Radius Definition and 1000 Threads

Hi there, I was reading one of my textbooks and I had a thought. For a black hole, there is minimum orbiting radius of ##R_{min}=3R_s## where ##R_s## is the Schwarzschild Radius. This minimum orbit is created by the fact that in order to obtain an orbit of that radius around a black hole, you...

Homework Statement z ∈ ℂ What is the radius of convergence of (n=0 to ∞) Σ anzn? Homework Equations I used the Cauchy-Hardamard Theorem and found the lim sup of the convergent subsequences. a_n = \frac{n+(-1)^n}{n^2} limn→∞ |an|1/n The Attempt at a Solution I think that the radius of...

About: As a project, I'm trying to solve for the approximate radius and mass of a approximately earth-sized planet, Mann, from Interstellar. According to what was provided, g = 7.84m/s2 The solid part of the planet is composed of a honeycomb of rock and ice The space inside the honeycomb is...

I'm a beginner in GR (as you may conclude from some of my previous posts) so any help is greatly appreciated. I was recently studying alternative metrics for the Schwarzschild metric and one of them was the Kruskal Szekeres metric. In Schwarzschild, the radius r is defined which is the radius...

which formula is correct? or

Hi, I'm trying to solve the following problem: "What is the optical power (in dioptres) of a concave-convex eyeglass lens (n = 1.5) with the radiuses r1 = 12cm and r2 = 18cm?" The attempt at a solution: I'm usually solving such questions with the following equation: ## \dfrac{1}{f} =...

Homework Statement 45. Consider the ions Li+, Na+, Be2+, and Mg2+. Which two are closest to one another in size? (A) Li+ and Na+ (B) Be2+ and Mg2+ (C) Be2+ and Li+ (D) Li+ and Mg2+ Homework Equations N/A The Attempt at a Solution I thought it wouldn't be A, B, or D due to the pairs having...

Homework Statement The radius for the inside of a curve is half the radius for the outside. With 2 cars of equal mass, car A travels on the inside and car B travels on the outside at equal speed. Which statement is correct? a. The force on A is half the force on B b. The force on B is half the...

If we take two planets One Earth and another one with half the radius of Earth. The planet with half the radius has lesser than half of the volume of the Earth. Also given that mass is half. Why? Is it because lower radius and lesser mass means lesser gravity and lesser gravity can pull lesser...

When a stellar object falls into the Earth's surface, it creates a crater on the ground. Most of the times, when people refer to these things, they refer to their age and their diameter/radius. My question is mainly about the radius. Is there a dynamical way to solve for the shape and radius of...

Homework Statement A 3.75 kg bucket pile of water is swung in a vertical circle. If the speed of the bucket at the top of the loop is 6.20 m/s, then the radius of the largest circle through which this pail could move without the water leaving the bottom of the pail would be what? m = 3.75 kg...

So, I'm working on my semester finals for my high school physics class, and I've run across a problem that has me stumped. I've included the pertinent material below. Homework Statement A rocket with a mass of 2kg and traveling at 14,008.34 meters/second loses 10% of its velocity as finishes...

I figure that at large enough distances, the potential field of an ion is just the Coulomb potential for its net charge. But what happens at scales comparable to the ion's Bohr radius? Could there be, for example, some sort of screening effect from the electron shell that changes the potential...

Homework Statement Imagine one of those amusement park rides where you have a large rotating disc with seats hung by chains around it. As the disc spins, the seats also spin whilst rising up as well. The question asks for all answers to be written given the constants L, the length of the chain...

I know the original schwarzschild formula for finding the radius of the black hole, but what equation can be used to find its mass if you ONLY know its radius?

1. So for homework my teacher gave us this question (and this is quoted from his worksheet): You graduate college with a degree in astrophysics and are assigned as an astronaut to explore a distant planet for NASA. You land on this planet and are told to determine the mass of the planet...

Homework Statement [/B] I have to find the radius of convergence and convergence interval. So for what x's the series converge. The answer is supposed to be for every real number. So the interval is: (-∞, ∞). So that must mean that the limit L = 0. So the radius of convergence [ which is...

I want to know the equation by which we can calculate the turing radius of a car with respect to speed or track length as I am designing a racing track for my thesis project. Regards, M.Tayyeb

I found http://physicspages.com/2013/05/05/schwarzschild-metric-gravitational-redshift/: \frac{\lambda_R}{\lambda_E} = \sqrt{\frac{1-2GM/r_R}{1-2GM/r_E}} where the indexes R and E are for receiver and emitter respectively, and the speed of light is normalized to 1. Most other sources on the...

Homework Statement I have this problem to consider the power series, \sum_{n=1}^{\infty}\frac{(-4)^{n}}{\sqrt{n}}(x+4)^{n} So, i need to find the R and interval of convergence. Homework Equations The Attempt at a Solution This is what i did: \lim_{n\rightarrow \infty}...

Hi, I have been referencing this (https://www.physicsforums.com/threads/radius-of-ellipsoid.251321/) previous post to calculate the radius of a Triaxial Ellipsoid (a>b>c), but I'm running into some issues. Let 0 ≤ ϕ ≤ π 0 ≤ θ ≤ 2π and x=r * cos(θ) * sin(ϕ) (1) y=r * sin(θ) * sin(ϕ)...

Homework Statement ∞ n=3 ∑ ((-1)n (x+3)3n)/(2nlnn) Find radius of convergence, interval of convergence, values for x which series is: absolutely convergent, conditionally converge or divergence. Homework EquationsThe Attempt at a Solution I applied the Ratio Test and got |(x+3)3| lim...

Homework Statement ∑ x2n / n! The limits of the sum go from n = 0 to n = infinity Homework EquationsThe Attempt at a Solution So I take the limit as n approaches infinity of aa+1 / an. So that gives me: ((x2n+2) * (n!)) / ((x2n) * (n + 1)!) Canceling everything out gives me x2 / (n + 1)...

A number of recent threads have discussed what happens when an observer falling into a massive black hole passes the event horizon. What I would like to know is this. For a massive BH of mass M, Schwartzchild Radius Rs, how long would it take for such an observer (who, presumably crosses the...

Homework Statement I have to determine the radius at which 50% of energy is in a Gaussian profile.Homework Equations The intensity is given by I=Ioe^(-r/2c)^2. This is just a gaussian function ofcourse. The Attempt at a Solution I know c is the standard deviation. I searched through charts...

Homework Statement Hey guys, I have a problem where we measured the gravity on separate floors of a building using a gravometer. It gave us values in mgals. So each floor has a distance of 0.5m. How do we take this into account as we move up and down the floors? As we move up, there's and...

Homework Statement A stunt driver for a movie needs to make a 2545kg car skid on a large, flat, parking lot surface. The force of friction between the tires and the concrete surface is 1.75x10^4N and he is driving at a speed of 24m/s. As he turns more sharply, what radius of curvature will he...

Hi, I am likely just missing something fundamental here, but I recently just revisited series and am looking over some notes. In my notes, I have written that if ## \lim_{x \to +\infty} \frac{a_{n+1}}{a_n} = L ## Then ## | x - x_o | = 1/L ## But shouldn't the correct expression be $$ | x -...

Homework Statement Consider a simplified model of the human eye, in which all internal elements have the same refractive index of n = 1.40. Furthermore, assume that all refraction occurs at the cornea, whose vertex is 2.50 cm from the retina. Calculate the radius of curvature of the cornea such...

Homework Statement An observer is orbiting at a radius r = 3GM, \theta = \frac{\pi}{2} and \phi = \omega t where w is constant. The observer sends a photon around the circular orbit in the positive \phi direction. What is the proper time \Delta \tau for the photon to complete one orbit...

Homework Statement A civil engineer is asked to design a curved section of roadway that meets the following conditions: With ice on the road, when the coefficient of static friction between the road and rubber is 0.12, a car at rest must not slide into the ditch and a car traveling less than 70...

Homework Statement If NASA wants to put a satellite in a circular orbit around the sun so it will make 2.0 orbits per year, at what distance (in astronomical units, AU) from the sun should that satellite orbit? The Earth's orbit is 1.0 AU from the sun. T_E = \frac {1.0orbit}{yr} T_s = \frac...

I know that the schwarzschild radius is proportional to the mass. But in case of black holes the mass remains the same only the size and density changes. So does the schwarzschild radius stay same when it is the sun and when it becomes a black hole?

How to derive the formula: v=wr where v is the tangential velocity, w is the rotational velocity, and r i the radius vector? From the attached image, it can be concluded that (each quantity is a vector): w=r x v, also v=w x r, and r= v x w. All three vectors are perpendicular to each other...

Homework Statement Two parallel plates with opposite charges are 0.01 m apart and have a potential difference of 100 V. A charged spherical object has 20 excess electrons stays motionless between the plates. If the density of the object is 1000 kg/m^3, what is the radius of the spherical...

I'm a bit confused about the derivation of the Schwarzschild radius. I can do it quite easily using Newton's Law of gravitation, but this law is only an approximation, so I am wondering whether the result I obtain, r_{s}=\frac{2GM}{c^{2}}, is an approximation or not. It seems to me that it...

Homework Statement :[/B] An atomic explosion can be approximated as the release of a large amount of energy ##E## from a point source. The explosion results in an expanding spherical fireball bounded by powerful shock wave. Let ##R## be the radius of the shock wave and assume that...

I'm not sure if this question fits here, but I've had trouble finding a good simple physics forum, so I signed up here :) I'm trying to think if the below wheel (image below) could allow for my push mower to have a zero or near zero turn radius. The edges of the wheel contour up (from the...

If one simply swings a rope with an object tied to the end of it, the object describes a circle. But if one were to create a contraption that caused the radius of the rope to periodically decrease 4 times every revolution, one could cause the path of the object to describe a square. My...

Homework Statement What is the acceleration due to gravity at an altitude of 1.00 x 10^6 above the Earth's surface, given that the radius of the Earth is 6.38 x 10^6 m? How do i go about solving that? Homework Equations Using g = Gm/r^2 The Attempt at a Solution g= GMm/(R+h)^2 R= radio of...

So for BiConvex Lenses, increasing the lens radius (by making the lens fatter) brings the image and focus closer to the lens, thus making it smaller given constant object position. As demonstrated in this demo http://micro.magnet.fsu.edu/primer/java/lenses/lensvariations/index.htmlYet for the...

I don't know if this can be calculated. I have tried for hours and days to isolate/calculate the radius and angles of the circle in order to be able to calculate length 1. I have tried using cos/sin-relation formulas and triangle formas - but Iam stuck. Any hints would be greatly appreciated...

Photons with smaller and smaller wave lengths have a higher and higher energy and these engeries have an increasing Schwarzschild radius r_s. Consequently i can ask when half the wave length \lambda/2 is equal to r_s, such that one wave length fits into the sphere of the Schwarzschild radius. I...

Can someone either derive or point me to a derivation of Møller's formula for the relativistic minimum radius of a rotating body? I've been searching for about an hour and it's driving me crazy! The only "minimum radius" equation I've seen imposes the speed limit c on a classical rotating body...

Homework Statement Show that ##\vec{E}_x## on the axis of a ring charge [I'm assuming they meant "of charge Q"] of radius "r" has its maximum value at ##x=\pm \frac{r}{\sqrt{2}}## Homework Equations Linear charge density ##\lambda=\frac{Q}{2\pi R}## ##dQ=\lambda ds = \frac{Qd\theta}{2\pi}##...

Homework Statement Both Newton's gravitational law and Coulomb's law are inverse-square laws: The force of attraction between the sun (S) and Earth(E) has (G*m_S*m_E)/r^2, whereas the force of attraction between an electron and a proton in a hydrogen atom is (e^2)/(4*pi*epsilon_0*r^2). Derive...

I've been working with NFW Dark Matter Halos recently. This is a particular density model for the halo developed by Navarro, Frenk, & White (NFW). The density structure has the form \rho (r) = \frac{\delta_c \rho_c}{(r/r_s)(1+r/r_s)^2} where \delta_c = \frac{200}{3}...

I've only recently started learning basic electrodynamics, but I don't understand why a loop of coil with a small area and a magnet falling through will produce a larger peak to peak emf amplitude than a loop of coil with a larger area with the same magnetic field falling through. To clarify...

Find the radius of convergence of the power series $\displaystyle\sum_{n=1}^{\infty}\dfrac{(-1)^{n+1}(z-1)^n}{n+1}$, $z\in \mathbb{C}.$

Recently I have been researching black holes, and came across the "Schwarzschild Radius". The wikipedia page on Schwarzschild radius's mentioned that the Sun has a radius of 3km. If that is so, then how can that be so, as that would mean that light cannot escape it. So when it said "3km", did...