Calculus, With Applications; An Introduction to the Mathematical Treatment of Science
Calculus, With Applications; An Introduction to the Mathematical Treatment of Science
Ellen Hayes
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The planets revolve around the sun in ellipses, and these ellipses are, as a rule, characterized by small eccentricities. Thus the eccentricity of the earth's orbit is at present 0.01677. Of all the major planets Mercury has the most elliptic orbit, its eccentricity being 0.2056. The orbits of comets, on the other hand, may be described as parabolic, by which v^e mean that they are either ellipses of great eccentricity (almost unity), or hyperbolas whose eccentricity differs but little from uni...ty. In many cases the eccentricity cannot be found to differ from unity ; the orbit is then of course described as a parabola. Of the periodic comets which have been observed at more than one perihelion passage, Tempel's comet has the least eccentricity, namely : 0.4051. 92. In putting r^ and r^ equal to a(l + e) and a(l — e) respectively, the argument has much the air of begging the question, seeming to assume that the orbit is a conia section and then using the assumption in the proof. But it is to be noted that when we adopt the expres- sions a(l + e) and a(l — e), e does not mean eccentri- city, neither does a mean semi-major axis.
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