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Consider stars A and B, which are identical except for theirradii. The ratio of radii is 1.2. What is the expected ratio ofphoton diffusion times?...

Question

Consider stars A and B, which are identical except for theirradii. The ratio of radii is 1.2. What is the expected ratio ofphoton diffusion times?

Consider stars A and B, which are identical except for their radii. The ratio of radii is 1.2. What is the expected ratio of photon diffusion times?



Answers

Star A and star B appear equally bright in the sky. Star A is twice as far away from Earth as star B. How do the luminosities of stars $A$ and $B$ compare? a. $\operatorname{Star} \mathrm{A}$ is 4 times as luminous as star $\mathrm{B}$. b. Star A is 2 times as luminous as star $B$. c. $\operatorname{star} \mathrm{B}$ is 2 times as luminous as star $\mathrm{A}$ d. $\operatorname{Star} \mathrm{B}$ is 4 times as luminous as star $\mathrm{A}$

No discussion. We have two stars A and B where? ISS at a distance twice. That's off p away from our off right, which is where we are. We are given that the study and start be appears similarly as, uh, there similarly bright on earth. Right? So they appear, right? So what determines how brain they look or they appear on earth? Well, that depends on the intensity. So the intensity off light that iss hitting off will determine how bright the sea or the whole brightly appear. So the intensity is the same right on earth. Now what about luminosity? Luminosity is different. Luminosity depends on how much in total the star iss actually meeting every second right. How much radiation is emitting in all directions? Every second. So this luminosity and for us to actually experience the same intensity, it's such to differences. We want to find out what It's the actual luminosity between A and B, right? Why Steve a show now? How does intensity relate to luminosity? Well, let's see if I have We're considering the distance this distance away from me. All right. Just a short distance away. There is some intensity over here there is different then that is that it's experience on earth is different. What is the luminosity? Well, we just have to multiply this intensity by the entire surface area off this fear over here because the power is being ready to in a symmetrical sphere in all directions. And so to get back to the original total power irradiated, we just have to take the intensity multiply by the surface area. Same with this over here Taking this intensity, we can get the luminosity by multiplying by he surface area office fear with radius. Given this this value are I saw this. Imagine a large, large sphere. There'll be where all off the luminosity is spread across right before it reaches our earth. So they look nasty for a would be given s testy off A times for pie are square What about four p ready for B? The distance is half right. So this is actually four pi times are over two square Now we know that intensity off A and B is the same When on earth. So we can place this with just test off a Let me see that this luminosity is a four pi R squared, divided by four. So the luminosity off B sexually goes to one quarter off the luminosity off A. And therefore you can say that a is four times more luminous, then beat.

So um if the force is G M one M two over our got the wrong G. In there, well then the acceleration due to gravity is going to be G mm over our. So um The ratio of the gravity gravitational field strength and star A two star b. Okay, Star A. Is nine times larger then Star B. So the acceleration for gravity if it's nine times larger but it has the same mass then it's going to be Gm over um nine are oh wait gm over R squared sorry. And the other one it's just gonna be Gm over R squared. Well nine squared is 81. So The larger one is going to be one 81st Of the gravity of the smaller one. The gravity of the larger one is 188 1st The gravity of the larger one.

We have ordered by does B V egress crowded off GM over R. So if we have, we want a course. So from there we can say that for same mass. We want over V two. It was squared it off. I love what Our lord. So from here we can find that our do over our Lord equals square. It was square off the one of what they do. Ik was we want over video. It was to be bar square of that, it was 1/4. It was in a point. Bill five. Now we will be using kept. Those are where b squared equals for vice. Where our cube over g m e. So for same mass we have Do you do over? Do you are squared equals? Are you over our Lord Cube? From here we can find do you over. Do you wanna? It was are lower our lord times 3/2 where are over our what is found to be one foot so that comes out believe one of eight equals 0.1 to 5

In this problem. As we all know that Linda is equal to catch by M b. It can be further return edge m e equal to add by B Lindy for electron. Also for Proton. I can write MP equal to add by Linda B. V. B. Now going forward As we all know, that the mass of fort own age greater than mass of the electron so the equation can be further return edge as by BP, Lambda P is greater than at by B M d since P is equal to P. P. So I can write one by Lynda P is greater than one by Linda E. Or I can write Lambda P is greater than Lambda E. So for the same speed, the it's for the same speed of electron in photon electron has longer the vocalist web land than for tune. Now going forward, I can also right the express Annette, just look at it carefully Here I just write something wrong here it will be Linda, and here it will be lamed api. So the for the same speed of electron and photon electron has longer. The bottle is prevalent than proton. Now I will solve part B. So in part B, I can ride the express an edge Anybody M P is equal to add by v. E Lind Die by Age by VP Linda P which can be further return and just look at it carefully. Linda He by Linda P. Is equal to empty by EMI now going forward and just putting the value in that express. And I can write Lindy by Lambda P is equal to 1.673 to 10 to the power minus 27 kg by 9.11 into 10 to the power minus 31 kg, which is equal to 1836.44 This is the ratio.


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