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—6 October 2015). Orbiting Jupiter (1st, hc ed.). Houghton Mifflin Harcourt. ISBN 978-0-544-46222-9. Archived from the original on 14 May 2018; (2015). Orbiting Jupiter (eBook ed.). Houghton Mifflin Harcourt. ISBN 978-0-544-46264-9.; — (December 2015). Orbiting Jupiter (1st UK ed.). Andersen Press. ISBN 978-1783443949.; Characters. Key children. Joseph Brook – 14-year-old father, served ...
The orbits are ellipses, with foci F 1 and F 2 for Planet 1, and F 1 and F 3 for Planet 2. The Sun is at F 1. The shaded areas A 1 and A 2 are equal, and are swept out in equal times by Planet 1's orbit. The ratio of Planet 1's orbit time to Planet 2's is (/) /.
If k 2 is greater than one, F 2 − F 1 is a negative number; thus, the added inverse-cube force is attractive, as observed in the green planet of Figures 1–4 and 9. By contrast, if k 2 is less than one, F 2 − F 1 is a positive number; the added inverse-cube force is repulsive , as observed in the green planet of Figures 5 and 10, and in ...
Because SparkNotes provides study guides for literature that include chapter summaries, many teachers see the website as a cheating tool. [7] These teachers argue that students can use SparkNotes as a replacement for actually completing reading assignments with the original material, [8] [9] [10] or to cheat during tests using cell phones with Internet access.
and are the masses of objects 1 and 2, and is the specific angular momentum of object 2 with respect to object 1. The parameter θ {\displaystyle \theta } is known as the true anomaly , p {\displaystyle p} is the semi-latus rectum , while e {\displaystyle e} is the orbital eccentricity , all obtainable from the various forms of the six ...
It was derived by Johannes Kepler in 1609 in Chapter 60 of his Astronomia nova, [1] [2] and in book V of his Epitome of Copernican Astronomy (1621) Kepler proposed an iterative solution to the equation. [3] [4] This equation and its solution, however, first appeared in a 9th-century work by Habash al-Hasib al-Marwazi, which dealt with problems ...
In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (from Ancient Greek ἐπίκυκλος (epíkuklos) 'upon the circle', meaning "circle moving on another circle") [1] was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets.
An elliptic Kepler orbit with an eccentricity of 0.7, a parabolic Kepler orbit and a hyperbolic Kepler orbit with an eccentricity of 1.3. The distance to the focal point is a function of the polar angle relative to the horizontal line as given by the equation ( 13 )