be 60ns longer. Then I thought, how will this effect the orbit of the Earth about the Sun? Any thoughts?

Warning read on your own risk: This is my first post here. I'm new to english, sorry for my bad grammar. Homework Statement A satellite is launched one time Earth radius straight above the northpole (two times radius from center), with an angle of 60° to vertical. Find the launch velocity...

Homework Statement Ringworld is an artificial world constructed in the shape of a giant ring that rotates around a star similar to our sun. The radius of the ring is 1.53x10^11m (from the sun to the ring). The mass of ringworld is 2.1x10^27kg and its simulated gravitational acceleration is...

Homework Statement Given the parametric equations for a satellite in orbit around a spherical mass find angular momentum L in terms of ε, a, k, m, where k=GMm. Also, find the energy E in the same terms. Lastly, I can only use the equations provided and "fundamental definitions." Homework...

If I wanted to set up some initial conditions for a 3 body figure eight orbit, what would I have to set the position and velocity vectors? Say I have three vector inputs: initial position <x,y> initial velocity <x,y> mass of bodies <m1,m2,m3> The solutions for position use f=mi*x''...

[b]1. Homework Statement A 7655 kg satellite has an elliptical orbit. The point on the orbit that is farthest from the Earth is called the apogee and is at the far right side of the drawing. The point on the orbit that is closest to the Earth is called the perigee and is at the far left side...

Ok I know our moon is getting farther away due to gravity (tidal force indirect), basically giving it kinetic energy and exchanging that for orbital energy. If the moon was in retrograde orbit, i.e. Triton around Neptune, it would work the opposite way and pull the moon closer to the...

Homework Statement A space vehicle is in circular orbit about the earth. The mass of the vehicle is 3300 kg. The radius of the orbit is 2RE. It is desired to transfer the vehicle to a circular orbit of radius 4RE. An efficient way to accomplish the transfer is to use a semielliptical orbit...

Homework Statement There's no specific question, but mostly a theory I wanted clarified. According to my textbook, the measurement of the total mechanical energy E of a mass orbiting a much larger mass in an ellipse is: E = radial (change in radius) kinetic energy + rotational kinetic energy...

Homework Statement A projectile of mass m is fired from the surface of the Earth at an angle α from the vertical, where α = 0.46 radians. The initial speed v0 is equal to √{GM/Rearth}. Calculate the maximum height that the projectile will reach. Neglect air resistance and the Earth's rotation...

Homework Statement A satellite is launched into a circular sun-synchronous orbit at a height of 900km above Earth's surface. What is the implication on the orbit's inclination (in deg) and on the change of the position of the right ascension of the ascending node per day.Homework Equations The...

Homework Statement What is the total mechanical energy of a 290 kg satellite in a geosynchronous orbit around the Earth? Homework Equations W= K + UG where K= 1/2 (mv2) and UG= -(GmM)/r Fc= mac where ac= v2/r The Attempt at a Solution I think the geosynchronous part is what is...

Hello there :), Homework Statement We have a molniya orbit with an eccentricity of e = 0.72 and a semi-major axis a = 26554 [km]. The task: Calculate the angular displacement of the ascending node Ω after 100 sidereal days Homework Equations Moreover I know from Wikipedia that a...

Homework Statement What is the total mechanical energy of a 380kg satellite in a circular orbit 3.0 Earth radii above the surface? Homework Equations W= E2- E1 E= 1/2 mv2- \frac{GmM}{r} The Attempt at a Solution I'm not sure if the equations above are suitable to solve this or...

Hi Astro gurus, Is there any limitation on the inclination of the achievable orbit because of the latitude of the launch location? For example, latitude of Baikonur is roughly 46° E. Does that limit somehow the inclinations of the orbits that can be achieved from Baikonur? I think there...

I realize the answer depends how where in the atmosphere speed is increased more, and whether a higher orbit or lower orbit is desired, and the shape size and weight of the craft. But I'm just curious about typical ratios. About what fraction of the fuel goes to lifting the weight of the...

Or get so close that human life will be destroyed

I may be being stupid here... But I'm trying to derive such an equation to no avail. Maybe such a formula requires more than one variable - but I would like to easily display this graphically. To start out the derivation I stated that the Surface Velocity = (2pi/T)-(v/r) where v/r=angular...

Can light be bend in such a way that it is essentially trapped in an orbit?

Homework Statement I've been stuck on this problem forever, any help is greatly appreciated. A satellite is in a LEO at h=300km and it is sent to a geosynchronous orbit at 4.224x10^4 km. Calculate velocity at pericenter i.e v_pe Homework Equations v_pe = (2πa_to)/p_to[2a_to/a_leo -1...

Homework Statement Hi! I have a problem with an assignment and need som help. The question is: You’ve just completed an analysis of where the Space Shuttle must be when it performs a critical maneuver. You know the shuttle is in a circular prograde orbit and has a position vector of: ro=...

Hi everybody, I've registered to PF because after searching the web and this forum too, I couldn't find a clear answer to my dilemma. I've read this article but something seems wrong: http://www.scientificamerican.com/article.cfm?id=half-mass-moon What if the mass of the Moon would be...

I am trying to get my head around these equations. I am not sure they are correct. My logic is an orbit exists at a starting point (x0,y0,z0) with a starting velocity at time zero (vx0,vy0,vz0) changing with time (dx/dt, dy/dt, dz/dt). The gravity is (d^2x/dt^2, d^2y/dt^2, d^2z/dt^2). How do...

I'm given the position vector as a function of time for a particle (b, c and ω are constants): \vec{r(t)} = \hat{x} b \cos(ωt) + \hat{y} c \sin(ωt) To obtain it's velocity i differentiate \vec{r(t)} with respect to time and i obtain: \vec{v(t)} = -\hat{x} ωb \sin(ωt) + \hat{y} ωc...

Homework Statement Two asteroids (approximately the same size and mass) are orbiting each other at a given radius a. The center of mass is orbiting the sun at a distance (semimajor axis) b with an orbital period of P. I would like to estimate the mass/size of each of the asteroids. By...

This is a fun TikZ picture to play with. \documentclass[convert = false]{standalone} \usepackage[utf8]{inputenc} % Euler for math | Palatino for rm | Helvetica for ss | Courier for tt \renewcommand{\rmdefault}{ppl} % rm...

Studying the movement of a particle on bound orbits around a black hole I found a fact that seemed a little strange for me -- that on these orbits particle's total energy on infinity must be less than unit (E<1). As far as I understrand, it is not so horrible, since here we deal with an...

lets say a rogue star or black hole pass by our solar system and disrupt the orbits of the planets and pull the Earth away from the sun, can it regain or get back to its original orbit if the black hole is gone? some people say the chances of a black hole passing by our solar system is slim but...

Homework Statement The problem and its solution are attached as TheProblemAndSolution.jpg. Homework Equations *The (“instantaneous”) dust tail is opposite the direction of motion. *The plasma tail is oppositely directed to the star in question (at all times). The Attempt at a Solution...

Let an electron is orbiting in a orbit with the principal quantum number n =1. According to wave mechanics its angular momentum is √ l(l+1) h/2∏ and angle : cosθ = ml/ √ l(l+1) How one can explain the electron angular momentum and its possible orientations for l =0? Off course for n =2, l...

Homework Statement Is there any position in an elliptical orbit where the tangential component of the acceleration is greater than the component perpendicular to the tangential component? If so, what conditions on the orbit must there be for such a position to exist? Homework Equations...

I would like to have a nice picture/simulation of the Earth - Apophis encounter on April 13th 2029. I found this applet http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=aPOPHIS;orb=1;cov=0;log=0;cad=0#orb but it seems to produce too great error for the time of encounter - the minimal distance much...

If an object is orbiting on a circular time-like geodesic path around a mass then the Wikipedia claims that the first component of its four-velocity is given by \frac{dt}{d\tau} = \frac{1}{\sqrt{1-\frac{3}{2}\cdot \frac{r_0}{r}}} where r_0 is the Schwarzschild radius. Is this right and how...

What is the radius of a photon's circular orbit around a mass M? My guess would be the Scharzschild radius. Is that true?

I get that they have to be at the same position relative to the earth but why is it that they have to be specifically above the equator? thats the sense I get from the textbooks, they all seem to emphasize the satellite being above the Equator can't you have a geosynchronous satellite...

Homework Statement Show that in the Bohr model, the frequency of revolution of an electron in its nth In classical physics, the frequency of revolution of the electron is equal to the frequency of radiation it emits. Show that when n is very large, the frequency of revolution is equal...

The regular spin orbit Hamiltonian is H_{SO} = \frac{q\hbar}{4 m^2 c^2}\sigma\cdot(\textbf{E}\times \textbf{p}) If I consider a 2D system where E = E(x,y) and p is treated as an operator, i.e. \hat{p} = \hat{i}p_x + \hat{j}p_y then, clearly E and p do not commute, so this doesn't look like...

Homework Statement A satellite in low-Earth orbit is not truly traveling through a vacuum. Rather, it moves through very thin air. Does the resulting air friction cause the satellite to slow down? Homework Equations The Attempt at a Solution Evidently, the answer is, "Air...

If the reason why the planets orbit around the sun is the deviations in the fabric of spacetime,what keeps the planets from crashing into each other? Like if I put a boulder on a trampoline and then I put a baseball next, the baseball would go toward the boulder. I think it could be dark matter...

Why are the electrons so far away from the nucleus of an atom ?

The Moon is close enough to Earth that it is tidally locked, however it is also slowly but steadily moving into a wider orbit around Earth. Will there be a point in tile when the Moon is no longer locked and able to freely rotate and if so how far apart would that need to be? Don

Homework Statement Initially, a planet with mass m moves on a circular orbit (r = R) around a star with mass M. Now M is instantaneously decreased to M'. Find the eccentricity e of the elliptical orbit the planet now follows. Homework Equations specific angular momentum l = L/m...

If I am in orbit around Earth that means that I am in constant free-fall around earth. Is this an inertial reference frame?

Homework Statement Two particles pigs of mass ##m## and ##M## undergo uniform circular motion about each other at a separation of ##R## under the influence of an attractive force ##F##. The angular velocity is ##\omega## radians per second. Show that R = \frac{F}{\omega^2}\left( \frac{1}{m} +...

What is the radius of the de broglie circular orbit with n=1?

I would like to know in what ways the earth’s orbit might be modified by the close approach of a massive body from beyond the solar system, such as an orphan earth, Jupiter, super Jupiter planet or brown dwarf. The “variables” of interest being the amount of warning we would receive by virtue...

Homework Statement Choose an even number in the interval [100,199] and compute its orbit under the proper divisor function. Homework Equations Proper Divisor Function = σ(n) = Sum of all divisors of n, excluding n The Attempt at a Solution I am unsure what it means by "compute the...