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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 ...
The X/Y plane coincides with Earth's equatorial plane, with the +X axis pointing toward the vernal equinox and the Y axis completing a right-handed set. The ECI reference frame is not truly inertial because of the slow, 26,000 year precession of Earth's axis , so the reference frames defined by Earth's orientation at a standard astronomical ...
Since the motion of a particle under a central force always lies in a plane, the position of the particle can be described by polar coordinates (r, θ 1), the radius and angle of the particle relative to the center of force (Figure 1). Both of these coordinates, r(t) and θ 1 (t), change with time t as the particle moves.
Velocity and acceleration in non-uniform circular motion. In non-uniform circular motion, an object moves in a circular path with varying speed. Since the speed is changing, there is tangential acceleration in addition to normal acceleration. The net acceleration is directed towards the interior of the circle (but does not pass through its center).
The state of an orbiting body at any given time is defined by the orbiting body's position and velocity with respect to the central body, which can be represented by the three-dimensional Cartesian coordinates (position of the orbiting body represented by x, y, and z) and the similar Cartesian components of the orbiting body's velocity.
For example, the Schwarzschild radius r s of the Earth is roughly 9 mm (3 ⁄ 8 inch); at the surface of the Earth, the corrections to Newtonian gravity are only one part in a billion. The Schwarzschild radius of the Sun is much larger, roughly 2953 meters, but at its surface, the ratio r s / r is roughly 4 parts in a million.
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.
Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle ) is called the reference plane (sometimes fundamental plane ).