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The formula is dimensionless, ... In Schwarzschild metric, the orbital velocity for a circular orbit with radius is given by the following formula: = where = is the ...
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
In the special case of perfectly circular orbits, the semimajor axis a is equal to the radius of the orbit, and the orbital velocity is constant and equal to = where: r is the circular orbit's radius in meters, This corresponds to 1 ⁄ √2 times (≈ 0.707 times) the escape velocity.
The innermost stable circular orbit (often called the ISCO) is the smallest marginally stable circular orbit in which a test particle can stably orbit a massive object in general relativity. [1] The location of the ISCO, the ISCO-radius ( r i s c o {\displaystyle r_{\mathrm {isco} }} ), depends on the mass and angular momentum (spin) of the ...
All bounded orbits where the gravity of a central body dominates are elliptical in nature. A special case of this is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M can be derived as follows:
Figure 1: Vector relationships for uniform circular motion; vector Ω representing the rotation is normal to the plane of the orbit. For motion in a circle of radius r , the circumference of the circle is C = 2 πr .
Or one can have a circular orbit at that radius. Or one can have an orbit that spirals down from that radius to the central point. The radius in question is called the inner radius and is between and 3 times r s. A circular orbit also results when is equal to , and this is called the outer radius. These different types of orbits are discussed ...
All attractive central forces can produce circular orbits, which are naturally closed orbits. The only requirement is that the central force exactly equals the centripetal force, which determines the required angular velocity for a given circular radius. Non-central forces (i.e., those that depend on the angular variables as well as the radius ...