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$\bullet$ Calculate the earth's speed in its orbit around the sun, in $\mathrm{m} / \mathrm{s}, \mathrm{km} / \mathrm{h}$ and $\mathrm{mi} / \mathrm{h},$ using information from Appendices $\mathrm{D}$ and $\mathrm{E} .$

6.7$* 10^{4}$ mile $/ \mathrm{hr}$

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

University of Winnipeg

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This is Chapter one problem. Six. We are asked to find the speed of the earth in its orbit around the sun. In three different units and rest get all the data we need for appendices A, D and E in the back of the book. So first off, looking for the speed of the earth, we aren't told the speed directly in the appendix, but if we can find the distance, it goes in one orbit and the time it takes to go from one orbit we could divide distance by time and get speed so we can see from appendix either radius of the Earth's orbit around the sun. Is this one point five five seven eleven meters? That means if the orbit is circular, the circumference is two pi r. So that's here. This top of this fraction is this circumference the orbit, how far it goes in one orbit and then the period of the orbit. We can look up three, sixty five point three days and so we divide distance by time. This here is our speed, but you'll notice this is going to be a units of meters per days and that's not any of the units were asked for. So first we're looking for this in meters per second. So we're going to take this original value The meter's air find We gotta convert days two seconds. So we'LL multiply by a fraction that's equal to one. So the top in the bottom of the same value You want to cancel out the days So let's put one day appear on a day. We knows twenty four hours that's converting in the direction of seconds but it's not there yet, so we can do another conversion. We know that one hour is thirty six hundred seconds. You can look that up or just think We've got sixty seconds in an hour. We're sorry. Sixty seconds in a minute. Sixty minutes in an hour. Fifty times sixty is thirty six hundred. That is how many seconds Air in an hour. Great. And now looking here this day cancels with the stay this hour canst with this hour and real est with meters per second as their units and our number is going to be two point nine nine times ten to the force for the other two parts of the, um, the technique that we follow is going to be the same we're going to start with. We're still looking for the same quantity Speed of the earth. So we're going to start with this fraction over here. But then we're going to multiply by different conversion factors to get it in different units. So for part B, we're going to multiply. Um, we've got again restarting in meters per days. We want kilometers per hour so we're going to have to multiply by. Actually, that's whips Sarees This we want We want this our conversion factor because I am for kilometres per hour. So everything in this green circle here will multiplied all together. You'll get meters per hour and then you've got a multi bye. Convert those meters in two kilometers, so multiply by affections ableto one we want kilometers. Let's put them on the top one kilometer people to a thousand meters or tend to the three meters. So multiply what's in the green by this fraction and that gets that's gonna get your answer in kilometers per hour which is one point oh, eight times ten to the fifth kilometers per hour and we're almost done. Our last one asks for it in miles per hour. So all we got to do, we've got the hours we've already set. So we just got to take this one point oh eight times ten to the fifth kilometers per hour and convert those kilometres into miles and the bladder conversion factor up. But the top port says one kilometer is point six two one four miles. So we'LL take this. Multiply that by a fraction equal the one we're canceling out the kilometers. So now Kilometers goes on the bottom point six two one four miles goes on the top. I'm going around here but you should put in all the decimals you have in your calculator when you do this and that gets you your final answer which is six point six eight times ten of the fourth miles per hour.

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