devising the most
available before the
invention of the
Initially Tycho designed
a zodiacal armillary
sphere, which could be
used to obtain the
ecliptic co-ordinates of
(celestial longitude and
without any calculation.
His observations of planetary motion,
particularly that of Mars, provided crucial
data for later astronomers like Kepler to
construct our present model of the solar
Brahe proposed a model of the solar
system that was intermediate between the
Ptolemaic and Copernican models (it had
the Earth at the center).
It proved to be incorrect, but it was the
most widely accepted model of the Solar
System for the time.
Adhered to Copernicus
theories and as a result
he was brought forward in
1633, and, there, in front
of his “betters,” he was,
under the threat of torture
and death, forced to his
knees to renounce all
belief in Copernican
theories, and was
thereafter sentenced to
imprisonment for the
remainder of his days.
5. Kepler (1571 – 1630)
Developed the 3 laws
on planetary motion.
Described how planets
moved around the sun.
1st Law (Eccentricity):
The orbit of each planet is the shape of an
ellipse (oval –shaped) with the sun located at
one focus. (There are 2 foci in an ellipse).
Ellipses can have different shapes, usually characterized by their "eccentricity." A circle
is a special case of an ellipse. It has zero eccentricity.
When planet is at its farthest point from
the sun. 93 million miles!!!
When a planet is at its closest point from
the sun. 91 million miles!!!
2nd Law (Law of Equal Areas):
In any time interval, a line from a planet to the
sun will sweep out equal areas.
NOTE: As the planet goes around the sun, the
further away it is, the slower it ORBITS. This is
due to the gravitational attraction between the
Sun and Earth.
A planet sweeps out at equal amounts of area in
equal amounts of time.
Planet will “sweep”
Time: AB = CD
Planet will “sweep”
Gravity gets stronger as the planets come “near” the sun.
Universal Gravitational Law
Example: There are 2 objects in space. One is
50 kg and another is 65 kg. They are 12 m
apart. What is the gravitational force between
6.67300 × 10-11 [(50 kg)(65 kg)]
1.505 x 10-9 N
Basically, a) the bigger the object, the stronger the
gravity and b) the closer the object, the stronger
3rd Law (Law of Harmonies)
The ratio of the squares of the
periods of any two planets is
equal to the ratio of the cubes of
their average distances from the
sun. P2 = a3
P = time2 it takes to go around
Using the 3rd Law (write out):
We can use the 3rd law to find:
Distance from sun.
Orbital period of a planet.
Jupiter’s average distance from the sun is
5.20 AU. What is its orbital period?
If a = 5.20, then a3 = 140.6.
Use formula: P2 = a3
The orbital period must be the square root
of 140.6, which equals about 11.8.
Let’s try… Determine the orbital period:
P2 = a3