Download KepLERS LAWS - DrGHonorsPhysics

KEPLERS LAWS
With some Law of Universal Gravitational Examples thrown in for good measure
How much would a 70.0-kg
person weigh on Mercury?
Explore Kepler’s Laws of Plenary
Motion on your own for a few
minutes
◦ http://www.regentsprep.org/Regents/physics/phys06/keplers/default.htm
Law 1: All planets move in elliptical
orbits with the sun as one focus
Anatomy of an Ellipse
An ellipse is defined as the set of points that
satisfies the equation:
R + R’ = 2a
F, F’ – Foci of the ellipse
A = semi major axis
B = semi minor axis
Eccentricity
◦ Eccentricity of an ellipse is the ratio
between the distance between the
foci and the major axis of the ellipse
◦ 𝐸𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑓𝑜𝑐𝑖
𝐿𝑒𝑛𝑔ℎ𝑡 𝑜𝑓 𝑚𝑎𝑗𝑜𝑟 𝑎𝑥𝑖𝑠 𝑜𝑓 𝑒𝑙𝑙𝑖𝑝𝑠𝑒
How to create an ellipse
Go to http://www.mathwarehouse.com/animated-gifs/images/how-to-create-anellipse-animation-of-locus-and-focus.gif
Law of Equal Areas
◦ When the planet is closer to the sun, it moves faster, sweeping through a longer path in
a given time.
Implications
◦ Although the orbit is symmetrical, the motion is
not The planet speeds up and slows down
along its orbit
◦ A planet speeds up as it approaches the Sun, gets
its greatest velocity when passing closest, then
slows down again.
◦ As the planet moves away from the Sun (or the
satellite from Earth), it loses energy by overcoming
the pull of gravity, and it slows down, like a stone
thrown upwards. And like the stone, it regains its
energy (completely--no air resistance in space) as it
comes back.
Perihelion and Aphelion
Kepler’s Third Law (Law of
Harmonics)
◦ The ratio of the square of the periods T of any two planets revolving about the Sun is
equal to the ratio of the cubes of the mean distances, s, from the Sun:
◦
𝑇1 2
𝑇2
=
𝑠1 3
𝑠2
◦ Note that s is the length of the Semi-Major Axis
Astronomical Units (AU)
◦ IF the distance from the earth to the Sun is set = 1, then we can scale distances relative
to the distance from this value
◦ Example
◦ Distance from Mercury to the Sun (59 x 106 km)
◦ Distance from Earth ot Sun (149.6 x106 km)
◦ If Earth to Sun = 1, Earth to Mercury = (59/149.6 = 0.39 AU)
Derivation of Kepler’s Laws
◦ Notes
Jupiter’s Moons
◦ Use graphic of Jupiter’s moons to confirm Kepler’s Third Law
General equation of an ellipse (for
you mathematicians in the group)