Y-coordinate of Keplerian Orbit

This calculator computes the Y coordinate of a body moving in a Keplerian orbit, using Kepler's equation. Kepler's equation is fundamental in the field of orbital mechanics, relating various geometric properties of orbits. 
CalculationInputs﻿﻿b
:1.500e+11m​
﻿
﻿﻿E
:56.00deg​
﻿
Output﻿﻿y
:1.244e+11m​
﻿
﻿﻿y=b×sin(E)
﻿
Where:
﻿﻿y
 is the y-coordinate of the body's displacement along the minor axis of it's elliptical path (﻿m
).
﻿﻿b
 is the semi-minor axis, which is half of the smaller diameter of the elliptical orbit, and is also the radius of the auxiliary circle. It defines the maximum extent of the orbit along its minor axis (﻿m
).
﻿﻿E
 is the eccentric anomaly, an angular measurement that, unlike the true anomaly, does not directly correlate with the object's position (﻿degrees
).
ExplanationDerived by Johannes Kepler in the early 17th century, Kepler's equation enables the calculation of the position of celestial bodies subject to central forces, using the 'eccentric anomaly' E. 
The Y-coordinate of a body moving in a Keplerian orbit, is a measure of the body's position along the minor axis of its elliptical path. 
﻿
Parameters in Kepler's equation for the y-coordinate of an elliptical orbit
Kepler's approach to celestial mechanics revolutionized our understanding of planetary motion, emphasising the elliptical nature of orbits rather than circular. 
ApplicationsAstrophysics and Celestial Navigation: For predicting the positions of planets, stars, and artificial satellites, enabling navigation and the planning of space missions.
Satellite Deployment and Space Exploration: Accurate orbit predictions are crucial for the deployment of satellites and the trajectory planning of space exploration missions.
Astronomical Studies: For the study of comets, asteroids, and other celestial bodies, providing insights into their origins and behavior.
Related ResourcesKepler's First Law Calculator
Kepler's Third Law Calculator
Check out our full library of CalcTree templates here!
ReferencesPerryman, M. (2018). The Exoplanet Handbook (2nd ed.). Cambridge University Press.
Curtis, H.D. (2020). Orbital Mechanics for Engineering Students (4th ed.). Elsevier.
Danby, J.M.A. (1988). Fundamentals of Celestial Mechanics (2nd ed.). Willmann-Bell, Inc.
Murray, C.D., & Dermott, S.F. (1999). Solar System Dynamics. Cambridge University Press.