5

18. Calculation: A new planet has been discovered by the exoplanet exploration team at NASA called DH Tauri-B with a mass 5 1027kg and a radius of 90 million m This...

Question

18. Calculation: A new planet has been discovered by the exoplanet exploration team at NASA called DH Tauri-B with a mass 5 1027kg and a radius of 90 million m This planet has an apparent magnitude of 8.5 and is 437 light years from EarthWhat is the density ofthe planet d What type of planet should this be considered What is the absolute magnitude of the planet?

18. Calculation: A new planet has been discovered by the exoplanet exploration team at NASA called DH Tauri-B with a mass 5 1027kg and a radius of 90 million m This planet has an apparent magnitude of 8.5 and is 437 light years from Earth What is the density ofthe planet d What type of planet should this be considered What is the absolute magnitude of the planet?



Answers

An Earthlike Planet. In January 2006 , astronomers reported the discovery of a planet comparable in size to the earth orbiting another star and having a mass of about 5.5 times the earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. If this planet has the same density as Neptune $\left(1.76 \mathrm{g} / \mathrm{cm}^{3}\right),$ what is its radius expressed (a) in kilometers and (b) as a multiple of earth's radius? Consult Appendix $F$ for astronomical data.

Before proceeding to solve the problem. They just write down a few important numbers. The radio's off earth is six one, six thousand three hundred and sixty kilometers, which is six three six zero, multiplied by ten par three meters, which is six point three six into tend bar six meters on the mass ofthe earth is six times then part twenty four kilograms. Notice that I have left him in the unit that is usually recommended. No, let's go to a new planet. Our new planet has a mass five point five times that of birth and sit must its most would be five point five point five multiplied by any riches. Thirty three I'm sorry, five point five multiplied by six into and twenty four kilograms, which turns out to be thirty three into ten part twenty four kilograms. On the density off this planet is one point seven six graham percent Emitter cube. Now we know that one gram is ten pound ministry kilograms. And let's use that and we know that one centimeter is tend bar minus two meters because one meter has hundred centimetres. But this is sentimental cubed. So we killed this holding and so we can write this as one point seven six, multiplied by ten part ministry by ten four, minus six kilograms per meter. Cubed, which is one point seven six into ten, part three kg per meter cubed. Now we know that density is masked by William. Hence, volume would be masked by density, which which is in this case thirty three into ten. Part twenty four the mass in kilograms divided by one point seven six in toto and part three kilograms per meter. Cubed as you can see if you write down unit even when you're doing calculations, you're easily rectify if you use the property in it. When you use the proper units, you can cancel them and you can see that our volume will turn out to be in meter cubes, which is good. Now, By planning this into a calculator, we can see that this is equal to eighteen. One, seven, five into ten or twenty one it'LL cubed. But we know that this is a spherical planet on. Hence, its volume would be four by three by r cubed Hence I like you is eighteen point seven five, multiplied by three by four by into a ten part twenty one meter cubed hence, and this turns out to be a four point four eight into a ten Part twenty one now. Hence I would be for one for eight into a ten part twenty one gold bar, one by three acute fruit, which turns out to be one point six five into ten for seven meters. This is the radio's off the new plan. No for party. We want to find out the radio's off this planet in terms ofthe multiples off the radius of planet Earth. So we know that the radius is one point six five in two or ten for seven meters. We've seen that the raiders ofthe earth is six point three six. They do tend bar six meters. We simply do. The ratio are divided by Ari, one point six five into ten, Part seven, divided by six point three six into ten past six. If we bring in one of the ten from the powers into the number into the multiplication number, we can see that this is sixteen point five into ten past six. He wanted by six point three six into tend Bar six by the way. Both of these are in meters and hence the Councilor. And to speak of this racial becomes numberless. Now we can also concert in Bar six of Excuse us Amnesty. I don't I don't like this so that you can have an estimate off how large this number is. We know that six times three is eighteen and we expect this number to be somewhere between two. Entry. If you like this into a calculator, we can see that this is two point six. Hence, this planet would be two point six times larger than that ofthe Earth. If Arthur aliases Ari, the radius off this planet would be two point six. Artie.

And this question. We're told that the mass of the planet in which we discovered which I label here as Impsa P. Is equal to 5.5 times the math mass of the Earth and Savi and the mass of the Earth, which I write is in Sabi than is equal to 5.97 times 10 24 kilograms. We're also told that the density of the planet which I call Ro is equal to 1.67 grams per centimeter cubed and I converted that and take kilograms per kilometer. Cute. So that way we have more reasonable units when we do our calculations. So to do that I multiplied it by one kilogram per 1000 grams and by the fact that there is one times 10 to the six centimeters and everyone claw me kilometer and you have to cube that value since we're in centimeters cubed, only one of the in kilometers cubed. So I end up with the value of one place 76 times 10 to the 15 kilograms per kilometer. Cute. So now for part A, I'm gonna use the fact that the volume of the planet is gonna be equal to the massive planet divided by the density of the planet. And if we assume that the planet is a perfect sphere, it might not be a good assumption. But it's a good approximation. We can say that it's people of 4/3 times pi times the radius of the planet are soapy, uh, cute. Well, since we know everything in this expression except for the radius of the planet, which is what we've been asked to find, we can go ahead and solve for the radius of the planet. We find that it's equal to three divided by four pi multiplied by the mass of the planet divided by the density of the planet. And all of this has to be rates to the 1/3 power to get rid of the cube radius. Playing those values into this expression, we find that this is equal to 1.64 times 10 to the fourth kilometers weaken box that in is their solution For part a part B wants us to find a value for this in relationship to the radius of the earth. You can look this up. The radius of the earth is equal to about 6.37 times 10 to the third kilometers. So if we take the ratio of the radius of the planet to the radius of the Earth, we can get an expression for the radius of the planet in magnitudes of the radius of the earth. So our superior over our city plugging in our values for our city and our value that we just found for our sippy, we find that this is equal to two 0.57 Therefore, we can deduce from this that the radius of the planet is equal to 2.57 times the radius of the earth so we can go ahead and box set in as their solution apart B

Everybody's a couple are detected a planet diameter of 1.7 Earth. So of that how much larger the volume and assume that don't see the plane seamer. So how much more massive is a planet? So here we have the volume unequal high six times the d you? Yeah. So we have high six times the diameter. So we have to wine at 68 five kilometers Ty Cube. And that's gonna be wine. Appoint one point. Oh, too times time to the 13 kilometers And here. So now we have the couple our planet times value divided by the volume Earth 1.2 times tied Teoh the 13 divided by the volume Earth, which is 1.8 times tired to the 12 kilometers. So it's gonna be 9.4 times earth. Okay, And now we have the density because the question for here is asking us because we're given the diameter of the earth. So it's gonna be time center, and that's what we have. You You're just curious where I got that number. And now for the density, we have density of mass and volume and what's gonna tried to get this down a little bit. There we go. And here we could Dio we want the mass and we have five 0.5 times 10 and 12 till the ground. Okay? Squared times 1.2 times title 2 13 kilometers feud. Who's I don't know why I did that. I was thinking There you go. And that's gonna be 5.6 times 10 to the 25th kilogram. And now we can dio I am of the Kepler. And what did I have it? As I had as Katie. Whose number? Marea que he over the mass of earth. And what is gonna put 5.6 times 10 Teoh the 25th divided by the mass of Earth? It's a 5.98 times time, uh, 10 to the 24 annals. Tickets 9.4 times the earth's. So there we go. Ok, thank you, guys.

So in this problem, we know that Ah, the radius off the planet is full times 10 to the six meters and the optical masses one kilogram. And, uh, so we're gonna figure out the gravitational force on this object af equal G m Y m two over our squid. Right. So, uh, em to is the mess of the planet so we can see that I am too equal after times are squid. Well, I g times then one right and one. So this gives you Ah, 1.2 times 10 to the 24 Cue grams. All right, so there's a part. Ay, any part B. We already know that the force acting on this object is five Newton's. So the acceleration is ah f over em. Right? So this is five meters meter, five meters per seconds. Quit. And we also know that Ah, the acceleration on the on the earth, it's g equal 10 meter second squid. So this equal half g and in part of see the average density of the planet row a pull the mass of the ah mess. So the mass of the planet they mined by the volume of the planet, which is full of the three high are cute. Right? So this gives you 4.47 times 10 to the third Kita grabs meters. Cute. All right.


Similar Solved Questions

5 answers
8Ji 7 3 Doo} appears / ~olanun Rejei QiH larTn; rinicod jodojd 01
8 Ji 7 3 Doo} appears / ~olanun Rejei QiH larTn; rinicod jodojd 0 1...
5 answers
Your great uncle has an antique telescope that is L long: The spherical objective lens has a radius of curvature of R. Unfortunately, vou broke the eyepiece and need to buy a new one. In terms of L and R, what focal length eyepiece fe should you buy, and what is the magnification m that the telescope provides?
Your great uncle has an antique telescope that is L long: The spherical objective lens has a radius of curvature of R. Unfortunately, vou broke the eyepiece and need to buy a new one. In terms of L and R, what focal length eyepiece fe should you buy, and what is the magnification m that the telescop...
4 answers
Battery has € = 30 V, and an internal resistance of 2 Q What is the terminal voltage when it is connected to R= 10 Q?a. 12.50 Vb. 25.00 V c8.33 Vd. 16.67 Ve. 30.00 V
battery has € = 30 V, and an internal resistance of 2 Q What is the terminal voltage when it is connected to R= 10 Q? a. 12.50 V b. 25.00 V c8.33 V d. 16.67 V e. 30.00 V...
5 answers
Hide their loot, Inieves pul the |.50 kg gold Ihat they had hrew it in a lake. The mass of the robbed Into a small DOX I0 cm', When the empty box was 500 grams, and its dimensions are enter it . Will the box bOloG Oosed with the gold inside it, if is well sealed s0 thatwaterd float on the water or sink? Density of water L.00. g/cm] IcCOke
hide their loot, Inieves pul the |.50 kg gold Ihat they had hrew it in a lake. The mass of the robbed Into a small DOX I0 cm', When the empty box was 500 grams, and its dimensions are enter it . Will the box bOloG Oosed with the gold inside it, if is well sealed s0 thatwaterd float on the wate...
5 answers
1 Find the total derivative dz}dy, given (a) z = f(x,w)=Sx+xy-Y where * = gly) = 3y2 (b) 2 = 4x2 3xy + 2y2 , where x = I{y (c} 2 = (x+y(* 2y), where x = 2- Ty
1 Find the total derivative dz}dy, given (a) z = f(x,w)=Sx+xy-Y where * = gly) = 3y2 (b) 2 = 4x2 3xy + 2y2 , where x = I{y (c} 2 = (x+y(* 2y), where x = 2- Ty...
5 answers
Is the furction given by f(x) =x2 15x 56 conlinuous over Ihe interval 6,71? Why ' Or why not?No, since ((x) iS not continuous atx=7 Yes; I(x) iS continuous at each point on (- 7,7)
Is the furction given by f(x) =x2 15x 56 conlinuous over Ihe interval 6,71? Why ' Or why not? No, since ((x) iS not continuous atx=7 Yes; I(x) iS continuous at each point on (- 7,7)...
5 answers
Problam IV (Quastions 13 t016) The Fourer Transform i5 used to solve the followng Dirichlet problem for the upper semiplane: PDE Au= V'u=uxtum= -c<X<0,0<y < & BC ulx,0) = f(x) 00 <* <0 BC uI5 bounded asy + o,for Gll x. Lel U = u) be Ihe Fourer Transform of U. The ODE satisfied by U may be witten a5
Problam IV (Quastions 13 t016) The Fourer Transform i5 used to solve the followng Dirichlet problem for the upper semiplane: PDE Au= V'u=uxtum= -c<X<0,0<y < & BC ulx,0) = f(x) 00 <* <0 BC uI5 bounded asy + o,for Gll x. Lel U = u) be Ihe Fourer Transform of U. The ODE satis...
5 answers
These exercises involve counting subsets.A travel agency has limited numbers of eight different free brochures about Australia. The agent tells you to take any that you like but no more than one of any kind. In how many different ways can you choose brochures (including not choosing any)?
These exercises involve counting subsets. A travel agency has limited numbers of eight different free brochures about Australia. The agent tells you to take any that you like but no more than one of any kind. In how many different ways can you choose brochures (including not choosing any)?...
1 answers
Solve each problem. Spring The position of a weight attached to a spring is $$ s(t)=-5 \cos 4 \pi t $$ inches after $t$ seconds. (a) What is the maximum height that the weight rises above the equilibrium position? (b) What are the frequency and period? (c) When does the weight first reach its maximum height? (d) Calculate and interpret $s(1.3)$
Solve each problem. Spring The position of a weight attached to a spring is $$ s(t)=-5 \cos 4 \pi t $$ inches after $t$ seconds. (a) What is the maximum height that the weight rises above the equilibrium position? (b) What are the frequency and period? (c) When does the weight first reach its maximu...
5 answers
A city's population is currently 29,000 and is growing by 3.2%each year. If this continues, in how many years will the town'spopulation reach 86,000?
A city's population is currently 29,000 and is growing by 3.2% each year. If this continues, in how many years will the town's population reach 86,000?...
5 answers
Cells haploid or diploid? surrounding 8 4number of the chromasome 4 i1slide 1 Mcss
cells haploid or diploid? surrounding 8 4 number of the chromasome 4 i1 slide 1 Mcss...
5 answers
StepsOhHzNKCN; CucnNaNj0 H,O , HzO, heatKMnOaCuzO, Cu(NOslz HzoHNOz; HzSO4C H,PozCH;Ci; AICI;pyridine, heatLIAIHAK HNOz, HzSO4R 1. BH; 2. HzOz NaOHE Cro3Brz' FeBrjS HBr; CuBrF LDAM HBr, BrzT Hz; Pdic CH;H;c ci pyridineNHsC 'OHHyc CI AICIy
steps Oh HzN KCN; Cucn NaNj 0 H,O , HzO, heat KMnOa CuzO, Cu(NOslz Hzo HNOz; HzSO4 C H,Poz CH;Ci; AICI; pyridine, heat LIAIHA K HNOz, HzSO4 R 1. BH; 2. HzOz NaOH E Cro3 Brz' FeBrj S HBr; CuBr F LDA M HBr, Brz T Hz; Pdic CH; H;c ci pyridine N HsC 'OH Hyc CI AICIy...
5 answers
Express the sum using summation notation: Usc Js the lower himit ol summalion jndthe Inder of summalion;0 2+2'*+2+-+2"
Express the sum using summation notation: Usc Js the lower himit ol summalion jnd the Inder of summalion; 0 2+2'*+2+-+2"...

-- 0.020026--