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 assume familiarity 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 … college math 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 to comprehend the more advanced concepts. None of this is very complicated and even what 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 mathematical derivations 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 the lectures however if you really want to learn the material I recommend you do your own calculations and do the algebraic derivations yourself. Along the way I’ll teach you how to do the calculations and will introduce you to the tools I use to develop this course. I teach a lot of history in this course. If you understand the foundational discoveries behind the laws of physics and mathematical formalisms you get a better intuition for how the math and physics work. I start with the ancient Greeks and go forward in time to Kepler, Galileo, Newton, Einstein and beyond. Most of the foundations of orbital dynamics involves physics and astrophysics so I touch on astronomy as well. This course is called orbital dynamics as opposed to orbital mechanics. The terms are synonymous in the way we use them. Mechanics is the branch of applied math that deals with motion and forces producing motion. Dynamics is a branch of mechanics concerned with motion of bodies under the action of forces. The other part of mechanics of statics which is the branch of mechanics concerned with bodies at rest and forces in equilibrium. This course deals mostly with dynamics and a bit with statics. Orbiting bodies at least the interesting parts are dynamic systems. The key discoveries that led to the theories of orbital motions started with the study of orbiting planets. Ancient astronomers noticed that certain lights, as they called them, moved across the sky differently from stars. This animation is the path of Mars against the 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 to west in the night sky but against the stellar background they tended to travel travel eastward then westward then eastward. Like I showed you before this is Mars plotted against the stellar background. It travels across the night sky from east 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 opposite direction 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 it doesn’t move that much against the stellar background. It was missed by the ancients. Astronomers like Copernicus, Tycho Brahe, and Johannes Kepler studied the 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 orbit naturally the study of orbital dynamics enables us to understand how they orbit if that’s all over Thomas was meant for it would be part of astronomy Isaac Newton realized that an artificial satellite could be put into orbit around the Earth as this animation shows if you throw a rock fast enough it will circle the Earth endlessly much of what we use orbital dynamics for deals with man-made satellites the pictures on the right or man-made satellites Sputnik on the top the first man-made satellite to orbit the Earth and the international space station on the bottom probably the biggest thing we’ve ever put in orbit here’s the movie by Stuart gray that depicts the number of satellites orbiting the Earth from 1957 when the first satellite was launched to 2015 in 1957 the Soviet Union launched Sputnik the first man-made satellite put in Earth orbit back man there were only 48 US states Eisenhower was president and before it was launched there were no man-made objects in space in 1958 the u.s. launched its own satellite Vanguard 1 and it’s still up there since 1957 30,000 objects have been launched there’s now about 20,000 objects larger than 10 centimeters still in orbit and about 3,000 are operational this depicts graphically how many man-made objects orbit the earth the dots however not in proper perspective if they were their actual if they were their actual relative size you wouldn’t see them well there’s a lot of stuff in orbit it’s all very small relative to the earth why send satellites into space space offers a unique perspective at high altitudes and you’re above the atmosphere which has certain advantages this is a map of the electromagnetic spectrum much of what’s done in space involves transmitting and receiving electromagnetic energy the radio frequency part of the electromagnetic spectrum is in the area depicted by the red line I just drew these frequencies pass almost transparently through the atmosphere these are the frequencies used for communications space is an excellent place for worldwide communications this is most of what’s done by satellites in space they’re parts of the electromagnetic spectrum that are blocked by the atmosphere that’s shown in these regions looking from the earth and into space you can’t see infrared radiation very well same goes with x-rays we place satellites above the atmosphere so we can see these parts of the electromagnetic spectrum that get blocked by the atmosphere and these frequencies we can learn a lot about the universe space-based senses looking inward can send energy in and measure what is reflected back because the chemical composition of the atmosphere part of the allure of the electromagnetic spectrum these satellites can sense the composition of the atmosphere here are a few examples of satellites that operate above the atmosphere the Chandra x-ray Observatory and Hubble Space Telescope infrared sensors enable the discovery of a supermassive black hole at the centre of our galaxy ground-based telescopes couldn’t have done that infrared radiation doesn’t penetrate our atmosphere the new James Webb Space Telescope will operate mainly in the infrared spectrum it will be able to see the distant edge of the universe within 400 million of a 13.8 billion life of the universe probes can travel well beyond Earth orbit to get a closer look at planets comets and distant celestial objects ground telescopes can never see the kind of detail these probes collect here are before-and-after images of Pluto and its moon Charon the left was taken with the Hubble Space Telescope the right was taken with the NASA New Horizons spacecraft in 2015 New Horizons got 12,000 472 kilometers from the surface of Pluto let’s go back to prehistoric times people they were familiar with the Sun the moon and the stars the stars moved across the night sky the Sun and Moon Rose is sent every day but at different times these are the first observations that while intuitive today ultimately led to the discoveries that resulted in the formalisms of orbital dynamics things were in motion in the heavens that inspired astronomers and physicists to try to measure and characterize these motions there’s no written record of this but it wouldn’t be that far-fetched to believe that ancient peoples thought that the Sun went out each night and before it rose in the morning some God rekindle the fire today we know this isn’t true the Sun that rises each morning is the same Sun that rose the day before it’s conceivable that the first astronomical discovery was that the big bright thing in the sky that came up each morning and set each evening and then came up the next day was the same thing the moon goes through phases ancient people who kept records realized they cycled every twenty nine to thirty days twenty nine point five three days to be exact the phases of the Moon are caused by his proximity with both the earth and the Sun ancient astronomers didn’t realize this for many years those who live away from the equator would have observed dramatic seasonal changes that was close to the equator less so people in higher latitudes for people at higher latitudes life adapted in a yearly rhythm with the cycle of the seasons those who were keeping good records realized that the cycle repeats every 365 days or 365.2422 be exact the cleverer ones developed systems for predicting the timing of the seasons which is a big aid to agriculture stars appeared to the ancients and even to us as a projection on a celestial sphere with the Stars fixed and the earth rotating within within the celestial sphere stars were grouped into constellations each representing a portion of the sky star patterns in the constellations were associated with shapes like a fish for Pisces a hunter for Orion or a crab for cancer in 1922 Henry Norris Russell helped the International Astronomical Union in organizing the celestial sphere into 88 official constellations that account for every star ancient astronomers notice that the constellations shifted over the early cycle at time some weren’t visible the Sun gets in the way it obstructs a different part of the celestial sphere during various times of the year after the Sun and the moon venus is the brightest object in the sky it was popularly thought to be two separate stars phosphorus in the morning and Hesperus in the evening Pythagoras was Leone and Greek philosopher and mathematician best known for the Pythagorean theorem he was also one of the first to realize that the bright evening star was the same as the bright morning star while Pythagoras put this theory forward it took thousands of years confirm it many remain steadfast in their belief that Venus in the morning and Venus in the evening were two separate stars by the way if you see Venus in the morning you’ll never see it in the evening and vice versa that’s what gave Pythagoras the clue that these two were the same star three ancient Pythagorean Greeks proposed that the motion of the stars was apparent that it was created by the rotation of the earth on an axis this contradicted the model that many believed that the earth was fixed many who disputed the rotating earth asked if the earth spun on an axis why don’t objects fly off why don’t we feel the spin why aren’t their massive winds all the time we know today that the rotation of the earth well measurable is too subtle for us to feel the Jetstream buzz winds from west to east if the ancients had gone high enough they would have known this on the surface of our planet there’s friction we either feel the light breeze is still there it only occasionally gets windy we don’t fly off of spinning earth because of a combination of momentum and gravity if the earth spun faster and we’d likely fly off but it would have to be very fast from this section we’ve learned that the stars move across the sky from east to west the earth spins with a kind of within a kind of celestial sphere the seasons change over the year the moon goes through phases five apparent stars move against the stellar background the Sun that rises today is the same one that rose yesterday and that the morning and evening stars are in fact one star these are some of the key discoveries