June 01, 2018 Friday
Bedtime Story
The Big Splash
When the giant protoplanet Theia had struck
our newly formed Earth, part of its iron core would have got merged with our
young earth’s core, and yet because of the collision being perhaps tangential a
sizable portion of the mantle of both the earth and that of Theia would have
got ejected out and would have found itself trapped in the orbit around our
planet.
This happens whenever the velocity of a
missile leaving planet earth falls between orbital velocity and the escape
velocity as it would have happened with this large chunk that got released post
“Big Splash”.
So this chunk that got discharged out
violently after the big hit along with other material floating around Earth’s
orbit coalesced into to what we see every day as our Moon.
Yet my chief point was not the explanation
of the origins of the moon, but the fact that such as impact greatly added to
Earth both mass and angular momentum and immediately after the impact our Earth
was spinning so rapidly that a day was merely 5-hour long.
So when it comes to earth, even though the
law of conservation of angular momentum is applicable, it is only approximately
applicable.
Earth’s rotation has slowly but certainly
has been slowing over time, at a miniscule rate of 2.3 milliseconds per century
since the 8th century AD (gleaned from the study of historical
astronomical records).
We may not be very sure of the earlier rate
of slowing down but surely it had always been slowing at some rate.
The main cause for slowing down the Earth’s
rotation (and nothing much else as there isn’t any air around Earth to induce
friction) and thereby prolonging our days is the tidal effects the moon has
over the Earth’s rotation.
There is a mention of this fact in Newton’s
Principia when he was giving some examples of the First Law of motion:
“A top, whose parts by their cohesion are
perpetually drawn aside from rectilinear motions, does not cease its rotations,
otherwise than as it is retarded by the air.
The greater bodies of the planets and
comets, meeting with less resistance in more free spaces, preserve their
motions both progressive and circular for a much longer time.”
The Moon and the Earth for several
practical reasons can be considered as an isolated two-body system exerting
gravitational torque on each other, resulting in transfer of angular momentum
and energy, even though as a whole they are conserved.
So what happens in this two-body system is
that the gravitational torque leads Earth to lose energy thereby reducing its
angular momentum and prolonging its day with the Moon gaining energy and
getting elevated to higher orbit distancing itself from Earth.
These two processes have been going on for
4.5 billion years, almost from the time of formation of the Solar System, and
this is doubly confirmed from the geological and paleontological evidence that
Earth really did rotate faster and the Moon was indeed closer before.
All this was an interesting detour from the
law of conservation of angular momentum which was our primary area of storytelling
to its applicable to the Earth’s rotation.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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