Vaisakhan Thampi D S
AASTRO-Kerala
• The stars move in the sky but
not with respect to each other
• The planets (or “wanderers”)
move differently from stars
– They move with respect to the
stars
– They exhibit strange retrograde
motion
• What does all this mean?
• How can we explain these
movements?
A flash back of Astronomy…
Aristotle
(BC 384-322)
Earth is round
Earth is the center of Universe
Stars are all stationary
Celestial bodies are made up of immortal aether
Universe above moon is different from Universe
below moon
First Heliocentric theory
Aristarchus
(BC 310-230)
A flash back of Astronomy…
Ptolemy
(AD 90-168)
Earth is the centre
A flash back of Astronomy…
Earth is thrown out from the throne!
Concluded that Earth is a planet.
Proposed a model of the solar
system with the sun at the center
Copernicus
1473-1543
Heliocentric model
De revolutionibus Orbium Celestium
A flash back of Astronomy…
Along the way of Copernicus
Many objects in the sky like earth
Sun is just one among many other stars
Giordano Bruno
(1548-1600)
All other stars are just like our sun
Burned alive for what he said!
A flash back of Astronomy…
Designed and built instruments to
measure the locations of the heavenly
bodies.
Observations, especially of Mars, were
far more precise than any made
previously.
Tycho Brahe
1546-1601
Father of Observational Astronomy
A flash back of Astronomy…
Planetary laws
Johannes Kepler
1571-1630
1. The orbit of every planet is an ellipse
with the Sun at one of the two foci.
2. A line joining a planet and the Sun
sweeps out equal areas during equal
intervals of time.
3. The square of the orbital period of a
planet is directly proportional to the
cube of the semi-major axis of its orbit.
A flash back of Astronomy…
Described the behavior of moving objects.
Developed his own telescope and made
important discoveries:
Galileo Galilei
1564-1642
1. Four satellites, or moons, orbit Jupiter.
2. Planets are circular disks, not just points
of light.
3. Venus has phases just like the moon.
4. The moon’s surface is not smooth.
5. The sun has sunspots, or dark regions.
In the year Galileo died,
On a Christmas day….
Isaac Newton
(1642-1727)
The legendary Apple!
The Apple & The Moon
Isaac Newton realized that the motion of a
falling apple and the motion of the Moon
were both actually the same motion, caused
by the same force - the gravitational force.
Centripetal force
Newton’s deductions from Kepler’s laws
Law of areas is a consequence of force acting
towards sun
Third law is a consequence of the fact that
farther the object, weaker the force
When two planets at different distances are
compared, the force is inversely proportional
to the square of its distance
Newton’s laws of Motion
• 1st Law
– A body at rest, or in uniform motion, will remain
so unless acted upon by an unbalanced force.
• 2nd Law
– The change in motion (acceleration) is
proportional to the unbalanced force
• 3rd Law
– For every action there is an equal and opposite
reaction
1. Earth’s circumference, originally estimated by
Eratosthenes (about 200BC), and improved by
French surveyors during Newton’s lifetime.
Their best value, in today’s units,
69.2miles/degree = 69.2 x 360 miles
= 24900miles = 40 100km.
This implies a radius (Re) of 6380km.
Fact 2
The Moon’s distance from Earth(radius of Moon’s orbit, Rmo)
Estimated by Aristarchus and Hipparchus
Using the size of the shadows during a lunar eclipse, they
found the Moon’s distance, Rmo to be about 60 x Earth’s
radius, 60Re.
i.e., about 60 x 6380 = 383000km = 3.83 x 108m
Fact 3
Length of a lunar month
(time taken for Moon to make one complete orbit)
=27.32 days = 27.32 x 24 x 3600 sec
= 2.36 x 106seconds.
This is easily measured by counting the number of days
taken for several lunar months.
Fact 4
Acceleration of falling objects on Earth = 9.8m/s2
Estimated by Galileo
Idea 1
The force used to keep an object rotating in
a circle depends on the object’s speed and
the circle’s radius in this way:F = m v2 / r
This implies that the centripetal acceleration
(directed towards the centre on the circle)
is equal to v2 / r.
This was proved in
Newton’s Principia.
This is his own copy.
Possibly the first proof.
Idea 2
The Moon is in orbit around the Earth because
gravity supplies this centripetal force.
Why doesn’t moon fall to earth?
• Of course it does!
• But the surface of earth falls down as the
moon falls down
• So it never reaches the ‘ground’
There are two places where we can
compare the Earth’s gravitational field:
One at the Earth’s surface and the other at
the orbit of the Moon.
This uses idea 3.
Idea 3
The force is inversely proportional to the square
of the distance from source and force is
proportional to acceleration
1 / (radius of Earth)2
1/ (radius of Moon’s orbit) 2
ge =
gm
=
(radius of Moon’s orbit) 2
(radius of Earth) 2
= Rmo2 / Re2
Rearranging slightly
ge = Rmo2 x centripetal accn of Moon(gm)
Re2
To get a numerical value for ge, all we
need to do is to insert the centripetal
acceleration from Idea 1 and the known
value of the ratio of the orbital sizes (60/1).
Idea 1
Centripetal accn of Moon = v2 / Rmo
First - the Moon’s velocity, v,
= circumference of Moon’s orbit
time for one revolution
= 2πRmo / 2.36 x 106 = 1019m/s
and, second, the accn of Moon,
gm =
v2
Rmo
= 10192 = 1.038x106
Rmo
Rmo
= 1.038x106 / (60 x Re)
= 1.038x106/(60 x 6.38 x 106)
gm = 0.00271m/s2
Now we can substitute this into our
expression for ge
ge = Rmo2 x gm
Re2
where Rmo2 / Re2 = 602
and so, finally,
ge = 602 x 0.00271m/s2
ge = 9.8m/s2
Universal Gravitation
Newton realized that gravity was a universal
force acting between any two objects.
It has become the ‘Universal Law of Gravitation’
The Universal Law of Gravitation is formulated as
F = Gm1m2/r2
G = 6.67 x 10-11 N m2/kg2
Gravity is too weak a force that the entire
mass of earth is required to pluck a
ripened apple from the tree!
Occurrence of tides
Spherical Shape of Earth
Prediction of Neptune
Binary Stars
Globular Star Cluster
Shape of Galaxies
Star formation
The universe is so beautiful,
you just have to look at it.