Download Kepler`s first law is: The orbit of every planet is an ellipse

Kepler's first law is: The orbit of every planet is an ellipse with the Sun
at one of the two foci.
LEARNING OBJECTIVE [ edit ]
Apply Kepler's first law to describe planetary motion
KEY POINTS [ edit ]
An ellipse is a closed plane curve that resembles a stretched out circle (see. The Sun is at one
focus while the other focus has no physical significance. A circle is a special case of an ellipse
where both focal points coincide.
How stretched out an ellipse is from a perfect circle is known as its eccentricity: a parameter that
can take any value greater than or equal to 0 (a circle) and less than 1 (as the eccentricity tends to
1, the ellipse tends to a parabola).
Symbolically, an ellipse can be represented in polar coordinatesas: r
=
p
ϵ
1+ cos
θ , where (r, θ) are
the polar coordinates (from the focus) for the ellipse, p is the semi-latus rectum (see, and ε is the
eccentricity of the ellipse.
Perihelion is minimum distance from the Sun a planet achieves in its orbit and is given by rmin =
p
ϵ . Aphelion is the largest distance from the Sun a planet reaches in his orbit and is
1+
given by r
max
=
p
−ϵ
1
.
TERMS [ edit ]
semi-latus rectum
The latus rectum is a chord perpendicular to the major axis and passing through the focus. The
semi-latus rectum is half the latus rectrum. See distance p in.
eccentricity
The coefficient of variation between rmin and rmax: $\epsilon=\frac{r_{max}-r_{min}}
{r_{max}+r_{min}}$. The further appart the foci are, the stronger the eccentricity.
perihelion
The point in the elliptical orbit of a planet or comet etc. where it is nearest to the Sun. The point
farthest from the Sun is called aphelion.
Give us feedback on this content: FULL TEXT [edit ]
Kepler's First Law
Kepler's first law states that
The orbit of every planet is an ellipse
with the Sun at one of the two foci .
An ellipse is a closed plane curve that
resembles a stretched out circle (see ).
Note that the Sun is not at the center of
the ellipse, but at one of its foci (marked
with an "M" in the figure). The other focal
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point, f2, has no physical significance for the orbit. The center of an ellipse is the midpoint of
the line segment joining its focal points. A circle is a special case of an ellipse where both
focal points coincide.
Ellipses and Kepler's First Law
(a) An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two
foci (f1 and f2) is a constant. You can draw an ellipse as shown by putting a pin at each focus, and
then placing a string around a pencil and the pins and tracing a line on paper. A circle is a special
case of an ellipse in which the two foci coincide (thus any point on the circle is the same distance
from the center). (b) For any closed gravitational orbit, m follows an elliptical path with M at one
focus. Kepler's first law states this fact for planets orbiting the Sun.
How stretched out an ellipse is from a perfect circle is known as its eccentricity: a parameter
that can take any value greater than or equal to 0 (a circle) and less than 1 (as the eccentricity
tends to 1, the ellipse tends to a parabola). The eccentricities of the planets known to Kepler
varied from 0.007 (Venus) to 0.2 (Mercury). Minor bodies such as comets
an asteroids(discovered after Kepler's time) can have very large eccentricities. The dwarf
planet Pluto, discovered in 1929, has an eccentricity of 0.25.
Symbolically, an ellipse can be represented in polar coordinates as:
r =
p
ϵ
θ
1+ cos
,
where (r, θ) are the polar coordinates (from the focus) for the ellipse, p is the semi-latus
rectum (see ), and ε is the eccentricity of the ellipse. For a planet orbiting the Sun, r is the
distance from the Sun to the planet and θ is the angle between the
planet's current position and its closest approach, with the Sun as the vertex.
http://en.wikipedia.org/wiki/File:Ellipse_latus_rectum.PNG
Heliocentric coordinate system (r, θ) for ellipse. Also shown are: semi­major axis a, semi­minor axis
b and semi­latus rectum p; center of ellipse and its two foci marked by large dots. For θ = 0°, r =
rmin and for θ = 180°, r = rmax.
At θ = 0°, perihelion, the distance is minimum
rmin =
p
1+
ϵ.
At θ = 90° and at θ = 270°, the distance is p.
At θ = 180°, aphelion, the distance is maximum
p
rmax =
−ϵ
1
.
The semi-major axis a is the arithmetic mean between rmin and rmax:
rmax
−a=a−r
p
a =
−ϵ
1
2
min
.
The semi-minor axis b is the geometric mean between rmin and rmax:
r max
=
b
b
r min
p
b =
√1−ϵ
2
.
The semi-latus rectum p is the harmonic mean between rmin and rmax:
1
r min
−
1
p
=
1
p
−
1
r max
2
pa = rmax rmin = b
.
The eccentricity ε is the coefficient of variation between rmin and rmax:
ϵ=
r max
−r
min
r max +r min
.
The area of the ellipse is
A =
π ab .
The special case of a circle is ε = 0, resulting in r = p = rmin = rmax = a = b and A = π r2. The
orbits of planets with very small eccentricities can be approximated as circles.
Understanding Kepler's 3 Laws and Orbits
In this video you will be introduced to Kepler's 3 laws and see how they are relevant to orbiting
objects.