(Topic ID: 293922)

Math Question

By TexasJustice

4 months ago


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    #1 4 months ago

    Earth has supposedly 57,308,738 Sq miles of land on it.
    Earth's land coverage is approximately 29% of the total 196,900,000 sq Miles worth of total surface area.
    Let's say an another planet is 2.4 times bigger then Earth, but is covered by 31% of land.

    How much land, in Sq miles, does the other plant have?
    What formula did you use to arrive at your answer, so that I can learn from your answer as well.
    Should I delete this thread after I get my answer?

    Thank You.

    #2 4 months ago

    Is this homework?

    Take the total surface area of earth, multiply by 2.4 (to get the total surface area of the new planet), and multiply by 31% (to get the available land on the new planet).

    [Edit]: nevermind, this would work for flat surface area, but not a sphere.

    #3 4 months ago

    Googled it and:

    A=4(pi)r^2

    so new A is 2.4 times old A
    real land area is that times 0.31

    so new land A is 2.4 X .31 X 196,900,000 Sq miles =146,493,600 Sq miles

    if 2.4 times bigger means the radius is 2.4 times bigger than the formula involves 2.4^2

    #4 4 months ago

    Vote for weirdest thread yet.

    #5 4 months ago

    326,066,400 square miles

    #6 4 months ago
    Quoted from Coindork:

    326,066,400 square miles

    Edit, sorry 146,493,600 square miles,

    #7 4 months ago
    Quoted from Coindork:

    Edit, sorry 146,493,600 square miles,

    It's for a novel I'm writing

    Ok, I just rewrote what I had written, becasue you had me going with that 326 million. I thought maybe I was looking at this even more wrong. I mean if NASA classifies the Alien planet as being 2.4 times bigger then Earth, then it isn't expodentially bigger, right? It's not like when you go from a 14 inch pizza, to a 16 inch, and the area increases by 30%, is it? It's just slightly bigger then Earths area times 2.4, right? Is that how that works?

    #8 4 months ago
    Quoted from TexasJustice:

    It's for a novel I'm writing
    Ok, I just rewrote what I had written, becasue you had me going with that 326 million. I thought maybe I was looking at this even more wrong. I mean if NASA classifies the Alien planet as being 2.4 times bigger then Earth, then it isn't expodentially bigger, right? It's not like when you go from a 14 inch pizza, to a 16 inch, and the area increases by 30%, is it? It's just slightly bigger then Earths area times 2.4, right? Is that how that works?

    Now your questions makes more sense. What are you writing?

    #9 4 months ago

    Bigger question.

    How many pinball machines can you stick on this new planet ?

    LTG : )

    #10 4 months ago
    Quoted from RyanStl:

    Now your questions makes more sense. What are you writing?

    YA Sci-fi. I'm just outlining the series, typing up about 20K words of notes as I go along. The fourth one takes place on an actual alien world, as in a planet that really does exist out there, as I want it all to be somewhat plausible, and as I was world building what the planet looks like based on reasonable terraforming that has taken place, I came up against this question.

    I also have to now "logically" transform the gravity. I"m thinking that Earth created a micro black hole near by this planet?! LOL That's the best I can come up with having tried to read through the Wikipedia page on Gravity. Zzzzzz
    I'm not married to that idea though, although it sounds cool and has some potential possibilities for conflict and drama. Me thinks I will have to join a science forum soon.

    #11 4 months ago
    Quoted from LTG:

    Bigger question.
    How many pinball machines can you stick on this new planet ?
    LTG : )

    All of them!

    #12 4 months ago

    Let us know when you publish. Sci-fi and Fantasy are my two favorite genres.

    #13 4 months ago

    I guess it would depend on what you mean by bigger. 2.4 times the volume, surface area, diameter, etc.

    It probably wouldn't make too much of a difference but the topography would also change how much land area there is. For instance a hill has more area to walk on that a flat area that takes up the same space.

    #14 4 months ago

    Iron Maiden pro all the way.

    #15 4 months ago
    Quoted from LTG:

    Bigger question.
    How many pinball machines can you stick on this new planet ?
    LTG : )

    Depends on how many women are on this new planet.

    #16 4 months ago

    Assuming “bigger” refers to volume.

    Let R be the radius of a sphere.

    The surface area of a sphere is A = 4*pi*R^2.

    The volume of a sphere is V = pi*R^3*4/3.

    The volume of the new planet is Vnew = 2.4*Vearth.

    This means that
    pi*Rnew^3*4/3 = 2.4*pi*Rearth^3*4/3,
    which implies
    Rnew = (2.4)^(1/3)Rearth.

    The area of the new planet is therefore
    Anew = 4*pi*(2.4)^(2/3)*Rearth^2 = (2.4)^(2/3)*Aearth.

    The land area on the new planet is then
    Lnew = 0.31*(2.4)^(2/3)*Aearth.

    Using Aearth = 196,900,000 sq. miles we then have
    Lnew = 0.31*(2.4)^(2/3)*196,900,000 = 109,416,185 sq. miles.

    #17 4 months ago
    Quoted from RyanStl:

    Let us know when you publish. Sci-fi and Fantasy are my two favorite genres.

    Thank you, will do.

    Quoted from jester523:

    I guess it would depend on what you mean by bigger. 2.4 times the volume, surface area, diameter, etc.
    It probably wouldn't make too much of a difference but the topography would also change how much land area there is. For instance a hill has more area to walk on that a flat area that takes up the same space.

    This has been fascinating, because I have only now tonight, understood that 2.4 times bigger, is not just to say, 1 times 2.4 It turns out it is in fact a radius thing. Take this wiki page for example on Super Earths:

    "On 5 December 2011, the Kepler space telescope discovered its first planet within the habitable zone or "Goldilocks region" of its Sun-like star. Kepler-22b is 2.4 times the radius of the earth and occupies an orbit 15% closer to its star than the Earth to the Sun. This is compensated for however, as the star, with a spectral type G5V is slightly dimmer than the Sun (G2V), and thus the surface temperatures would still allow liquid water on its surface. "

    I point this out because this is in fact the planet I was using as the planet in my fourth book. So according to this, Kepler-22b is far bigger then just Earth times 2.4, right? Like way bigger, right? Which I guess would make Kepler-22b's land mass of 31% way bigger then Earths, right? It sounds like KozMckPinball was on to something here.

    Quoted from KozMckPinball:

    Googled it and:
    A=4(pi)r^2
    so new A is 2.4 times old A
    real land area is that times 0.31
    so new land A is 2.4 X .31 X 196,900,000 Sq miles =146,493,600 Sq miles
    if 2.4 times bigger means the radius is 2.4 times bigger than the formula involves 2.4^2

    If so, then 146,493,600 square miles is way to low, right?
    See, this is why I have to ask! I clearly should have paid more attention to this in school. LOL

    #18 4 months ago

    You pinheads will be glad to know that I have signed up over at scienceforums.net under the same name, a site I am sure is the place to be for all of the preeminent and fashionable science aficionados. No doubt some Poindexter over there will be more then capable of answering my math question with the greatest of ease, as well as all of my other weird science questions that I am sure to both dazzle and disorient them with. Thank you to all who attempted some help. It was appreciated.

    #19 4 months ago

    Does gravity increase equally with more mass?
    Or is there a curve.
    If its equal, your human characters will need some sort of mech suit, or reinforced space suits.

    Love syfy, keep us informed Captain.
    Mission Kepler 22-B, day 1.

    #20 4 months ago

    You also have to consider whether your Kepler has an equivalent water mass.
    Is it in a warm phase or an ice age? Remember much of the Mediterranean, Persion Gulf, and continental shelves were dry land during the last ice age.

    There are great short vids on YouTube showing ice age sea levels, you could almost walk from Malaysia to Australia.

    #21 4 months ago

    It sounds like you want the surface area of a sphere.

    https://www.google.com/search?q=surface+area+of+a+sphere&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari

    Gravity is a little more complicated, but this page can help.

    https://www.omnicalculator.com/physics/gravitational-force

    Good stuff here. I love Sci-Fi. Please post when you finish your book.

    #22 4 months ago
    Quoted from ForceFlow:

    Is this homework?
    Take the total surface area of earth, multiply by 2.4 (to get the total surface area of the new planet), and multiply by 31% (to get the available land on the new planet).
    [Edit]: nevermind, this would work for flat surface area, but not a sphere.

    You have just discovered why the flat earth movement began. Someone was having a hard time with the math....

    ED7B036A-61CC-484F-A081-405F22CD7705 (resized).jpeg
    #23 4 months ago

    Why can’t you just multiply by 2.4? 2.4 times bigger literally means that no?

    #24 4 months ago

    I’ve always heard you could fit a million earths inside the sun,so does that mean you can fit 2.4 earths inside the new planet?

    #25 4 months ago

    Math teacher here. I'm assuming bigger = volume. A ball that's twice as big is not also twice the surface area.

    You have to take the volume of Earth and multiply that by 2.4 first, find the radius, then take the surface area of your new planet (using S/V = 3/R) and multiply that by 0.31.

    Earth's current volume = 259,875,159,532 mi³

    New Earth volume = 623,700,382,877 mi³

    New Earth radius = 5300.24323572 mi

    New Earth total surface area = 353,021,751 mi²

    31% = 109,436,742 mi²

    Which is also what RonaldRayGun got but in a different way, and he showed his work. Full credit.

    #26 4 months ago
    Quoted from ThePinballCo-op:

    Math teacher here. I'm assuming bigger = volume. A ball that's twice as big is not also twice the surface area.
    You have to take the volume of Earth and multiply that by 2.4 first, find the radius, then take the surface area of your new planet (using S/V = 3/R) and multiply that by 0.31.
    Earth's current volume = 259,875,159,532 mi³
    New Earth volume = 623,700,382,877 mi³
    New Earth radius = 5300.24323572 mi
    New Earth total surface area = 353,021,751 mi²
    31% = 109,436,742 mi²
    Which is also what RonaldRayGun got but in a different way, and he showed his work. Full credit.

    If the new planet is gaseous, solid land area is zero. Or much smaller than the volume indicates if it has a solid core.

    #27 4 months ago

    On this new planet Diner > Taxi, still.

    #28 4 months ago
    Quoted from TexasJustice:

    You pinheads will be glad to know that I have signed up over at scienceforums.net under the same name, a site I am sure is the place to be for all of the preeminent and fashionable science aficionados. No doubt some Poindexter over there will be more then capable of answering my math question with the greatest of ease, as well as all of my other weird science questions that I am sure to both dazzle and disorient them with. Thank you to all who attempted some help. It was appreciated.

    Good idea.
    SciFi fans are brutal on math and science mistakes in writing.

    #29 4 months ago

    I just woke up and I opened this thread. I need coffee....

    #30 4 months ago

    pasted_image (resized).png
    https://en.wikipedia.org/wiki/File:Clifford-torus.gif

    Maybe someone could explain it in the 4th dimension.

    #31 4 months ago

    OK, people, calm down. There's a terminology gap here. NASA refers to exoplanets' sizes in terms of multiples of earth's RADIUS, not VOLUME. That means you have to use the 2.4 times radius logic, not volume, so the exoplanet's surface area would be 2.4^2 times that of earth, i.e. a multiple of 5.76.

    The reason NASA does it this way is that most people have difficulty understanding what "twice the size" means when construed as volume. If you were asked to create a ball "twice the size of a baseball" using volume, you'd struggle with it. Twice the size using radius you'd just measure and go.

    As for the application here, a lot of science fiction writers have written about "world building", plus there have been hundreds of panels on it at conventions in the past 80 years (I attended a large number of these). Have you used any of those resources? Take a look at Murasaki or Medea for starters.

    Of course for real surface area, try Ringworld (Larry Niven) or a Dyson Sphere.

    #32 4 months ago
    Quoted from Completist:

    You have just discovered why the flat earth movement began. Someone was having a hard time with the math.... [quoted image]

    pasted_image (resized).png
    #33 4 months ago

    i asked 'Alexa'. it replied "you think too much!" lol

    #34 4 months ago
    Quoted from bobmathuse:

    OK, people, calm down. There's a terminology gap here. NASA refers to exoplanets' sizes in terms of multiples of earth's RADIUS, not VOLUME. That means you have to use the 2.4 times radius logic, not volume, so the exoplanet's surface area would be 2.4^2 times that of earth, i.e. a multiple of 5.76.
    The reason NASA does it this way is that most people have difficulty understanding what "twice the size" means when construed as volume. If you were asked to create a ball "twice the size of a baseball" using volume, you'd struggle with it. Twice the size using radius you'd just measure and go.
    As for the application here, a lot of science fiction writers have written about "world building", plus there have been hundreds of panels on it at conventions in the past 80 years (I attended a large number of these). Have you used any of those resources? Take a look at Murasaki or Medea for starters.
    Of course for real surface area, try Ringworld (Larry Niven) or a Dyson Sphere.

    post #3

    #35 4 months ago

    I like Reece’s

    #36 4 months ago

    You could address the gravity issue by making the bigger planet only a bit more massive than Earth (ie, less dense) to account for the greater distance from the surface to the centre of gravity. Don’t ask me to do the math, though

    #37 4 months ago

    I definitely way jumped the gun in asking this question. I clearly did not have nearly the math and science background on any of this coming in. This isn't the kind of sci-fi that I am normally into. In addition to the fact that I really love to write parody and comedy, I'm more of a fantasy, time travel, paradox, or alternate reality type of writer. I have never in 25 years went to another planet in my writing. I've written lots of stuff over the years, even some alien stuff, but nothing like this. I actually thought this was going to be an easy question. Easy enough to maybe not even even ask it. I definitely did not know, when I picked Kepler-22b from a list of planets, that this was kind of a famous planet in the Astronomy world. This is why I was so cavalier in my first post. I thought this was a simple math question.

    Quoted from bobmathuse:

    OK, people, calm down. There's a terminology gap here. NASA refers to exoplanets' sizes in terms of multiples of earth's RADIUS, not VOLUME. That means you have to use the 2.4 times radius logic, not volume, so the exoplanet's surface area would be 2.4^2 times that of earth, i.e. a multiple of 5.76.
    The reason NASA does it this way is that most people have difficulty understanding what "twice the size" means when construed as volume. If you were asked to create a ball "twice the size of a baseball" using volume, you'd struggle with it. Twice the size using radius you'd just measure and go.
    As for the application here, a lot of science fiction writers have written about "world building", plus there have been hundreds of panels on it at conventions in the past 80 years (I attended a large number of these). Have you used any of those resources? Take a look at Murasaki or Medea for starters.
    Of course for real surface area, try Ringworld (Larry Niven) or a Dyson Sphere.

    Thanks for the help. I'm definitely not thinking I'm discovering fire or anything. At the end of the day, as of right now, this story on this world is more character and story driven. To me this is more of just a large Earth, but with interesting idiosyncrasies. Definitely not dystopian or even environment driven per se. The world should be the sauce, not the steak. I see my conflict in this fourth or fifth book as more of a new world land grab by competing factions as told by youths with issues, as it is YA. I'm definitely not thinking anything on the scope of a Ringworld.

    Does Murasaki or Medea mean to look into "The Tale of Genji"? That's what I found. The Tale of Genji does seem worth reading about.

    Quoted from Eightball88:

    You could address the gravity issue by making the bigger planet only a bit more massive than Earth (ie, less dense) to account for the greater distance from the surface to the center of gravity. Don’t ask me to do the math, though

    At the end of the day, I'm terraforming the whole thing from a water world into a large Earth, using rockets, nanobots, biologic packs, and a massive amount of BS. The whole thing is like just four paragraphs that have a tinge of plausibility, as long as it is humans doing this 300 years from now, more then us doing this today. I simply state it as fact, and then I walk away into the story. I'm honestly not worried a ton about it sounding 100% accurate at all. It just as to sound well thought out.

    Think Matrix. You go, "That can't work!", but it sounds good and everyone just accepts it. It's like how does the Flux Capacitor work? Who knows. We get a crude drawing, and then 30 year later, there it is! Sometimes the less said, the better.

    I just wanted it to have some "verifiable" stuff, because I know that Neil Degrasse Tyson ripped into "The Martian", and I figured if I could spend a few minutes having some "facts" in the book, then that was ok. I thought this post would be 3 comments deep at best.

    Quoted from gonzo73:

    Does gravity increase equally with more mass?
    Or is there a curve.
    If its equal, your human characters will need some sort of mech suit, or reinforced space suits.
    Love syfy, keep us informed Captain.
    Mission Kepler 22-B, day 1.

    Hi. I love your enthusiasm, but this is more of a deep outline that you spend awhile thinking on. This series would span 1000 years from 10 years from now, to 3000AD, as it continues with the characters ancestors in a new time and setting. It goes current Earth, Future Earth, a planet in Alpha Centauri, spaceship, and then Kepler-22b. It's really not one of those books that you just start writing, and see where it goes. This is the type of series you plan, and plan, and plan, or it will suck, and suck, and suck.

    I appreciate everyone's support, but this got a bit out of hand. I really thought this was a simple math problem. Although some of what people said, did get me thinking about new things I might not never have thought about, so that is really good. I mean this has not been, from my viewpoint, unproductive or anything.

    I'm still not sure we have really got the right answer. Kepler-22b is apparently freaking huge compared to Earth

    Kepler 22b (resized).jpg
    #38 4 months ago
    Quoted from Eightball88:

    You could address the gravity issue by making the bigger planet only a bit more massive than Earth (ie, less dense) to account for the greater distance from the surface to the centre of gravity. Don’t ask me to do the math, though

    Yea, the funny thing about gravity on alien worlds is, people don't really expect you to explain it. I might toss in an explanation, but ultimately, as anyone who has ever watched Star Trek, or Star Wars knows, gravity is a thing we just take for granted. If they can breath, they can walk.

    It's honestly not a big deal. Knowing the land mass number is not a big deal even. The first version of The Hobbit didn't' even describe what Gollum looked like. These things ultimately are not important. That's not to say I don't care, because I do, but it's really more about my pathologies for some realism in my fantasy, then it really being important. My thirst for realism, has really always been my achilles heel in fantasy writing. I have been trying really hard, to ditch it. I mean could I write any of those Wizard of Oz books? Or Alice in Wonderland? Because those are like from the mind of a schizophrenic. I mean look at me. I'm worried about land mass on an alien world? smh LOL

    #39 4 months ago

    Final update here, just for those who were wondering. According to someone on a science and math forum, this is the answer:

    "The surface area of a sphere is 4πr². If the radius of Kepler 22b is 2.4 x that of Earth, that would be ~9600 miles.

    So the surface area will be 4 x π x 9.6² x 10⁶ sq.miles ~1.2 x 10⁹ sq. miles if my arithmetic is right. Or in "ordinary" notation that is 1,200,000,000 sq. miles. So you can divide that between land area and ocean area as you wish.

    If you want ocean mass, however, as opposed to area, you have to calculate the volume of water, which means you need to say how deep you think the ocean is on average. You can then use the formula for the volume of a sphere 4/3 πr³. Since the water is a spherical shell around the planet it will be the volume at full radius, (call it R) minus the volume at the radius at the ocean floor (call it r) : i.e. 4/3 π(R³ - r³). You can then apply the density figure you want to use to get the mass. That would be for a planet whose surface is all ocean , so then you would pro-rate for the proportion that you want to be ocean. "

    Basically I can divide 1.2 billion out how ever I want, or in my case 31% land is 372 Million sq miles, and the Ocean is 828 million sq miles.

    And unless anyone has anything else to add, I guess that concludes this thread. Thanks y'all!

    #40 4 months ago
    Quoted from TexasJustice:

    If the radius of Kepler 22b is 2.4 x that of Earth

    This is the info I asked for earlier: "Did you mean 2.4x volume, surface area, etc?" I solved for volume, but you meant to solve for diameter/radius. Kind of hard to answer the question without the proper info.

    But I'm glad you got your answer. Pretty cool about Keplar-22b. I remember hearing about this planet but completely forgot to read about it. This is good stuff, thanks!

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