# What is Circular orbit: Definition and 90 Discussions

A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle.
Listed below is a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is the gravitational force, and the axis mentioned above is the line through the center of the central mass perpendicular to the plane of motion.
In this case, not only the distance, but also the speed, angular speed, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no radial version.

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1. ### I Circular Orbit in Schwarzschild: Orbital Period

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} =...
2. ### Calculate the Speed of a Satellite Moving in a Stable Circular Orbit

V = ? m/s V = D/T V = Square root (6.67 * 10^-11)(m)/r
3. ### Two black holes moving in a circular orbit around a point

I tried solving it and i was able to do a) and b) here is what i did on c), but its not correct according to the solution
4. ### From circular orbit to elliptical orbit

Problem: a particle of mass m is in a circular orbit around a planet at a distance R from the center. The planet mass is M and it's radius is R_0. What is the tangential impulse that will cause the particle to brush against the back of the planet? Describe the orbit. The attempt at solution...
5. ### Using Lagrangian to show a particle has a circular orbit

Hi :) This is a problem from David Tong's Classical Dynamics course, found here: http://www.damtp.cam.ac.uk/user/tong/dynamics.html. In particular it is problem 6ii in the first problem sheet. Firstly we can see the lagrangian is ##L = \frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+\dot{z}^2) -...
6. ### Potential Energy and raising a satellite from Earth into a Circular Orbit

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...
7. ### I Formula: velocity of circular orbit wrt Schwartzschild metric

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...

37. ### Circular Orbit / Practice Quiz #4, Question 27

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?Homework Equations Using g = GMm/r^2 Fc = mv^2/r The Attempt at a Solution Fc = mv^2/r How can I solve this equation if I am...
38. ### Uniform Circular Motion vs Circular Orbit due to Gravity

In uniform circular motion, (eg, a mass on the end of a string moving in a horizontal circle) centripetal force is the only thing causing acceleration. we have the kinematic relationship V=RW or velocity is proportional to radius. I.e a bigger radius means greater linear speed? For the...
39. ### Stability Condition for Circular Orbit

Homework Statement Show that the stability condition for a circular orbit of radius a, i.e. f(a) + \frac{a}{3} (\frac{df}{dr})_{r=a} < 0 is equivalent to the condition \frac{d^2V(r)}{dr^2} > 0 for r=a where V(r) is the effective potential given by V(r) = U(r) +...
40. ### 3D Harmonic Oscillator Circular Orbit

Homework Statement I found this in Binney's text, pg 154 where he described the radial probability density ##P_{(r)} \propto r^2 u_L## Homework Equations The Attempt at a Solution Isn't the radial probability density simply the square of the normalized wavefunction...
41. ### Circular Orbit Four-Velocity and Schwarzschild Metric

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...
42. ### Radius of a photon's circular orbit around a mass

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

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} +...
44. ### What is the radius of the de broglie circular orbit with n=1?

What is the radius of the de broglie circular orbit with n=1?
45. ### Period of circular orbit with in terms of varying speeds and radius.

Homework Statement A particle of unknown mass moves in a circular orbit of radius R under the influence of a central force centred at some point inside the orbit. The minimum and maximum speeds of the particle are vmin and vmax respectively. Find the orbital period T in terms of these speeds...
46. ### Standing Waves in Bohr's Circular Orbit: Interference Explained

If electron waves weren't standing waves in Bohr's circular orbit, why and how would the waves interfere ?
47. ### Shuttle moving in a circular orbit

The space shuttle is moving in a circular orbit with a speed of 7.8km/s and a period of 87min. In order to return Earth, the shuttle fires its retro engines opposite to its direction of motion. The engine provide a deceleration of 6m/s^2 that is constant in magnitude and direction. What is the...
48. ### Universal Gravity Circular Orbit

Homework Statement What is the radius of a circular orbit about the Earth where the acceleration is 0.1g? Homework Equations g=9.8m/s^2 F=(Gmm)/r^2 Radius of Earth= 6.38x103 km Mass of Earth= 5.98x10^24 m/s The Attempt at a Solution I said 1/(2^x)=1/10 then did log2(10)=x and solved...
49. ### What is the period of a photon in a circular orbit around a black hole?

Let be a photon in a circular orbit (r=3M). I want to know the period measured by a stationary observer at this radius. Because we are working with a photon we cannot 'talk' about proper time, that's why I don't understand how can I calculate this. If I had a massive particle I could do...
50. ### How much energy is required to move this satellite to a circular orbit

Homework Statement How much energy is required to move this satellite to a circular orbit with a radius of 2.50×104 miles? I've found the answer to Part A of this problem to be 1.59*10^10, if this helps solve the above^^ (Find the kinetic energy of a 1.80×103 kg satellite in a circular...