Orbital Definition and 790 Threads

For setting the fermionic state ## |n_1 n_2\rangle## where ##n_i## is the number of particles in the orbital ##i## we can use the following both representations for the state ##|1 1\rangle##: $$ \hat {\mathbf c_1} ^{\dagger} \hat {\mathbf c_2} ^{\dagger} |vac\rangle $$ or $$ \hat {\mathbf c_2}...

"However, accurate quantum-mechanical calculations (starting in the 1970s)... singly occupied orbitals are less effectively screened or shielded from the nucleus, so that such orbitals contract and electron–nucleus attraction energy becomes greater in magnitude (or decreases algebraically)."...

What is the orbital period in General Relativity using the Schwarzschild metric? In classical mechanics, it is something like T=2pi(GnM/a3). Where a is the semi-major axis, this is for a small body orbiting a larger one. I think I have an idea but I am not 100% sure. I am interested in an...

I've already solved the orbital speed by equating the kinetic and potential energy in the circle orbit case. $$\frac{1}{2}mv^2 = \frac{1}{2}ka^2.$$And so $$v^2 = \frac{k}{m}a^2$$Now when the impulse is added, the particle will obviously change course. If we set our reference point in time just...

I'm sure everyone here is aware of the hazards of orbital debris, and the difficulty of removing it. Lots of concepts have been proposed to help address it, but not many tests have been executed so far, mostly on larger debris like whole satellites. But what about the smaller stuff? Stuff that...

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} =...

Hi, I've just calculated the orbital precession for the earth using the sigma formula of general relativity. $$ \sigma=\frac{24 \pi^{3} R^{2}}{T^{2} c^{2}\left(1-e^{2}\right)}=\frac{24\pi^3×1.5×10^{11}}{3×10^7×3×10^8(1-0.0034^2)}=0.012 $$ What is the unit of the result? Degrees per century or...

What would happen if the protons started to have orbital movements with energy gain and loss, changing orbital bands, at the same time as the electrons?

Is there a difference between the orbital velocity of an eddy and the root mean square of the velocity fluctuations? I'm particularly interested in understanding the eddy turnover time of the largest eddies in a turbulent flow, which is given by the characteristic eddy size and the...

The section Kepler’s Second Law here describes the above equation. In this problem, ##\text{r = D, m = M and v = V}## What is the way to go about finding out ##\theta## as shown in Figure 13.21?

How did the first scientists figure out the orbital radius of a moon of Jupiter? How can observations lead to a calculation of the orbital radius of a moon of another planet?

Hello guys, i want to ask you a question about orbital and spin dipole, and how this is going to influence diamagnetic or paramagnetic substances. So my question is: we know in a atom there is orbital and spin motion by electrons so possibly two magnetic dipoles. Is it correct to say that in...

I think that the quantum numbers are l=1 and ml=0, so I write the spherical harmonic Y=Squareroot(3/4pi)*cos(theta). I would like to know how to compute the wave function at t=0, then I know it evolves with the time-evolution operator U(t), to answer the first request.

Hi, I wish to build an orbital shaker (a bigger version of these examples: https://learn.adafruit.com/crickit-lab-shaker https://www.thingiverse.com/thing:2983846 As my aim is that it will work continuously for months around 100rpm what is preferred in aspects of heat and weight on top of...

Has anyone looked into the details of stellar orbital speeds and required (visible) mass distribution in the Milky Way? Doing some math here - if the local mass density is significantly higher in the inner 10-15% of the galaxy, and then lower and gradually thinning outwards in the disk, we will...

In 1846 three astronomers and mathematicians discovered Neptune because Uranus wasn't quite moving as Newton's law of gravity explains. So they did calculations and point the telescope at a specific part of the sky. They discovered Neptune. What formulas did they use? How did they calculate this...

I'm interested in learning orbital mechanics but I haven't taken a class in numerical methods yet. Do I really need to take a whole class in numerical methods before learning orbital mechanics, or can I get by if I self-learn a smaller portion of the syllabus of a numerical methods class? If so...

Parallel: M1V1+M2v2=M1V1’+M2V2’ (0.5)(3)+0=(0.5)(cos60)(3)+V2’Cos(x)(0.5) V2’cos(x)= Perpendicular: M1V1+M2v2=M1V1’+M2V2’ 0=(0.5)(0.3)(sin60)+V2’sin(x)(0.5) V2’sin(x)= And the divide 2 by 1 Which is tan(x)=2/1 And then plug then back into solve, but I don’t think we do it like this because...

So, I think it's possible to place an object in an orbit such that it remains perpetually in the planet's shadow, like in my awesome graphical representation. But is it?

I have a question about what happen when an electron in the Bohr model of atom, gains energy because for example is "hitting" by a photon. Electron have an energy, and it is the sum of potential and kinetic. When they gain energy, they gain potential energy so they go further away from nucleus...

The Earth Rotates at complete revolution at 24 hours, the troposphere and stratosphere are dragged along with it at the equator, but what about 100km-1000km above the equator? Is there a formula or chart that astronomers can use to predict the tiny amount of drag that satelites have to encounter...

~ Shower Thoughts ~ Twin A is in a spaceship, Twin B is in a spaceship. Both in 'deep space'. B follows a highly elliptical geodesic which goes around a planet (or black hole) with strong gravity, very far away. When they meet again, who is younger and why? I genuinely don't know what this...

Saw China launched a project to get a system operating by 2050, but at ~2GW that is about the capacity of a single nuclear power station, the Three Gorges Dam, at 22.5 GW has over 10x the capacity. https://www.bbc.com/future/article/20201126-the-solar-discs-that-could-beam-power-from-space US...

Some estimates through calculating the sun mass loss and increase in mass loss say that the white dwarf phase of the Sun will have roughly about 50% the current mass of the Sun (not sure about it). Whatever the actual mass loss is going to be, assuming that the 50% mass loss is true, where would...

What is the quantum spin of the valence electron in the silver atom in the furnace in the Stern-Gerlach experiment? . Up, down, at random, alternating, in a (quantum) superposition (of both), or none? Does it even have/get one until it's measured/observed /needed? . Does the second electron, in...

Watch the progress live This is a fully stacked Starship (top) and Super Heavy (bottom). A couple of too-small-to-see cars near the bottom for scale, I also added a Saturn V and the Statue of Liberty for comparison. 120 meters tall, about 5000 tonnes when fully fueled. Twice the mass and over...

If I understand correctly, orbital resonances of some of Saturn's moons are responsible for clearing out gaps in Saturn's ring structure (like the Cassini division). But I've also read that Neptune and Pluto are in a roughly 2:3 orbital resonance. So, do orbital resonances pull matter out of a...

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...

Hello, I would like to calculate the orbital velocity using the geometrical way of reasoning. But I have a hard time to understand and apply some basics into my calculations. The reasoning is pretty simple. After some time: dt ,the particle travels the distance: Vtot1 * dt = R*sinθ (see the...

hi every one what is the amount of orbital magnetic dipole moment of proton? this different with the intrinsic magnetic.

All spacecraft that have been put into orbit around other planets have required engines to decelerate them and inject them into their orbits. So-called "ballistic capture", from what I've read, always seems to call for at least a minimum application of force to change the trajectory; I get...

Find the probability distributions of the orbital angular momentum variables ##L^{2}## and ##L_{z}## for the following orbital state functions: ##\Psi(x) = f(r) sin(\theta) cos(\theta)## ##\Psi(x) = f(r) cos^{2}(\theta)##I am aware that the prob. distribution of an observable is ##|<a_{n} |...

I'm watching the Next Generation episode Relics and Riker has just ordered the helm to "go into orbit above that point" which I took to mean geosynchronous orbit. No biggie except that the point is on the outer surface of a Dyson Sphere with a RADIUS of more than 1AU. So, assuming the sphere has...

Could someone please tell me if I'm on the right track with understanding this. The periods of the comet and Uranus is different because of Kepler's second law? Is it because planets orbit the sun in a circular path whereas for comets it's a highly elliptical orbit? Thank you.

The author of my textbook writes that a spacecraft 's "thrust in the radial direction at perigee changes the energy but not the angular momentum". Such a thrust increases the eccentricity of the elliptical orbit of the spacecraft because ##\epsilon \equiv \sqrt{1+2EL^2/\mu C^2}##, where...

I know that in QM, there is LS coupling. So the interaction is there. But is such an interaction possible in macroscopic objects like a planet?

https://techcrunch.com/2020/12/03/space-startup-aevum-debuts-worlds-first-fully-autonomous-orbital-rocket-launching-drone/ The Ravn X launch vehicle is 80 feet long and has a 60-foot wingspan, with a total max weight of 55,000 lbs including payload. Seventy percent of the system is fully...

So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m. Then I found change in potential energy, -5.597*10^11 m. Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial...

Homework Statement:: I'm working on a personal project to convert objects from a simulation using state vectors for position and velocity to Keplerian orbital elements (semimajor axis, eccentricity, argument of periapsis, etc.). However, the equations I am using do not calculate the...

Hey guys, I decide I need to learn the mathematics of molecular-orbital theory, to build on the qualitative approach of my chemistry coursee. To do this I also first need to study single-electron systems and then many-electron systems, the Born-Oppenheimer approximation, and relevant topics...

Summary:: Hypotetical structure in the style of Dyson ring In the style of Dyson's proposal of an orbital superstructure, I wonder if in the specialized literature wasn't suggested that an evolved civilization could make a kind of orbital shutter, in order to delivery optical signals...

$$cos\theta = \frac {s}{1-s} = \frac{p-1}{p}$$ in this equation ##\theta## is the bond angle and ##s## and ##p## are the fractional s-character of the orbital and p-character of the orbital. This is equation is used rigorously in showing that the s-character of the axial orbitals in a ##sp^3d##...

Using Kepler's Formula, I tried to solve for the answer but was told that it's incorrect.

Hello, The sigma $(\sigma)$ molecular orbitals are symmetrical around the bond-axis while pi $(\pi)$ molecular orbitals are not symmetrical. For example, the linear combination of 1s orbitals centered on two nuclei produces two molecular orbitals which are symmetrical around the bond-axis. Such...

The Wikipedia page for angular velocity makes a big fuss over "spin" and "orbital" angular velocities, but I have checked through Gregory and Morin's textbooks on classical mechanics and haven't found any reference to them at all. They just work with a single quantity, the angular velocity...

The equation can be seen in the picture. I was assuming it was an Sn2 reaction given the polar aprotic solvent and strong nucleophile. For b), I assumed that the question asked me to draw the orbitals as shown above (as opposed to orbital diagram) because it asked me to identify the HOMO and...

The equations of motion are: \ddot{r}-r{\dot{\theta}} ^{2} = -\frac{1}{r^{2}} for the radial acceleration and r\ddot{\theta} + 2\dot{r}\dot{\theta}= 0 for the transverse acceleration When I integrate these equations I get only circles. The energy of the system is constant and the angular...

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...

In this article it discusses the generation of something called super chiral light and claims with metamaterials they can make it have very high angular momentum like l=100. What does that really mean? How does that relate in magnitude to the normally computed linear momentum of a photon p=h/λ...

Is it possible for an electron in the 1s orbital of an hydrogen atom to be indefinitely far from the nucleus in a given instant? From the Schrodinger equation we can see that the radial probability is NEVER zero, so it would be possible to see an electron in the moon, for example. But if I...