Orbital Dynamics Part 01 First Discoveries

Welcome to orbital dynamics. This is a multi-part course on the basics of orbital dynamics. The orbital dynamics
or orbital mechanics textbooks assumefamiliarity with calculus and all the
algebra and trig that goes along with that. They also assume familiarity with
physics–mechanics primarily. I learned orbital dynamics well after college and didn’t remember any of my math . . . collegemath or physics I had to relearn the
basics and out of that developed this course. In this course I go over all the
math and physics you’ll need tocomprehend the more advanced concepts. None of this is very complicated and evenwhat it is I try to present the material
in an accessible way with lots of animations. I take you through all the
algebraic steps in the mathematicalderivations and unlike the textbooks,
which have to conserve space,I don’t skip steps. You can get a lot out of this course if you just listen to thelectures however if you really want to
learn the material I recommend you doyour own calculations and do the
algebraic derivations yourself. Along the way I’ll teach you how to do the
calculations and will introduce you tothe tools I use to develop this course. I teach a lot of history in this course. If you understand the foundationaldiscoveries behind the laws of physicsand mathematical formalisms you get abetter intuition for how the math and physics work. I start with the ancient Greeks and go forward in time toKepler, Galileo, Newton, Einstein and beyond. Most of the foundations of orbital dynamics involvesphysics and astrophysicsso I touch on astronomy as well. This course is called orbital dynamicsas opposed to orbital mechanics. The terms are synonymous in the way we use them. Mechanics is the branch of applied maththat deals with motion and forces
producing motion. Dynamics is a branch of mechanics concerned withmotion of
bodies under the action of forces. The other part of mechanics of staticswhich is the branch of mechanics concernedwith bodies at rest and forces in equilibrium. This course deals mostly with dynamicsand a bit with statics. Orbiting bodies at least the interestingparts are dynamic systems. The key discoveries that led to the theories oforbital motions started with the study
of orbiting planets. Ancient astronomers noticed that certain
lights, as they called them, moved acrossthe sky differently from stars. This animation is the path of Mars againstthe stellar background from mid-october
1996 to late July in 1997. Stars move east to west as the Earth rotates. This is what they look like in the night sky sped up considerably. There were five of
their objects that also went east towest in the night sky but against the
stellar background they tended to traveltravel eastward then westward then eastward. Like I showed you before this is Mars plotted againstthe stellar background. It travels across the night sky fromeast to west with the rest of the stars
but if you look closely it moves slightly eastward. At some point it drifts slightly in the oppositedirection westward and then it goes
eastward again. The Greeks called these lights Wanderers or by their Greek name planetoi. That’s how the word planet was derived. There are five planets that can be seen by the naked eye Mercury, Venus, Mars, Jupiter, and Saturn. Uranus can be seen if you know where to look but itdoesn’t move that much against the
stellar background. It was missed by the ancients. Astronomers like Copernicus, Tycho Brahe, and Johannes Kepler studiedthe motions of planets and from that
developed theories that explain the motions. This is where orbital dynamics got its start. in this animation I’m showing motions of Mars, Earth,Venus, and Mercury relative to the Sun. This is how we understand these motions today but
we’re getting ahead of ourselves. it took the ancients thousands of years
to work out this motion planet’s orbitnaturally the study of orbital dynamics
enables us to understand how they orbitif that’s all over Thomas was meant for
it would be part of astronomy IsaacNewton realized that an artificial
satellite could be put into orbit aroundthe Earth as this animation shows if you
throw a rock fast enough it will circlethe Earth endlessly much of what we use
orbital dynamics for deals with man-madesatellites the pictures on the right or
man-made satellites Sputnik on the topthe first
man-made satellite to orbit the Earthand the international space station on
the bottom probably the biggest thingwe’ve ever put in orbithere’s the movie by Stuart gray that
depicts the number of satellitesorbiting the Earth from 1957 when the
first satellite was launched to 2015 in1957 the Soviet Union launched Sputnik
the first man-made satellite put inEarth orbit back man there were only 48
US states Eisenhower was president andbefore it was launched there were no
man-made objects in space in 1958 theu. s. launched its own satellite Vanguard
1 and it’s still up there since 195730,000 objects have been launched
there’s now about 20,000 objects largerthan 10 centimeters still in orbit and
about 3,000 are operational this depictsgraphically how many man-made objects
orbit the earth the dots however not inproper perspective if they were their
actual if they were their actualrelative size you wouldn’t see them well
there’s a lot of stuff in orbit it’s allvery small relative to the earth why
send satellites into space space offersa unique perspective at high altitudes
and you’re above the atmosphere whichhas certain advantages this is a map of
the electromagnetic spectrum much ofwhat’s done in space involves
transmitting and receivingelectromagnetic energy the radio
frequency part of the electromagneticspectrum is in the area depicted by the
red line I just drew these frequenciespass almost transparently through the
atmosphere these are the frequenciesused for communications space is an
excellent place for worldwidecommunications this is most of what’s
done by satellites in space they’reparts of the electromagnetic spectrum
that are blocked by the atmospherethat’s shown in these regions looking
from the earth and into space you can’tsee infrared radiation very well same
goes with x-rays we place satellitesabove the atmosphere so we can see these
parts of the electromagnetic spectrumthat get blocked by the atmosphere and
these frequencies we can learn a lotabout the universe space-based senses
looking inward can send energy in andmeasure what is reflected back because
the chemical composition of theatmosphere
part of the allure of theelectromagnetic spectrum these
satellites can sense the composition ofthe atmosphere here are a few examples
of satellites that operate above theatmosphere the Chandra x-ray Observatory
and Hubble Space Telescope infraredsensors enable the discovery of a
supermassive black hole at the centre ofour galaxy ground-based telescopes
couldn’t have done that infraredradiation doesn’t penetrate our
atmosphere the new James Webb SpaceTelescope will operate mainly in the
infrared spectrum it will be able to seethe distant edge of the universe within
400 million of a 13. 8 billion life ofthe universe probes can travel well
beyond Earth orbit to get a closer lookat planets comets and distant celestial
objects ground telescopes can never seethe kind of detail these probes collect
here are before-and-after images ofPluto and its moon Charon the left was
taken with the Hubble Space Telescopethe right was taken with the NASA New
Horizons spacecraft in 2015 New Horizonsgot 12,000 472 kilometers from the
surface of Pluto let’s go back toprehistoric times people they were
familiar with the Sun the moon and thestars the stars moved across the night
sky the Sun and Moon Rose is sent everyday but at different times these are the
first observations that while intuitivetoday ultimately led to the discoveries
that resulted in the formalisms oforbital dynamics things were in motion
in the heavens that inspired astronomersand physicists to try to measure and
characterize these motions there’s nowritten record of this but it wouldn’t
be that far-fetched to believe thatancient peoples thought that the Sun
went out each night and before it rosein the morning some God rekindle the
fire today we know this isn’t true theSun that rises each morning is the same
Sun that rose the day before it’sconceivable that the first astronomical
discovery was that the big bright thingin the sky that came up each morning and
set each evening and then came up thenext day
was the same thing the moon goes throughphases ancient people who kept records
realized they cycled every twenty nineto thirty days twenty nine point five
three days to be exact the phases of theMoon are caused by his proximity with
both the earth and the Sun ancientastronomers didn’t realize this for many
years those who live away from theequator would have observed dramatic
seasonal changes that was close to theequator less so people in higher
latitudes for people at higher latitudeslife adapted in a yearly rhythm with the
cycle of the seasons those who werekeeping good records realized that the
cycle repeats every 365 days or 365. 2422be exact the cleverer ones developed
systems for predicting the timing of theseasons which is a big aid to
agriculture stars appeared to theancients and even to us as a projection
on a celestial sphere with the Starsfixed and the earth rotating within
within the celestial sphere stars weregrouped into constellations each
representing a portion of the sky starpatterns in the constellations were
associated with shapes like a fish forPisces a hunter for Orion or a crab for
cancer in 1922 Henry Norris Russellhelped the International Astronomical
Union in organizing the celestial sphereinto 88 official constellations that
account for every star ancientastronomers notice that the
constellations shifted over the earlycycle at time some weren’t visible the
Sun gets in the way it obstructs adifferent part of the celestial sphere
during various times of the year afterthe Sun and the moon venus is the
brightest object in the skyit was popularly thought to be two
separate stars phosphorus in the morningand Hesperus in the evening Pythagoras
was Leone and Greek philosopher andmathematician best known for the
Pythagorean theorem he was also one ofthe first to realize that the bright
evening star was the same as the brightmorning star while Pythagoras put this
theory forward it took thousands ofyears
confirm it many remain steadfast intheir belief that Venus in the morning
and Venus in the evening were twoseparate stars by the way if you see
Venus in the morning you’ll never see itin the evening and vice versa that’s
what gave Pythagoras the clue that thesetwo were the same star three ancient
Pythagorean Greeks proposed that themotion of the stars was apparent that it
was created by the rotation of the earthon an axis this contradicted the model
that many believed that the earth wasfixed many who disputed the rotating
earth asked if the earth spun on an axiswhy don’t objects fly off
why don’t we feel the spin why aren’ttheir massive winds all the time we know
today that the rotation of the earthwell measurable is too subtle for us to
feel the Jetstream buzz winds from westto east if the ancients had gone high
enough they would have known this on thesurface of our planet there’s friction
we either feel the light breeze is stillthere it only occasionally gets windy we
don’t fly off of spinning earth becauseof a combination of momentum and gravity
if the earth spun faster and we’d likelyfly off but it would have to be very
fast from this section we’ve learnedthat the stars move across the sky from
east to west the earth spins with a kindof within a kind of celestial sphere the
seasons change over the year the moongoes through phases five apparent stars
move against the stellar background theSun that rises today is the same one
that rose yesterday and that the morningand evening stars are in fact one star
these are some of the key discoveries

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