 Any questions from the ones that I gave you to try or from the orbital mechanics homework from last day or from the gravitation The day before Any of these that you want me to go over now is your chance to ask yo from lesson five Number three love to so from gravitation lesson three. No from orbits lesson three Okay, find the speed required to orbit that high above the moon's surface Okay, I'm gonna do my work up here cuz I got room here Are we in orbit Okay, if they're talking about orbital speed or orbital period or orbital radius Caitlyn I always start out by going well Gravity is what's moving me in a circle and And gravity is gonna be big g big m little m over r squared Equals and since they want orbital speed I'll use the circular motion equation with the speed in it the v squared over r That okay so far and yay the mass cancels and one of the ours cancels in Fact I'm gonna get now. I got to be careful which numbers I use G is good still gonna be six point six seven times ten to the negative eleven. We're pretty sure that's constant throughout the universe We're doing the moon. So what's the mass of the moon seven point three five times ten to the twenty two Now I need the orbital radius of the moon. What they've given me is the distance above the surface Which is Seven times ten to the third But I'm going to add the radius of the moon to that that's the r that we're using here. Yes Oh, they gave it to me in kilometers. So 1740 times a thousand 1740 times a thousand and then plus Seven times ten to the third That's going to be my orbital radius I'll just keep that on my calculator So I should be able to go six point six seven times ten to the negative eleven times seven point three five times ten to the twenty two divided by my previous answer One seven four I'll write down the radius before I forget one seven four seven and three zero Square root of this Is the answer is sixteen seventy So why am I getting something different? I wonder if maybe there's a typo. I wonder if they meant to do seven times ten to the fourth Oh, it's kilometers That's also kilometers There I did the same thing. Okay, so the radius is going to be Seven times ten to the third Times a thousand but like fix that plus 1740 times a thousand That's your radius eight seven four zero zero zero zero. Let's fix that eight seven four and four zeros eight seven four and one two three four zeros and Now if I'm clever. Ah, there it is quick and then square root of that There it is seven hundred and forty nine I'll give you everything in meters by the way Silly mistake on both our parts, but don't you feel better because I did the same thing not sure. I feel kind of dumb that okay fine Any others? Yeah From this lesson as well. Sure So I talked about it last class, but I'll do it again. I don't mind when it talks about the gravitational field Katie it's talking about this which again is not on your formula sheet, but it's pretty easy to drive Okay, it's the acceleration that goes with mass And what they want you to find is this now how fast it's moving I just derived the equation with Caitlyn over there I think the speed in orbit was this big G big M over R And you know the mass of the earth Katie what we don't know is the radius of the orbit We're going to use this Don't move over here. So I have more room We're going to use this to find the radius because they told us that G is eight point seven five Big G big M over R squared Could you now cross multiply and get the R squared by itself and then square root and then that's what we'll go there G is six point six seven times ten to negative eleven mass of the earth both of these and you should be able to It's a two-step question. Okay, is that all right and The units are all good this time now. I'm going to be paranoid and check Any others so Connor let's pick up where we left off them two more questions Now we derived escape velocity. I don't actually memorize this equation I can redraw it if I need to how do I redraw it? I realize that out at infinity if we really want to leave the planet We want to have no more energy left and want to use it up just perfectly We want the fuel to have turned out to be just enough Kayla to get us to a potential energy at zero because that's what we Defined out an infinity and to have come to a stop at the edge of the universe. So your equation starts up by saying Your initial energy has to be zero Which sounds kind of strange, but actually no it works out Okay, because kinetic energy is a half MV squared your potential energy on the earth because we're going cosmic now I can't use Mgh is negative Which means when you plus it over you do get two positive answers What we're really saying is this all of your kinetic energy from firing the fuel all at once and one mighty burst Has to end up being enough potential energy to get to infinity and then cross multiply We get that So What is the escape velocity for the earth? well Escape velocity is the square root of two big g big m over r or r squared over r Can we leave the earth? Let's find out Which are oh, we're starting out on the earth surface. So it's gonna be the radius of the earth 6.38 times 10 to the 6th I think yeah, is it possible for us to leave our planet's gravitational field and get out to the edge of the universe What kind of a speed is the earth escape velocity? I get 1.12 times 10 to the 4th meters per second Or Caitlyn about 11,000 kilometers per hour. Can we do that? Yeah, actually we can space shuttle did it all the time It requires a lot of fuel and you just keep accelerating and accelerating and accelerating and accelerating and accelerating and eventually you're there And you can achieve escape velocity. It's what the Apollo rockets did when they went to the moon as well So it's doable, but it's a high enough number again. It requires enough fuel Joel that it's not easily doable, which is why Countries and multinational multinational corporations have satellites, but you know school district 42 does not have its own satellite Way too prohibitively expensive Would you expect the escape velocity of the moon to be bigger or smaller or the same? Think about it if you're not sure look at the equation and kind of ask yourself a little bit hmm Let's find out because B says for the moon Well It's still going to be the square root of two big GM over r Again not on your formula sheet, but easy enough to derive I think now it's going to be for the moon these I don't have memorized, but you have them on your data sheet So two six point six seven times ten to the negative eleven What's the mass of the moon? I know we just did it a few minutes ago, but I can't remember. I missed the first number Sorry seven point three five Okay, Brianna, what's the mass of the moon? 7.35 times ten to the twenty two Over and what's the radius of the moons? To the sixth that's going wait a minute. It's bigger than the earth now. I'm gonna cheat a little bit I'm gonna go backspace because All I need to change is the mass of the planet here is going to be seven point three five To the twenty two One Seven four times ten to the sixth square root Look way smaller This is why if the technology ever evolves The idea of putting a base on the moon would make much more economical sense if we're planning on exploring outer space because launching from there Here's the only problem. Is there a lot of fuel and oil on the moon? You'd still have to get any of the fuel from the earth up to the moon So I think actually the energy saving I mean no matter what you're still lifting that mass from the earth and burning the fuel to get it from the earth unless we found some way to Well, this is why they were interested in finding water on the moon because water we can turn into fuel We can break it up into hydrogen and oxygen pretty easily maybe Maybe in your lifetimes 2.37 okay 2370 meters per second So way smaller which makes sense because are you lighter on the moon or heavier on the moon? If you're lighter on the moon, I would assume it would take less energy to leave with gravitational field, right? Hasn't got a strong of gravitational field meteors Every day the earth is hit by dozens probably hundreds of meteorites They're called mirrors I think when they're out in outer space, but once they hit the atmosphere and start burning up They're called meteorites and most of them burn up in the atmosphere at night. We call them shooting stars and And there's two main times a year when there's lots of them because the earth is passing through Essentially a giant dust cloud. So we're clearing a path through the dust by burning it on our atmosphere I think in August and I think in December, but I have to look it up And have you ever gone meteor start shower watching at night sometimes? Sometimes they can be spectacular. I saw one a couple of years ago. I was out sailing and out on the ocean There's one took about six seconds to get across the whole sky and really lit up the whole sky Wow, that was that was way cool Is there anybody who has never seen a shooting star ever? Emily No, I saw that I saw you looking around and I don't want to meet you. So you've all seen them, right? They're not stars. They're meteorites. We call them shooting stars Did you make a wish? Because I'm sorry it won't help but still can Okay What's this question asking us to find Jacob how fast I'm gonna contradict you probably it's actually gonna be a speed We're gonna solve this probably with energies in all in all honesty Okay Now this is asking for how fast a speed, but are we in orbit in a stable orbit? Read the question carefully. How can you tell we're not in a stable orbit? Connor It's gonna hit the ground. Okay, so I am not I'll write this down. Don't write this down I am not gonna start out by going this Because we are not in a stable orbit Do we have a change in height? Yeah, and we have a change in speed This is a job for conservation of energy. This is a job for us to say The amount of kinetic energy at the beginning and the amount of potential energy at the beginning is gonna be equal to the Amount of kinetic energy at the end and the amount of potential energy at the end It says released. So I think my initial speed is zero is my initial potential energy zero. No Is my final kinetic energy zero in fact? I think that's gonna have to be final that I'm gonna solve for Andrew What about my final potential energy now if we were not going cosmic if we were using mgh We would define zero to be at the ground but because we're going cosmic Zero is defined at the center of the planet. So my final potential is not zero either. In fact Connor It's gonna look like this Negative big G big m little m all over my initial. There's my cosmic potential energy equation Equals a half m v final squared Plus negative big G big m little m all over our final Where our final is gonna be the radius of the earth? Our initial is my initial radius up an outer space. Oh It's gonna be that plus the earth's radius now 6,300 Not really all that big. Let's drop it from a bit more serious height Cross out the six thousand three hundred and make it sixty three thousand sixty three kilometers up How fast will you be going and we're going to ignore air resistance? Oh? Nicole is there a little M in this expression? Yeah, is there a little M in this expression? Is there a little M in this expression? Yeah, what can you tell me what little m's then? Which is nice. They didn't mean to tell me how in other words the mass doesn't affect how fast it's going to be going on impact The mass affects how much damage it does witness the extinction of the dinosaurs What are we trying to find Jacob? that Okay, I'm gonna plus this over to this side Multiplying by a half on this side is the same as what over on this side Timesing by two Okay, so really I can go like this Vf squared equals negative two big g big m over our initial plus two big g big m over our final That okay our vendor And how to get rid of a squared? I don't think I'm going to try typing this in into one fell swoop So I'm going to type this press equals type this press equals add them together on my calculator and square root the answer Because that's a lot of typing. Let's plug in numbers first V final is going to be great big square root sign. Mr. D negative two six point six seven times ten to the negative eleven five point nine eight times ten to the twenty-fourth all over Now my initial radius was sixty three Thousand meters up, but then don't forget to add the radius of the earth Andrew right plus To six point six seven times ten to the negative eleven five point nine eight times ten to the twenty-fourth All over my final radius is going to be six point three eight times ten to the sixth negative two times six point six seven the negative eleven times five point nine eight The twenty-fourth divided by bracket sixty three thousand plus six point three eight times ten to the sixth that's how much I Was going to say it's how much potential energy I have up an orbit That's actually not true because we canceled the ends up, but that's this first number The second number is going to be the same thing, but ditch the negative Don't and delete the sixty three thousand Don't oh and Shawn. You know what I'm going to get really clever. Am I supposed to add these two together? Plus my previous answer. Ah Hey, that should automatically add that number to this number Square root moving pretty fast basically a kilometer a second one thousand one hundred One point one times ten to the third meters per second. Is it just a coincidence? That's final minus initial Listen to the boy who's trying hard to suck up for being late and impress me Let's see By the way, what is final minus initial? So are you saying that all of the potential energy that you lose Becomes kinetic energy that you gain and would that not make sense and are the our understanding of the universe? You know what? I don't think it's just coincidence. I probably in fact see this equation right here Don't write this down now. I should be a little bit careful Whatever you gain You lose and whatever you lose you gain. What's changing anything? What's changing anything? But negative would be initial Mine is final Could I plus the initial to this side and plus that to that side and do I now have that equation? Oh Cool, I usually jump straight to here Because it's not a hard one for me to remember All of the energy before equals all the end after yeah moving pretty fast Now how do I know for this one that it's not a question? Do you notice there's a change in the height and we're running a final speed? It's not saying how much work How do I know this isn't an orbital radius fg equals fc question because a change in height and we're not in orbit How do I know Connor's gonna stay awake? I have no idea You're gonna make it. I Don't think so. Okay So What's your homework? I Already assigned one two and three try seven. I already assigned eight nine and ten try thirteen and Then here's the deal