Kepler's equation - y coordinate
In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.
It was first derived by Johannes Kepler in 1609 in Chapter 60 of his Astronomia nova, and in book V of his Epitome of Copernican Astronomy (1621) Kepler proposed an iterative solution to the equation.The equation has played an important role in the history of both physics and mathematics, particularly classical celestial mechanics.
After getting the The 'eccentric anomaly’ E you can get the y coordinate from this formula.
The 'eccentric anomaly’ E is useful to compute the position of a point moving in a Keplerian orbit. As for instance, if the body passes the periastron at coordinates x = a(1 − e), y = 0, at time t = t0, then to find out the position of the body at any time, you first calculate the mean anomaly M from the time and the mean motion n by the formula M = n(t − t0), then solve the Kepler equation above to get E, then get the y coordinate from the equation shown here.Related formulas
|y||The y coordinate (m)|
|b||In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. For the special case of a circle, the semi-major axis is the radius. (m)|
|E||n orbital mechanics, eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit. The eccentric anomaly is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the true anomaly and the mean anomaly. (degree)|