 Here we go. First thing I'm going to tell you right now This last question number five the roller coaster question not part of your quiz So this quiz is actually going to be out of 13 not 16 whoo-hoo an airplane. It says turns a complete horizontal circle in two minutes nice try 120 seconds you're not going to get me that easy if the plane speed is 170 meters. What's the radius of the circle? Well for this question here They're giving me the speed and the want they want to know the radius. They haven't given me an acceleration I have to use circular speed now circular speed speed going around a circle centripetal velocity We said you could figure it out by distance over time Can you see the meters per second hidden in there? But what's the distance around a circle? To pi r and what's the time to go once around a circle why we called that the period? Rob, let's get the r by itself. Where would the t move? To top and what about the two pi? So I think you're gonna say V t over to pi v 170 T 120 2 2 pi pi and I get 170 times 120 divided by bracket 2 pi I Get a speed of about three thousand two hundred and fifty meters per second three thousand two hundred and fifty Meters per second which at first seemed fast and then I know wait a minute. It's an airplane. That's three kilometers I'm out three. Sorry. That's Three three kilometers a second. Yeah, they can go that fast. Yo Radius, of course that makes more sense to me. Mr. Dock. Thank you Alex Three thousand hundred and fifty meters which doesn't bug me that makes like a yeah plane turns big circles I'm okay with that This equation Not on your formula sheet, but it's still did I try and show you how to derive it? It is distance over time in this guy. It's meters per second in disguise for circles Now I can do oh by the way, I would probably go one mark if I saw that half mark for that And a half mark for the answer I'm also gonna mention I read yesterday after school. I read two games day before I read in an ounce Tuesday night My voice is on its last legs. I'm very happy to be teaching you right now. I'm having fun But all I have right now is angry low voice if I try Nothing comes out if I go higher and more pleasant. So if it seems like I'm lecturing you guys, it's not so I'm getting through today Alex You had a question Yes, but it won't make a difference unless you're pressing sign or kosher tan, which we haven't yet Centripetal acceleration a c equals Well I Can either use v squared over r because they did give me the speed or I can use 4 pi squared r over t squared Because they gave me the period I'd prefer to use one that didn't have an r because I don't like to use stuff that I calculated But since they both have an r in them, I'll use the easier one, which is v squared over r It's gonna be a hundred and seventy squared over 3250 except I'm not gonna use 3250. I'll use the decimal value that still start on my calculator I'm gonna go a hundred and seventy squared divided by answer 8.9 meters per second squared almost, but not quite one whole g and again I'd probably give you one mark for that half mark for that Half mark for the answer anybody use the four pi squared r over t squared get the same answer. So it's fine number two Now they want me to find the central force. I'm gonna say okay fc equals and I'm gonna do a little bit of a defect data listing. I got the mass is 12 I got the radius is six. That's pretty obvious and then they gave me the frequency Five hertz problem is none of my equations have frequency and the my equations have period How are frequency and period related and I think this is on your formula sheet? Is it not? Yeah It's the reciprocal. It's one over five or point two as a decimal and now that decides it's gonna be mac it's gonna be m I'm gonna use the one with the period in it for pi squared r over t squared it's gonna be 12 times four times five squared times six all over point two Squared and I got a pretty big answer. I got 71,000 newtons 7.1 times 10 to the fourth newtons and I said, wow, that's a huge force another read the question. I said, hey, wait a minute What's the mass in this question candy a? bowling ball Basically, what's the radius that we're spinning this bowling ball around Cassidy? From me to it's a roughly so imagine me having a rope With a bowling ball in the end of it where it's a Liz and you know what it's spinning around five times every second around Yeah, you know what if you walked into that it would kill you Okay, you know what I'm not that unhappy with that that force now makes sense to me I was nervous at first and then when I stepped back up and actually Almost seems low now because the force required to spin a bowling ball around that big of radius Five times every second would be huge. In fact a rope wouldn't do it. You need a chain or something, right? So I Always try and ask does the answer make sense. Yeah, by the way same idea one mark half mark half mark Number five a belt passes over a wheel of radius 25 centimeters point two five meters nice job If a point on the belt has a speed of that what's the central acceleration? So they want AC and they gave me speed, so I'm gonna go v squared over our speed is five radius squared Mr.. Dook Radius is 25 centimeters of point two five. I can do this in my head five squared is twenty-five to that point two five hundred 100 meters per second squared now I wouldn't take marks off for this although they probably would on the old they did on the old provincial Why is this technically wrong? Because it is How many sig figs There's three or a one point zero times ten to the two or whatever They used to take marks off for sig figs on provincial exams And then I marked the provincials about four years ago and at the very beginning of that just suddenly said hey Let's not take marks off and everybody was good with that So I usually circle it on your test. I might take marks off once during a year But usually I just think bad thoughts about you Some of you more than others I mean turn the page Ferris wheel, okay at the top of the ferris wheel. Here's the person sitting What are the forces acting on him? Normal force, but I know gravity has to be bigger because they're moving in a circle and the net force has to be pointing toward the middle my equation here is going to be winner minus loser equals M Uh Did they give me the velocity did they give me the period? Oh, they gave me the period And I think I mentioned to you that you'll find when we do go to the land and analyze the rides Getting the velocity of the ride is tough Getting the period is really easy you start your stopwatch and then you stop it when the same person comes back around So most of the time if it's moving in a circle, you'll be using this one Oh, of course once you have this one you can calculate the tangent velocity nearly cool The one if any of you been on the rebel revelation the big thing that goes I've been on there once you've been on there if you're if you're Want to you can analyze that one find the tangent speed. It's stunning how fast you're traveling on that ride You are more than street legal Your so you're doing more than 60k well considerably more than 60 kilometers an hour sitting in a porch Yeah porch swing set right because really that's what you're sitting in a little stronger But it's the old porch swing sets that they used to make very cool That's the only ride I've gone on where I genuinely went. Wow. I'm actually frightened Mass 65 For high square r nine All over 45 squared No, hang on mr.. Do it you got to do the math Geez, what am I I'm plugging in numbers. I haven't even rewritten the equation. That's dumb Let's try that. How would I get the fn by itself? I think plus this over and minus this over I think the normal force is going to end up being That was brilliant mg minus m4 pi squared r Over t squared is that correct? I hope M65 times nine point eight minus 65 times four times Pi squared times radius nine divided by t 45 squared. Tell me you get 626 yeah B, what about at the bottom? Well at the bottom I Want normal force to be the winner and gravity to be the loser normal force is going to be bigger It's going to be winner minus loser equals m4 pi squared r over t squared It's going to be normal force equals mg plus m4 pi squared r Over t squared and conveniently on my graphing calculator it so I could just go second function enter and make the minus sign of plus sign And that's a way lot less typing I Get 648 newtons Ashley, what was the normal force at the top of the ride? What was the answer to a? What was the answer to be is There a big difference between those? That's why Ferris wheels are a chain ride the bigger the difference the better in my opinion the So if you get a normal force of like 300 at the top and 800 at the bottom who you're feeling that this You probably only be able to tell that you were moving because of the wind on your face Not really because of the internal built-in accelerometer that are got Fact you can rank rides based on what percent they change your normal force that would actually be an interesting physics way to rank a ride Just thought of that Number five now number five actually I'm going to be doing this question towards the end of the unit number five requires both energy and Certain centripetal force. I do like this question. I like this question I like this question, but we're gonna actually spend a half day looking at it Okay, so I'm just gonna tell you the answer in the interest of time because I got a whole lesson I got to get through I know that's not great teaching but shut up Sometimes I got cut corners. Do you have quiz version one or version two? quiz version one Answers 30 anybody get that Really doing it this way Give yourself two bonus marks. I'm impressed. I give yourself three bonus marks because I'm impressed the rest of you I'm ashamed of no and the bonus question is 14. Here's what we're really saying When you're in a roller coaster loop at the top of the loop You can figure out the minimum speed you need to be at in order to get a normal force of zero. Oh And if you know the minimum speed, do you know the kinetic energy at the top? Oh I say at the top of the loop you also have some potential energy And then you can work your way backwards and figure out how much potential energy you have to have at the beginning So the top of the loop you have enough potential to make it to the top and enough kinetic to make it around And it is actually a beautiful answer because you end up with a nice tidy expression of 2.5 times the radius But that's coming down Give yourself a score then please out of count them not 16, but 13. I think I said Make sure your name is on them pass them in if you want to get out the notes from last day I will start out as per my usual routine by saying Any questions you would like me to go over now is your chance to ask Alex you said you had a couple Number seven Okay, what does question seven want us to find? What do they mean by gravitational field now gravitational field we said the symbol for that is that? Which is 9.8 here on the we can calculate it. It's this Big G big M over r squared now again This is not on your formula sheet, but I'm gonna argue it doesn't need to be it kind of pops out of the fact that all Of you know that FG has always been MG But now if FG is also M this mess this mess has to be the same as our gravitational field That's our conclusion here. So it's going to be that Okay, which is going to be 6.67 times 10 to negative 11. Yes It says twice the mass so two times five point nine eight times ten to twenty four Right divided by and what the radius five times the radius Five times six point three eight times ten to the sixth all of that squared I'll probably have to put the bottom in brackets with the square itself That's it Now if you did that then I'm going to guess it's a calculator error Have I gone on a big rant about how you really want to be practicing your calculators because these are ugly This is about as complicated specifically new Potential energy required to lift a satellite into orbit. That's a that that's where I stop trying to get things by itself And start just go into my calculator and plugging in chugging because to try and rearrange them is just not Okay, Alex, and I think that should work. I hope I've tried it, but it should any others Give more okay, so it's going to be this again mass of the earth But we're 2,000 kilometers our radius is that but in kilometers so multiply that by a thousand and that's what's going to go there Okay, so 2,000 kilometers up. You're still under gravity, but you'd feel lighter. It's five point seven not nine point eight But if you drop something would it still fall down a brick? Yeah I'd like to do more, but I think today will also make some of the other stuff clearer Or you can ask me at the end of class or ask me next class Hey, oh nerdly cool. We're gonna look at how orbits work and it turns out the math It's great eight. It's gonna be cross multiplying Shannon with a vengeance, but we can do some nerdly cool stuff So Sir Isaac Newton came up with his law of universal gravitation Cavendish was able to calculate G and then somewhere along the line somebody said this Draw a force diagram for the mass M in orbit. Let's pretend earth and Moon and what we traditionally Simran do in orbit is we use a capital big M for the planet and The lower case M for the moon or the satellite or the spaceship or the space shuttle or the space station He should what are the forces acting on this now normally? I'd say get the obvious ones Can I now we're outer space What path is this guy tracing out? There has to be a force pointing that way What force is keeping this guy in orbit? Yeah gravity in fact The equation that describes anything in orbit starts out Courtney wonderfully simply gravity equals FC Cuz there's no friction and outer space. We don't even need to go where am I lose right now Then it can branch Gravity is always the same big G big M little M over R squared You can either go M V squared over R I use that one if they give me or they ask me the speed or velocity needed to stay in orbit or Big G well, that didn't work big G big M little M over R squared equals M For pie squared R over T squared I use that one if they ask me or give me how long it takes the satellite to go around the planet once We're the US military We want to spy satellite to orbit the earth every five hours We would give them the period they could calculate how high and then calculate how fast it needs to be going to keep it Turns out then an orbit is circular motion with gravity as the inwards force all of the astronauts in the space station right now Are feeling gravity? Well, no, they're not you just showed us a video yesterday of the guy playing baseball didn't look like he was feeling I'm telling you the force of gravity is acting on him patient example to a 10,000 kilogram satellite is orbiting 20,000 kilometers above the earth's surface a says right force equations It's so did I say orbit? Well, then the first thing I know is the force equation is Gravity is pulling me in a circle. What do they want me to find rub in B? I'll use the V equation. I'm gonna say okay Big G big M little M over r squared. That's gravity Equals m v squared over r because they talked about orbital speed. Hey You guys notice something a little strange here Turns out the space shuttle Can orbit right next to the small satellite that it's releasing because what happens not to the mass of the planet But to the mass of the orbiting thing Which makes it nice because then the space shuttle can launch satellites by going into their orbit going at the right speed Basically raising the satellite maybe 10 meters above from where it is and then just letting it go over good And then the space shuttle can use engines to get out of there. Oh I noticed one more thing This r could move up to there How many are is what I have on top one how many on the bottom how many left? Turns out one of the ours will cancel and I've got the v squared by itself already Shannon how to get rid of a squared Turns out Orbital speed is given by this It's not on your formula sheet Eric. I don't memorize it Eric you know what I memorize this line right here and then I can derive whatever I need to in about one second It's cross multiplying. Yes with a vengeance, but it is cross multiplying. Oh Let's find out how fast it needs to be going. Let's see G is 6.67 times 10 to the negative 11 M is five point nine Eight times 10 to the 24th. That's the mass of the planet divided by oh We got a little problem here You see this question gave us The altitude in kilometers. I think that's what it is in meters. Is it not? I? Got an extra zero plus two times thousand One two three four five six seven one two. No, yeah, I'm good two times ten to the seven The problem is Alex my equation wants are now are That's my orbital radius How can I figure out the orbital radius if they've only given me the altitude? What do I have to do or include Andrew just figured it out? I think I'm gonna have to add the radius of the earth and you have to read carefully Sometimes I will almost always just give you the orbital radius But sometimes they'll give you the altitude and the altitude is more practical because radar works from the altitude Not from the center of the earth, but whatever over here. Let's write down Orbital radius is gonna be the radius of the earth plus The altitude it's going to be what is the radius of the earth? I know it's six point three eight I can never remember that times ten to the okay six point three eight times ten to the six plus two times ten to the seventh That's the number that's gonna go here, which I think ends up being two point six three eight times ten To the seven double-check my math Is six point three eight times ten to the six plus two times ten to the seventh equal to Plus six point three eight Times ten to the sixth. Yeah, two point six three eight times ten to the seventh And now once again, I really encourage you the other reason I'm so bullish on getting you on your calculators now is you get faster at finding the scientific notation and the five buttons And the square root buttons and that saves you time on the test so try it see we get the same thing I Get an orbital speed of that Three eight eight eight three eight. I think three eight eight eight the three thousand eight hundred ninety if I go three six six Yes, no no Yes, no you get that I'm looking at you step. Did you get that? Oh you did okay? You get that okay? Oh, okay? Nobody was nodding or anything. I was like maybe I'm wrong Carson. Yes. Oh, oh Hello, Carson now I'm more nervous. No never mind Which seems fast, but then I went actually no when I see satellites It only takes about 30 seconds at night to get across the entire sky. So yeah, okay And again random notice turns out orbital speed Ends up being independent of how heavy the object is It costs no more to keep the space station up there Then it does to keep a tiny little spy satellite up there It costs way more to get stuff up there that have a year it is and we'll talk about that in a couple of days But once it's up there That's just cancel. So here's our equation orbital speed is equal to the square root of big G big M over Orbital radius Courtney do I memorize that now I write fc equals fg and away I go Some kids though like to memorize stuff. There it is example three Says fill in the proof below to show that when an object is in orbit It's inwards acceleration is the same as the gravity field at that distance now. We already said this Alex reminded us earlier Gravity field is equal to big G big M over r squared That's the gravitational field strength as you move further and further away from the earth Here it says a equals well V squared over r because we're moving in a circle. Yes and If I substitute now it wants me to substitute V Look up equals this. I'm gonna be clever I'm gonna substitute V squared equals big G big M over r I'm gonna get rid of the square root by squaring because there's a squared over here anyways I'm gonna plug it into V squared is GM over r and If I plug this then it's all into here for V squared. I'm gonna get this big G big M Over r over r. How many are is on the bottom? There's two of them those don't cancel trust me You get Big G big M over r squared, which is exactly the same As that now, what does that mean? That means that all astronauts all satellites the space shuttle the space station anything in orbit is actually in free fall It's falling to the earth It's falling to the earth Can't be mister do it. Otherwise things will be crashing down. I'm telling you it's falling to the earth No, I'm not slowly very rapidly. Ah But watch Rob Here's the explanation in an ingenious analysis of orbits Newton imagine standing on top of a large mountain So let's suppose you're a baseball player standing on top of a large mountain and you throw the baseball as hard as you can It'll land right there Now you do some steroids and you throw it even harder Oh It'll actually make it part way around the curvature of the earth before getting yes Rob is it not possible that I can find just the right speed so that when I throw it It's falling but it's also moving sideways at just the right speed to match the curvature of the earth and keep going and Going and going that's what an orbit is They're all falling But we give it just the right sideways circular velocity so that as they fall they Curve at exactly the same curvature of the earth so even though they're in free fall very rapid free fall They never get any closer that's and that's why the astronauts can be in gravity but not feel any mass because So the fact that an object in orbit is in continuous free fall is interesting for a couple of reasons It means that things in orbit are always falling to the earth even though they never get any closer It explains why astronauts seem to float around in the space shuttle Both the passengers and the ship are in free fall and since the air that they're inside is in free fall with them They can't tell that they're moving Therefore the ship cannot exert a normal force and I've said to you the past few days Ashley What you think of his weight is not it's the normal force They still have full mg, but they have no normal force so they feel weightless And it also means that astronauts experience Experience continuously until they get used to it the stomach feeling of falling Why you throw up a lot on the vomit coming so you get used to it You deal with a lot of vertigo because right now Spencer one of the ways that you keep your balance your inner ear has some liquids in it that always get pulled towards the ground And that's how you can close your eyes and know where the ground is even with your eyes closed With that gone, you know where the ground is you feel dizzy all the time until your brain compensates So they deal with vertigo they throw up a lot and then they get used to it Although on the Apollo moon landings couple the astronauts apparently never did get used to it with throwing up all the way there and all the way back That makes sense how orbits work. In fact if you wanted to you could orbit Around the earth a couple of hundred meters up although you'd run into mountains you'd have to be careful and Well, let's see next page in A cartoon a character kicks the football the wrong way, but the football goes all the way around the earth and Still goes through the uprights. I get the Popeye cartoon if I recall Removing the fact that it's a cartoon if you did want to orbit around the earth What speed would you have to be traveling if you wanted to orbit right at ground zero? Did I say orbit? Well, then the first thing I'm gonna do is I'm going to write Gravity is always big G big M the limb over our squared centripetal force is M In a are they asking for do they mention the speed or the period? Speed I'll use the V squared over R Yay, the mass is canceled Yay, one of the ours cancels and in fact I get what we wrote on the box on the previous page The velocity is going to be the square root of big G big M Over R. How fast would you need to kick a football? 6.67 times 10 to the negative 11 5.98 times 10 to the 24th all over Mass of the earth 6.38 times 10 to the what? Sixth, thank you. I can never remember that stupid thing. What's your orbital speed? If you wanted to orbit here on the earth You'd have to be a couple hundred meters up But a couple hundred meters with the radius won't make a difference it'll make a difference like on six Technically you could argue it was six point three eight zero zero zero zero zero zero zero two To be a couple hundred meters off the ground so you want to run into trees and things but whatever close enough Would you get it Cassidy? 79 Yeah, almost eight kilo eight kilometers a second almost Pretty fast Although we can get objects going that fast burns a lot of fuel. I'm curious. I Wonder how long it would take to get around the earth at that speed. Oh Alex what does B asked me to find? Oh, okay? I'll do that over here. Are we in orbit? Well then Gravity equals circular big g big m little m over r squared equals ma This time Alex. I'm going to use the one with the period in it for high squared r over t squared Once again Andrew The m's cancel But what are we trying to get by itself this time? T now this is a little bit more complicated still cross multiplying first of all this are here Spencer does not cancel with this are in fact if I moved it down diagonally, you know what I end up with There's gonna be our cubed in fact you ready I'm gonna move the t squared to there The r squared to there to give me an r cubed and the big g big m to there. I'm gonna get this T squared equals for High squared r cubed all over big g big m Eric how do you ever have a squared? Oh? Let's do that. I'm gonna get cheating This is our second equation keep by the way. Can you see why I don't bother memorizing these They're trying to keep me straight would be dumb, but I can get that across multiple This is if you know the radius and you want to know how long it takes to go around There you go. Do I know our? Yep, do I know g 6.67 times 10 to negative 11? Do I know the mass of the earth? Hey, it is plug-and-chug now ugly, but yes for High squared 6.38 times 10 to the sixth cubed All over 6.67 times 10 to the negative 11 5.98 times 10 to the 24th and then square root that puppy when you're done How long would it take you to go all the way around the planet at this speed? Backdoor Alice what you get 1.2 times 10 to 25 seems really high to me. Did you square root? Is it 1.2 times 10 to 25? I Don't think so Summer would you get yeah? Oh, no not that The negative seven takes you to throw it into a sec. I think you're going faster than light right now okay, I better type this for I squared times 6.38 Scientific notation button to the sixth all cubed you might need to put this in brackets on your scientific calculator on the TI I don't but you might have to divide it by bracket 6.67 times 10 to the negative 11 times 5.98 Times 10 to the 24th square root of this You get an answer right around a five right five thousand seventy or just because I'm a nerd if I divide that by 60 About 85 eighty four and a half minutes Pretty much 84 minutes 30 seconds problem See why can't we orbit the Earth's surface in this manner, but it's very possible on the moon What's the big issue here air resistance friction you'd have to keep firing your jets But on the moon you would not we could if we do ever have a settlement on the moon Which apparently newt gangritz promised to do yesterday or the day before and one of the presidential debates like he wants to turn the moon into state number 50 or 53 if you count Iraq and Afghanistan Well, yeah, I don't know yeah, right But it would be very possible to simply measure the highest mountain on the moon Go, let's say 200 meters higher than that for a safety margin and put stuff in orbit right there And as you can see the orbital period would be pretty quick like every couple of hours very doable But not here on the earth air resistance on Mars Possibly turn the page. Let's do the u.s. Spy satellite question that I bounced off you early So we're NASA and the u.s. Military comes and they say look we want to put a spy satellite up there And we want it to orbit the earth every 300 minutes. Oh, hang on 300 minutes how many seconds would you get Sabina? 18,000 every five hours So we want a satellite to orbit the earth every five hours Okay, how high do we need to put it? Did I say orbit? well then and Newtons by the way, we can't use mg here because you're not on the earth anymore You're out now to space g has gotten smaller So got to use big g big m little m all over our squared equals m which Acceleration equation am I going to use for moving in a circle the one with the v or the one with the t in it? How do you know? Oh, they gave me the period. Okay, so the four High squared r over t squared which is good because the CIA wasn't going to tell us how much it weighed It's in a box Fine. Well, no, they would have to tell me how much it weighed for fuel on the way up Uh Does an r cancel? I know if I had ours on the bottom they would cancel, but what are we trying to get? Or we're trying to get the r by itself This is about as tricky as it'll get we're going to move the r up to here How many will I have over here? Three of them the t squared there and the four five squared there. We're going to get this R cubed equals G m t squared all over for pi squared And this is like the first time in physics 11 or physics 12 where I have to ask you how did I get rid of a cubed? Cube root. Hey, cube rooting is useful. Yeah, let's show up someone r is going to be the cube root of Big g big m t squared all over For pi squared by the way have you clued in while I fly I said don't bother trying to memorize all these different ones because they All look very very similar with squares on the top and the bottom and they're inside root. Ah Know that and derive it. Let's see The cube root of This is also your chance on some of your calculators to figure out where the cube root function is mass orbiting around the earth the period 18,000 squared all over four pi squared Once again, do the inside get an answer and then cube root your answer. It's way easier squared divided by four Hi squared Double check before it's point six seven times ten negative five point nine. It looks good Cube root on my calculator is math option number four Cube root and I get an orbital radius of one point four eight four eight Times ten to the one two three four five six seven Which is not what they wanted by the way But first of all see if you can get this on your calculator If you can't now is your chance to call me over and I'll try and figure out how your system works on your calculator We're good. Anybody see it's very subtle. Why is this wrong? Why is this not what they actually asked me? If they want to know how high above the earth what I found is how far from the center of the earth I found its radius orbital radius How can I find it altitude the height? Is going to be our orb minus our Whatever's left right that makes sense now to visualize it, right? Distance from the center of the earth. Here's the earth. We want this. Oh, how about this minus this gives me this yes? I have this on my calculator. So minus Earth is six point three eight times ten to the six I think And I get an altitude of eight point four seven times ten to the sixth now I know exactly how high to put it. Of course, I bet you if we were doing this We would keep the extra six bigs in real life. We probably want at least be accurate to the nearest tan of a meter Now this isn't perfect Every satellite has to have some little booster rockets and stuff because the earth isn't the only thing out there the moon Tugs on them the Sun tugs on them. And so there's some wobble and so their orbits aren't Perfectly smooth. We're simplifying a little bit, but very minimal adjustments One of the things that used to drive us nerds crazy was in the old Star Trek series in The original and in the first couple of years of the next generation until they actually listened to all the physics nerds They would have the enterprise in orbit Something would go wrong with the engines and now they were in danger of classic crashing into the planet. No If you're in orbit, they would have shut off the engines Doesn't matter if the antimatter containment pods are about to blow. They're not going to crash into the planet They might not be able to leave the planet That's a different story But that was in the original series a plot line very very often They're getting closer and closer and getting hotter and hotter as the burning up in the atmosphere We got to get the engine stuff. No you in real life orbits are stable You are in free fall you just give yourself the right tangent velocity and you fall Continuously towards the planet in a curve that matches the planet's curve be All right, how fast is going to be going up there? um, I could probably use This radius to find how fast if I have to Or maybe I can use the period to find how fast. Let's see We're in orbit Big g big m little m over r squared equals mv squared over r because they're mentioning speed You know what? It looks like no matter what there's going to be an r kicking around So, you know as much as I dislike using information that I calculated to solve part two Yeah, suck it up buttercup and deal with it, right? Oh the mass does cancel it's and Are there r's on the bottom in the fractions then that cancels with that one Oh, we've seen this equation before V equals the square root of g m over r Which is the square root of 6.67 times 10 to the negative 11 m big m oh mass of the planet birth all over Oh, I got to use this number 1.4848 Times 10 to the seven Okay Once we get the satellite to the correct height how fast will we have to get it moving sideways before we can just let it go It'll stay there. You know, I really think I can save myself some typing here. Yeah, I got that times that nuke this divided by square root you get 5 0.2 times 10 to the third 5,200 Ish seconds Seconds meters per second Not a period at the So I guess if we want the second equation for period Uh, I guess technically the period ends up being the square root of what was it going to be 4 pi squared r cubed all over Big g big m I gotta memorize that Once you've done most of the homework you'll find you can almost do this completely in your head. Yep Stretch, okay Last one I think example six The satellite has an orbital altitude of 1.2 times 10 to the sixth meters a what's its radius b what's its velocity And b hey, how about make that a c whoops What's its orbital period What's its orbital radius if its altitude is 1.2 times 10 to the sixth? What do I have to do with that number? Okay, I'm just going to do that on my calculator 1.2 times 10 to the sixth plus 6.38 times 10 to the sixth You know what it's radius is 7.58 times 10 to the sixth Now try b and c on your own See you can get them. I'm going to freeze the screen. See if we end up in the same place Is that right for b? Or no Yeah, is that right for c? Woohoo Those orbits You can now upon now all apply at nasa Or the canadian space agency Mav you could be an astronaut your childhood dream could be realized. What's your homework stuff to practice? I assigned with my other class 1 2 3 4 5 7 9 10 let me circle that on yours homework 1 2 3 4 5 7 9 10 take a look at number seven by the way Number seven is talking about a geosynchronous orbit This is an orbit where the satellite stays above the same spot the whole time for it to do that What must its period be? Yeah, which is what? How many hours for the earth to go around was? Geosynchronous so all the gps satellites and many other geosynchronous satellites They all orbit the earth every 24 hours exact of course you have changed at the second by going time by 60 times by 60 But you actually know the period of a geosynchronous orbit, which means actually the turns out they're all at the same radius It's not getting crowded because the circumference is huge lots of room to spread stuff out, but Will eventually Then what? Hopefully by then we've left the planet