Download Kepler`s Second Law

2.3b illustrate Kepler’s second law of planetary motion with the aid of a
diagram
2.3c demonstrate an understanding of Kepler’s third law relating planetary
distances to orbital periods and perform simple calculations using the
formula:
T 2 = R3
where T is in years and R is in AU
Kepler’s Second Law
The Sun-planet line sweeps out equal areas in equal times
As a planet moves around the Sun, imagine a line joining the 2 objects (like their force of
attraction due to gravity). In a certain time, the line sweeps through a certain area of space.
Repeat the process at a different point in the orbit of the planet for the same length of time
and the line will sweep through the same amount of space as before.
PLANET ORBITS A SUN IN AN ELLIPTICAL PATH
The simulation from the University of Nebraska-Lincoln in the United States shows this
particularly well. Use the following link to load the Planetary Orbit Simulator:Kepler’s Second Law demonstration
http://astro.unl.edu/naap/pos/animations/kepler.swf
Simulation credit : University of Nebraska-Lincoln
Guides for use:Once loaded, click ‘Kepler’s 2nd Law’
Click ‘Start Sweeping’
Click ‘Start Sweeping’ when the planet is in a different part of its orbit around the Sun
The areas displayed in colour are equal, which is what is stated in Kepler’s 2nd Law. As the
planet gets closer to the Sun in its orbit, it will be moving faster due to the increased effects of
gravity. In a given time, the planet will travel further when it is closer to the Sun – but the area
of space the line passes through is going to be the same as the distance between the 2
objects is relatively small.
Once you are used to the simulation, other factors can be adjusted.
(Notice how the planet speeds up when it gets nearer to the Sun)
Kepler’s Third Law
Kepler's 3rd law - The orbital period of a planet squared is proportional to its
mean distance from the Sun cubed.
This can be put simply as:-
T2 = r3
where
T = the orbit (PERIOD) given in years
r = the mean distance from the Sun in Astronomical Units
1 and 2 are the orbiting bodies concerned in the calculation
(the size of the orbit's ellipse tells you how much time the planet takes to complete one orbit)
Calculations using Kepler’s 3rd Law
When Jeremiah Horrocks observed the transit of Venus in 1639, he realised that the timing of
the transit would allow the distance from the Sun to the Earth to be calculated accurately.
Weather conditions and other factors meant errors were made, but when the future transits
occurred, the distance was calculated more accurately. Once the distance of one planet was
accurately known, Kepler’s 3rd Law allowed the distances for the other planets in the Solar
System to be worked out.
Also, by knowing the length of time of an orbit, the distance of a planet could be worked out:-
T2 = r3
Saturn’s orbit is 29.5 years = T
T2 = 29.52 = 870.3
r3 = 870.3
r
= 9.5 AU
Saturn’s mean distance from the Sun = 9.5 AU
Kepler’s 3rd Law allows the distance of an exoplanet from its parent star to be worked out,
because the rotation period of the exoplanet can be observed and the distance from the
planet to its star can then be calculated.