Orbit Definition and 1000 Threads

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 tried in the first place to use the effective potential of a parabolic orbit which is 0 to get the angular momentum L. Evaluating the function U(r) at r = rP i get U(rP) = L^2/(2m(rP)^2) - GmM/rP = 0. Here I get L = m√(2GMrP). Now the relationship between angular momentum L and areal...

Recently, when reading an entry about Mercury's perihelion shift, someone mentioned a "hand-wavy" explanation as to why GR predicts the orbit so precisely. I was wondering if there was some elementary way to expound on what he was saying. Fundamentally, the comment said something to the effect...

Hi, They gave me this formula T = 2piR / v, with T the revolution period of the satellite, R the distance between the center of masses and v the velocity. They gave me the value of G and the eath's mass and asked to determine the value of R. I don't even see fromwhere I should start... Thank...

Which tends to fill first: p3/2 or p1/2? d5/2 or d3/2? And why is there no spin orbit coupling in the nucleus?

L = mvr = mr (dr/dt) = 2m*r*(dr/dt)/2 = 2m*(dA/dt) So, A = (L/2m)T so, ## L = \frac{2 \pi a b m}{T}## Now, ##T^2 = \frac{4 \pi^2}{GM} a^3## So from all these, I get ##L = \sqrt{ \frac{GM m^2 b^2}{a}}## But answer given is ##L = \sqrt{ \frac{2GM m^2 ab}{a+b}}## (This, they have derived from...

Hello everyone! This is from The Fundamentals of Astrodynamics Chapter 2 Questions. I'm doing this as a self-study (and never took Linear Algebra) so my "technique" might be a little sloppy 😖😖 Finding specific angular momentum Finding the orbital parameter Finding Eccentricity Vector...

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...

Hello, i'm doing a project where the goal is to get the relative position of a space object to the earth, roughly. Basically, i want to say that this object is currently e.g. above New York. The data for any given space object that i have is (It's sourced from an NASA API). The specific...

Hi. I don't know what prefix this question belongs in so I just chose advanced at random. What's the physical effect called when the Earth orbits around the sun at extremely fast speeds and also rotates around itself every 24 hours at the same time? Does that force cause anything in space...

a. V=-GM/r V=-6.67*10^-11*6.0 x 10^24/6.4 x 10^6 V grav = -62531250 ~ -62.5M Jkg^-1 b. To find the gravitational potential 200 km above the surface of the Earth; r=6.4 x 10^6 +2*10^5 m=6.6*10^6 V grav=-6.67*10^-11*6.0 x 10^24/6.6*10^6 V grav= -60636363 ~ -60.6 M Jkg^-1 Can I check that it is...

1. The satellite would be in a jovian-synchronous orbit, Rearranging the formula for the orbital period in terms of r, since T^2 is proportional to r^3: T^2=4π^2r^3/GM which becomes r^3=(GM/4π^2) T^2 M(mass of Jupiter)=1.89 x 10^27 G=6.67*10^-11 m^3kg^-1s^-2 T=9 hours and 55 minutes =...

Bohr's hydrogen atom model is outdated facing Schrodinger's wave equation. Now that wave mechanics doesn't use a concept of orbit for the electron in hydrogen atom. But can we suppose the electron is still circling around the atom core, not necessarily in circles or ellipses, but in chaos like a...

Hi everyone:) I have spend a couple of days trying to teach myself the math of orbital mechanics and have been able to generate a model of the orbital path of Haley's Comet, incorporating realistic distances and periods using Kepler's second law & ellipsoid functions. This is a GIF of the motion...

I cannot understand the solution at https://www.aapt.org/physicsteam/2015/upload/E3-2-5-solutions.pdf, because the solution is terse and skip steps (at least i think so). I figured out that the name of this transfer is "Hohmann-Transfer Orbit". A detailed walkthrough would be appreciated. If I...

Asimov pointed out that Earth's Moon is nowhere concave (looped) in its motion with regard to the Sun. What about Pluto and Charon - are both concave w.r.t. the Sun at certain times? Moreover, what is the largest body in the solar system which is sometimes concave w.r.t. The Sun? Thank you...

I am reading MWT gravitation and on page 676, they are talking about orbits of photon, and I don't understand it very well. Energy and angular momentum of the photon are important as a ratio when calculating the orbit. But not energy alone or angular momentum alone. Why is that, and the energy...

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?

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...

The orbit diagram https://en.wikipedia.org/wiki/C/2020_F3_(NEOWISE)#/media/File:Comet_2020_F3-skyview.png' in the Wikipedia article https://en.wikipedia.org/wiki/C/2020_F3_(NEOWISE) shows some very odd spirals. My first guess is the picture shows what Neowise does in one Earth year (mostly...

I am confused because the question implies that I need to do some sort of calculation with Kepler's law. I got ##r+d = \sqrt[3]{\frac{T^2 GM}{4 \pi^2} } ## But don't understand why I need this, since I already have the distance and the angular diameter should be ##\arctan (2R/d)## I think I...

Below are equations/formulas/text from https://en.wikipedia.org/wiki/Schwarzschild_geodesics https://hepweb.ucsd.edu/ph110b/110b_notes/node75.html I apologize for not remembering the source for the "v=" equation, or for my inability to find it again. For a circular orbit, the distance r and...

How can i know the resulting orbit of is symmetric about two turning points? Where m, l is constant. V is function of r u = 1/r and It is in polar coordinates. We could show that varying theta from 0 to -θ will be the same if we vary 0 to Θ, but i don't know where to start

I just have a question on the problem itself. If I am putting the satellite into orbit 450,000 m above the surface, then would r=6,371,000 m(earth's radius)+450,000 m? And what mass of Earth should I be using, in kg of course.

If you let a magnet free-fall down a copper or aluminum tube, the induced magnetic field in the surrounding conductive medium imposes a braking effect on the magnet, reducing its speed (explained by Lenz’s law). The earth, being a large magnet, is essentially free-falling around the sun. The...

I know this problem can be solved using energy conservation, but I tried another method that I don't know is correct or not, but yielded a similar result to what my classmates got: $$F_{C}=F_{G}\Rightarrow \frac{mv^{2}}{r}=\frac{GMm}{r^2}$$ $$\frac{v^2}{r}=\frac{Gm}{r^2}\Rightarrow...

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...

It is fairly trivial to do this with a circular orbit: $$(x,y) = (cos(\omega t),sin(\omega t))$$ where t is time, and $$\omega = \sqrt{GM/r^3}$$ How this parametric equation look for an elliptical orbit?

I am really stuck on what to do here in this question I have arrived at forming an equation to work out the radius of electron orbit from doing the following However I do not know what to do next as I don't know what the value of n (quantum number) must be? :oldconfused: Any help would be...

Trying to establish the conditions needed in order for a planet to have more than the standard 4 seasons. I may be wrong for assuming an elliptical orbit is required, but could make sense in order for there to be two winters for example.

Hi, I was reading about the general relativity to get some basic understanding and it was said that the proper answer to problem of precession of Mercury was provided by the general relativity. Then, I started reading about the precession of Mercury orbit. "Mercury deviates from the precession...

Hello! I am reading about spin-orbit coupling in Griffiths book, and at a point he shows an image (section 6.4.1) of the vectors L and S coupled together to give J (figure 6.10) and he says that L and S precess rapidly around J. I am not totally sure I understand this. I know that in the...

I know that the angular momentum of the particle orbiting in an elliptical path is constant and due to which the particle speeds up near the foci when r is small. But, I cannot figure out how to calculate the time period of rotation. I can do the same for an ellipse by taking mv²/r = central...

I believe I solved this. Is this solution true? Can please anyone just check?

Hi! This is a problem from my physics 1 high school course. I've tried using the first and third equations to determine period (answer of 8326.9544s.), however that was incorrect and I never even touched G. I'm not sure where to go from here at all. Any help is appreciated!

I am pretty confused where to even start with this question, which is not a good thing less than a week before the final :(. One thing in particular that I don't get is that I thought we were using the Clebsch-Gordon coefficients for ##\vert jm \rangle ## states, not for ##\vert J, J_z \rangle...

a) Eg = Gme/r^2 r = √Gme/Eg r = √[(6.67x10^-11 N*m^2*kg^2)(5.98x10^24 kg)]/(4.5 N/kg) r = 9.41x10^6 m h = r2 - r1 h = 9.41x10^6 m - 6.38x10^6 m h = 3.03x10^6 m that's over 3000 km. Did I not use for right equation? Is Eg not 4.5 N/kg? Also for b), isn't the force of gravity the centripetal...

I have yet to decide on values for the mass of the fixed object, M, the mass of the moving celestial body, m, the initial velocity, v, and the distance between the two objects, r. I will most definitely decide on a larger mass M because I would like the celestial body to spiral in towards the...

The exercise is to compare numerical and analytical solution. I have worked out the code from earlier exercise (see code under this text), but I don't understand how the analytical solution works. I have tried to use the equation r(theta) = a(1-e^2)/(1+e*cos(theta)), which is OK but I don't...

I want to understand this topic but I can not understand very well so please suggest any reading for good conceptual grasp of this topic.

The Earth's orbit around the Sun is an elliptical orbit. Why is that so? Does that mean Sun, much like Earth bulged at some points which makes the gravitational force between Earth and Sun stronger at some points and weaker at some comparatively?

Recently i read, that GEO orbit actually isn't enough for a space elevator, since its weight would pull it down, either it needs constant thrust, or build it much taller than 33.000 km, so upper GEO parts pull it up. That further lowers its plausibility level. Any other methods? Build a tall...

Hi, everyone can you help me with this question, please?

Summary: Achieving speed of light with Earth's rotation Excuse my ignorance, but I think of dumb things. If you theoretically built a strong, lightweight cable that traversed over 2.5 billion miles attached to the rotating Earth, the tip would be traveling at or greater than the speed of...

I tried it, but I am not getting no of the given answers According to the statement, it is saying that 3 KE (in the orbit ) = ΔUg So, beeing R the radius of the Earth and R2 the radius of the orbit: 3 (1/2)(GMm/r2) = -GMm/r2 - (-GMm/R) Canceling out the GMm: (3/2)(1/r2)= (-1/r2) + (1/R)...

This is something that one seldom stops to think about, but I suddenly thought of it myself: Why do oceans look deep blue when photographed from orbit? Oceans look blue when looked from the shore because they are reflecting the sky... But the atmosphere doesn't look deep blue when photographed...

In a circular orbit, the 4-velocity is given by (I have already normalized it) $$ u^{\mu} = \left(1-\frac{3M}{r}\right)^{-\frac{1}{2}} (1,0,0,\Omega) $$Now, taking the covariant derivative, the only non vanishing term will be $$ a^{1} = \Gamma^{1}_{00}u^{0}u^{0} + \Gamma^{1}_{33}u^{3}u^{3} $$...

From CNN: These two dead stars zip around each other every seven minutes https://www.cnn.com/profiles/ashley-strickland-profile By Ashley Strickland, CNN Updated 2:48 PM ET, Wed July 24, 2019 (CNN)While searching the skies for brightness and blinking, the California Institute of Technology's...