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45. State Kepler s Third law; explain what the law means in your own words:...

Question

45. State Kepler s Third law; explain what the law means in your own words:

45. State Kepler s Third law; explain what the law means in your own words:



Answers

Kepler's third law Complete the derivation of Kepler's third law (the part following Equation ( 34$)$ ).

We need to complete the derivation of Kepler's third Law so recall that the s interest city is equal. Thio are not V not squared over GM minus one The period is equal to two pi Excuse me The period is equal to two pi a squared over are not Vienna So square root of one minus he squared have to a is equal Thio Thio are not gm over to GM minus are not v not squared. Okay, so to complete this derivation, let's square both sides of So let's number this thes This is Equation five Equation nine and equation 10. So we're going to square equation nine. So this is t squared is equal to four pi squared eight of the fourth over are not squared. Be not squared one minus e squared. So now we will plug in Equation five into this and we get for pi squared Eight of the fourth over are not squared B not squared times one minus are not squared Vienna to the fourth over GM squared plus two are not v not squared over GM minus one So simplifying and doing some more algebra This is equal to for pi squared. Eight of the fourth over are not being on squared. Times are not V not squared to GM minus are not Be not squared over g m squared. Okay, so more algebra more simplifying. This is four pi squared. Eight of the fourth times two over GM times two gm minus are not being not squared over. Two are not GM. So notice that this term is equal to one over two A. So this is using equation 10. So this is one over to a So this is equal to four pi squared a cubes over g n. This is t squared. So t squared over a cubes is equal to four pi squared over GM and this completes the derivation.

We need to complete the derivation of Kepler's third Law so recall that the s interest city is equal. Thio are not V not squared over GM minus one The period is equal to two pi Excuse me The period is equal to two pi a squared over are not Vienna So square root of one minus he squared have to a is equal Thio Thio are not gm over to GM minus are not v not squared. Okay, so to complete this derivation, let's square both sides of So let's number this thes This is Equation five Equation nine and equation 10. So we're going to square equation nine. So this is t squared is equal to four pi squared eight of the fourth over are not squared. Be not squared one minus e squared. So now we will plug in Equation five into this and we get for pi squared Eight of the fourth over are not squared B not squared times one minus are not squared Vienna to the fourth over GM squared plus two are not v not squared over GM minus one So simplifying and doing some more algebra This is equal to for pi squared. Eight of the fourth over are not being on squared. Times are not V not squared to GM minus are not Be not squared over g m squared. Okay, so more algebra more simplifying. This is four pi squared. Eight of the fourth times two over GM times two gm minus are not being not squared over. Two are not GM. So notice that this term is equal to one over two A. So this is using equation 10. So this is one over to a So this is equal to four pi squared a cubes over g n. This is t squared. So t squared over a cubes is equal to four pi squared over GM and this completes the derivation.

Problem. Three, it asks, says about the hooks law, which is force equals K Times D. So in your own words, you can describe this as a basically the relationship between the force that's a pied and the, um, distance, or how much a spring is stretched. So, for example, this is a spring, and if you apply a force to it and you if you apply it fours up here. But so you push it, then it stretches de amount. This is D, and this force that you're adding would be at. And Kay is just the constant of the spring, the constant spring constant. And so the answer would be, That's just the relationship between the force and the distance. A spring is stretched, too.

Hello. My name is David. This video will cover capital loss. So for this problem, we just want to know which law states that the planets over the signing on the lips. And as we could see, uh, Kepler's first law stays. The planets already song along an elliptical path where the sun is one of the four K. So the answer will be Choice A. Which is the first lonely. Yeah. Thank you for watching.


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