Orbital Definition and 820 Threads

Has anyone seen the derivation of \(\ddot{\mathbf{r}} = -\frac{\mu}{r^3}\mathbf{r}\) into state matrix form? If so, can they provide a link?

Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model? Also, does the principal quantum number even correspond to energy in the shell model?

Look for help on these equations. Any help will be greatly appreciated. Thanks so much! :) The Apollo spacecraft must be traveling at what velocity in order to remain in a 110 kilometer orbit around the moon? The magnitude of the Apollo’s orbital velocity can be computed from the laws of...

The "s" in the geodesic equation refers to the "surface area" for that portion of the orbit around a star or black hole. For a small enough "delta t" the surface areas are the same. Around a small star the orbital surface area (without the other interfering gravitational sources) would...

Hi everybody, In most classical or quantum optics texts an angular momentum is considered for the EM radiation as the following: J = ε_0 ∫_V r × [E(r, t) × B(r, t)] d^3 r Then it is claimed that: "Using the usual formula for a double vector product and integrating by parts...

Hi I have a question regarding Molecular orbital theory: Is it correctly understood that if we combine 2 or more atoms the atomic orbitals can become 2 things: They can either become Hybrid orbitals which are the orbitals that form sigma bonds between atoms, or they can become Molecular...

Basically, I'm trying to come up with a function that determines the amount of force need to keep an object in a stable circular orbit if it were to suddenly lose altitude due to a collision or what not. Basically required force as a function of orbital radius. Here's what I've come up with...

Hello I would like to understand the resonance phenomenon that can occurs when we deals with satellite's orbits. Here what it is said about it : KAULA - Theory of satellite geodesy - p. 49...

I am very confused about the fact that, for example, Pluto moves around the Sun much slower then Earth and is also much further from the Sun, so its period is way longer that that of Earth's.. if I want to increase orbital height, I add speed to the object I want to raise, no? How come...

The Hulse-Taylor (PSR B1913+16) binary pulsar 'observed vs. predicted' orbit decay is one of the great validations of GR. The orbit decay over the recording period of 30+ years is very close to GR prediction as per predicted energy loss through gravitational waves. Hulse-Taylor experiment is...

Homework Statement A hydrogen atom is identified as being in a state with n=4. What is the magnitude of the total orbital angular momentum for the largest permitted value of l? Homework Equations n>l, l is bigger or equal to m The Attempt at a Solution The allowed l= 3,2,1 The allowed m for...

Homework Statement Consider an electron with spin \frac{1}{2} and orbital angular momentum l=1. Write down all possible total angular momentum states as a combination of the product states | l=1 , m_l > | s = \frac{1}{2} , m_s > Homework Equations Lowering operator : J_- |j, m> =...

Hello, I have a rather conceptual question I couldn't really find an answer to yet. The electric field lines of an isolated resting electron would simply point from everywhere in space towards the position the electron is located in, with a length inversely proportional to the squared distance...

Homework Statement Excited sodium atoms emit two closely spaced spectrum lines called the sodium doublet with wavelengths 588.995 nm and 589.592 nm. (a) What is the difference in energy between the two upper energy levels (n=3 l=1)? (b) This energy difference occurs because the electrons...

Homework Statement If a satellite is to orbit Earth at an altitude of 1.00x10^3 Km, what would be its orbital period? rs = 1.00x10^3 km, Mearth = 5.97x10^24 kg, Gravitational Constant = 6.67x10^-11 Homework Equations T= 2∏√r^3/GM The Attempt at a Solution rs = 0.815484549m...

Hi, I stumbled upon this while working on a problem on my physics homework. I still want to solve the problem myself if possible though so I won't post it here, instead, I'll post what is confusing me. Consider orbital motion with potential U(r), where U(r) is any arbitrary function of r. I...

Homework Statement If a particle has spin 1/2 and is in a state with orbital angular momentum L, there are two basis states with total z-component of angular momentum m*hbar l L,s,Lz,sz > which can be expressed in terms of the individual states ( l L,s,Lz,sz > = l L,Lz > l s,sz > ) as l...

Suppose we have some object with angular momenta \mathbf{L}_1 about rotation center O_1 and we have another object with angular momentum \mathbf{L}^\prime_2 about rotation center O_2. O_2 has some velocity \mathbf{v}_2 relative to O_1. Then we wonder what is the angular momentum of the second...

Homework Statement Solve for ##L^2_x## ##L_x = \frac{\hbar}{i} (-sin(\phi)\frac{d}{d\theta} - cos(\phi)cot(\theta)\frac{d}{d\phi}##** the d's should be partial derivatives, but I'm not sure how to do that symbol. Sorry! Homework Equations Solve for ##L^2_x## ##L_x = \frac{\hbar}{i}...

Homework Statement The three planets (v1, v2 and v3) in the diagram all have similar mass and are in a line equally spaced so that v1 and v3 are orbiting around v2 synchronously. If the mass of each of the planets are M and the radius of the orbit is R, what is the orbital period...

Hi! I need help with a problem regarding orbital maneuvre. The question is: You're doing a first-order analysis on a new satellite in an elliptical orbit with eccentricity e=0.20 and altitude 700 km. Can you design the orbit so that no maneuvers are necessary to maintain it? Where should...

If an electron orbital the Earth only influence by gravity,does it emit electromagnetic waves? if so, the radius will decay,eventually falling on earth?

Hi! Is there a way to calculate the classical orbital elements for a satellite or space shuttle around Earth using Matlab? I would like to get started with it since it is something that I've not tried before. so plese help Best regards

based on the data in the table I want to calculate the orbital period of the eclipsing binary but I want to state my answer in equation form so that any observer can predict the times of future eclipses. Does anyone have an idea on how I go about doing that with the given data. I tried to find a...

hi guys, i have a question about the orbit-spin relationship of the celestial objects. for example in our solar system i understand the orbital period becomes lengthy for the planets more distant than the sun, it's logical, but what happens with their spinning motion..? i don't understand why...

Hello I'm not a professional cosmologist but I wanted to know what the orbital length is equal to in Km units in this graph: http://ej.iop.org/images/1538-4357/707/2/L114/Full/apjl334146f3_lr.jpg Thank you so much.

Hi I am currently looking for the wavefunction of the bonding orbital of the hydrogen molecule. Does anybody here know how this one might look like? So, since there is no complete analytical solution for the Hydrogen atom Schrödinger equation, I am currently looking for approximations of this...

Consider 2 atomic orbitals with wave function a: σ(r), b: μ(r) in a diatomic molecules. σ(r) (or μ(r)) is localized around an atom a (or b) and is relevant for the discussion of the molecular orbital. These orbitals are orthogonal and normalised. The creation operators are x, y and vacuum, |0>...

According to Maxwell's Laws of electromagnetism , the orbital frequency (the number of complete orbits per second) of an electron will match the frequency of the emitted radiation. If an electron spirals into the nucleus, what would happen to the electron's orbital frequency? This is what...

Hi, Reading http://rmp.aps.org/abstract/RMP/v70/i4/p1039_1 I've run into a notational question of atomic p orbitals. The authors use symbols like p_\sigma and p_\pi. From their fig. 3 (attached), they do look like p_x and p_z orbitals, respectively, rather than anything close to σ or π bonds...

Homework Statement i need to calculate the orbital angular momentum for 3D isotropic harmonic oscillator is the first excited state The Attempt at a Solution for the first excited state...

From "Modern Quantum Mechanics, revised edition" by J.J. Sakurai, page 196. Equation (3.6.4), 1-i \left( \frac{\delta \phi}{\hbar} \right) L_z = 1 - i \left( \frac{\delta \phi}{\hbar} \right) (x p_y - y p_x ) Making this act on an arbitrary position eigenket \mid x', y', z' \rangle...

How can I determine Mars' orbital position in February 2009? Is there a website that tracks past positions? By position, I want to know where in its rotation around the Sun it was radians or degrees.

So here's a question I'm struggling with: The rotation speed of the sun around the Milky Way center is 220 km/s and it takes the sun around 200 million years to orbit once around center of the galaxy. Given that the rotation curve is relatively flat (i.e. the rotation speed stays the same as...

In sp3 hybridisation, how a tetragon is formed? As per book, in ch4 (methane) there are four sigma bond of same length and strength. But we are having three sp sigma bonds (between s of H and p of C) and one ss sigma bond( between s of H and s of C). Then how can sp and ss sigma bond be of same...

How to get N2 molecule orbital theoretically with quantum chemistry program like GAUSSIAN !for example, how to get the picture attached? Thank you!

The post-Newtonian expansion at the first post-Newtonian 1PN level under Schwarzschild conditions, a test-body in a spherically symmetric gravitational field, gives the following expression for the gravitational acceleration of the test-body: \frac{{\rm d}\bar{v}}{{\rm...

Earth to Venus Hohmann transfer alignment time. Earth is at periapsis and Venus is at 190 degrees at ##t = 0##. For a Hohmann transfer, Venus must be lagging Earth by ##36.0298## degrees. I am trying to find the time it takes for the planets to align from their current positions. Is...

Hi guys, I have a question which is probably stupid. I am studying angular momentum and I have found almost everywhere that, if we have orbital angular momentum higher than \ell=0 then it brings powers of the momentum of the system like k^\ell. What is the reason of that? Can someone suggest a...

Hi there I've been struggling to convert the following two vectors into orbital elements, the vectors are as follows: R = 0i - 7950j + 0k km V = 5i + 0j + 5k km/sec I would like someone to help with the calculations of the following COEs: - semimajor axis (a) - eccentricity vector...

I am trying to show that $$ \frac{\Delta v}{v_{c_1}} = \frac{1}{\sqrt{R}} - \frac{\sqrt{2}(1 - R)}{\sqrt{R(1+R)}} - 1 $$ where ##R=r_2/r_1##. ##r_1## is the radius of the circular orbit 1 and ##r_2## is the radius of the circular orbit 2. Similarly, ##v_{c_1}## is the velcotiy of the circular...

Hi, Could someone tell me if the following orbital diagram is correct for ozone? I added the bonds and lone pairs in color. Thanks in advance.

For a given space triangle, derive expressions for the terminal velocity vectors ##\mathbf{v}_1## and ##\mathbf{v}_2## between points ##P_1## and ##P_2## in terms of the unit vectors ##\mathbf{u}_1##, ##\mathbf{u}_2## and ##\mathbf{u}_c##. I know that ##\sin\left(\frac{\alpha}{2}\right) =...

Hello, I am not a physicist or a physics student. I am an author, and I am trying to see if a Trinary star system I've dreamed up could work, and if so, what are the details as applies to my book. I hope someone can take the time to help me with this. The situation is this: I have imagined a...

Hello, Is it true that according to molecular orbital theory valence electrons in molecules are not assigned to individual atoms? Does this mean that even lone pairs are not assigned to inidividual atoms in a molecule , but rather assigned to a specified area across the molecule? Thanks!

Help I am really confused! Orbital overlap in Hcl. Hi, The orbital overlap in HCl is due to hybridization between one sp³ oribital from Cl and one s orbital from H. So why does the following picture say that the orbital overlap is between one p orbital from Cl and one s orbital from H...

Hello all, been meaning to make an account here and participate but haven't been around to it. So sorry that my first post is asking for homework help! :| Homework Statement The planet Jupiter has a moon Europa (m = 5x10^22kg) that is orbiting at a velocity of 14,000m/s at a distance of...

i need to find the orbital transition frequency given by ω=ωa-ωb a and b represent orbital states a is higher energy state and b is lower energy state

Homework Statement A Titan IV rocket has put your spacecraft in circular orbit around Earth at an altitude of 397 km. What is your orbital velocity? Give your answer in m/s.Homework Equations http://as370.socialhwk.com/engr370i/ch04/ch4_3/IMG00015.GIF...

What is the meaning of "orbital energies"? Could someone please explain, because I am confused: or is it the same as energy level of an electron, I mean the energy that one electron contains in a certain shell? Thanks for the help!