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§ 236]
Variation of the Elements
303
in an elliptic orbit. For wherever a planet may be, and whatever (within certain limits[1]) be its speed or direction of motion some ellipse can be found, having the sun in one focus, such that the planet can be regarded as moving in it for a short time. Hence as the planet describes a perturbed orbit it can be regarded as moving at any instant
Fig 81.—A varying ellipse.
in an ellipse, which, however, is continually altering its position or other characteristics. Thus the problem of discussing the planet's motion becomes that of determining the elements of the ellipse which represents its motion at any time. Euler shewed further how, when the position of the perturbing planet was known, the corresponding
- ↑ The orbit might be a parabola or hyperbola, though this does not occur in the case of any known planet.
