Orbits of the Planets, Asteroids and Comets

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Orbits of the Planets, Asteroids and Comets
Keplers 1st Law tells us that The orbits of the
planets are ellipses with the Sun at one focus.
Perihelion, P
Sun
Aphelion, A
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Orbits of the Planets, Asteroids and Comets
Keplers 1st Law tells us that The orbits of the
planets are ellipses with the Sun at one focus.
Ellipse
eccentricity - e
foci


e
F
2
2a
major axis 2a a sem-major axis
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The closer the eccentricity is to 0 the closer
the ellipse is to a circle.
Pluto e ..2484
Sedna e .73
A circle has e 0
A straight line e 1 and is a degenerate
parabola
A parabola e1
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Note The sum of the distances from
the foci to the planet (anywhere on

the ellipse is 2a.
empty focus
F
F
2
1
Perihelion, P
Aphelion, A
Distance between the 2 foci
major axis
semimajor axis,
a
semimajor axis,
a
Also we can write
By definition
A - P 2ae
eccentricity, e

from the definition of eccentricity
2a
Adding the above equation to
Observe Dividing the 2
equations
A P 2a -gt
A a(1e) and if
and substituting
e, yields

A - P
we subract we obtain

P a(1-e)
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Why is the Loop a(1e) and the Foci, Pin, Spacing
2ae?
Because the distance from one focus to any point
on the ellipse and back to the other focus is A
P or 2a And the distance between the foci is A -
P which is 2ae.
Total loop length is 2a 2ae 2a(1e). So
place the pins half that distance, a(1e). apart
to construct the loop. And 2ae apart to draw the
loop.

empty focus
F
1
F
2
Perihelion, P
Aphelion, A
Distance between the 2 foci
A - P 2ae
major axis
semimajor axis,
a
semimajor axis,
a
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Although the Orbits of the Planets are
Ellipses, sometimes we can use a
circle to approximate the ellipse (draw a
circle with the center on the Sun, and so Sun
centered)