Gravity Assist: to slow ESA's JUICE down!

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  • Опубліковано 12 вер 2024
  • Hi Spacecats, I'm Dr Maggie Lieu and welcome to my channel, where you can find all things space, astronomy and physics! In this week's video, I'm going to break down the calculations to how we get to Mars. We will learn about the Hohmann transfer orbit to get us on a trajectory to Mars and why this particular trajectory is used. We will calculate how long it takes to get to Mars, when the launch window is, and how often it occurs.
    Links:
    www.cosmos.esa...
    iopscience.iop...
    Media credits:
    Jupiter close-up: ESA/Hubble/Kornmesser/Christensen
    Juice’s journey and Jupiter system tour: ESA/Lightcurve Films/R. Andres
    Earth gravity assist (EGA) NASA
    Juice orbits around Ganymede: ESA / ATG medialab
    Gravity assist angles: Rachelz9999
    Juice returns for a lunar-Earth flyby: ESA
    Juice Earth-Moon flyby: ESA/Lightcurve Films/R. Andres
    Juice antenna: ESA / ATG medialab
    JUICE lunar images: ESA/Juice/JANUS
    Special thanks to my UA-cam Members: Annex Celestial, Wheely Big Bike Trip, Steven Yee, Anders Welander, Bill Fratt, David Brant, John Lewis, Jordan Workshop, macgonzo, Christopher Senn & Mike B.
    You can also sign up on my channel page to get access to perks:
    / @spacemog
    Support me through my shop:
    www.maggielieu.com/shop
    If you enjoyed the video, please consider by liking, sharing and subscribing! I'm also on:
    twitter: / space_mog
    instagram: / space_mog
    facebook: / spacemog

КОМЕНТАРІ • 123

  • @joehopfield
    @joehopfield 18 днів тому +11

    Thanks for the planet-relative vs sun-relative explanation - now grav-assist actually makes sense.

    • @SpaceMog
      @SpaceMog  18 днів тому +2

      Yay - always happy to help

  • @hankseda
    @hankseda 18 днів тому +4

    Orbital dynamics is complicated and not without surprises! Thanks for breaking it down for us.

  • @Broken_robot1986
    @Broken_robot1986 18 днів тому +7

    What crazy trajectory used, I can't wait to see what we learn. I love that "jiggle it" still works in space!

    • @SpaceMog
      @SpaceMog  18 днів тому +4

      Jiggling it is usually risky - you dont want to break anything else. I was super nervous when they decided to heat up Euclid to fix their condensation problem 🙈

  • @Bob_C34
    @Bob_C34 18 днів тому +6

    I remember a professor discussing this once. You made it more interesting 🙌🏻 thanks Dr. Maggie 🤓

    • @SpaceMog
      @SpaceMog  18 днів тому

      that's great! thank you!

  • @targetmann100ify
    @targetmann100ify 18 днів тому +6

    Okay i just broke 3 pencils and some paper trying to calculate ,,,,,So with that in mind im just gonna give up for now and dream about slingshooting myself through space and hope somebody one day get to experience of the universe from a spaceship full of kittens and puppies and feel the happiness 😻😽 .And thank you dr lieu for your beautifull mind and work you do.

    • @SpaceMog
      @SpaceMog  18 днів тому +2

      thanks for trying! im definitely taking cats and dogs with me when i leave this planet, even if i have to kick out a human 😏

  • @patryn36
    @patryn36 18 днів тому +6

    You also have to account for the target of the gravity assist rotation.

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      You're absolutely right! The target planet's rotation plays a crucial role in the exact trajectory and energy gain

    • @patryn36
      @patryn36 18 днів тому

      @@SpaceMog That and a few other aspects i have learned about makes me think people in your portion of the world (science focused) have it wrong with relativity, it is allowing you to get over the seeming flaws in newton's equations but it is still not right as shown with the stars on galactic edges and with the collective ideas on black holes among others. There are other areas that i am wondering with all the data and known facts why you and others are so focused on like you all are.

  • @annexcelestial
    @annexcelestial 18 днів тому +10

    Thank you Dr Maggie for this great video...I love it!!!

  • @HarryNicNicholas
    @HarryNicNicholas 18 днів тому +4

    i invested in a large gold fish bowl and a kayak, and now all i need is elon to gravity assist me into orbit so i can paddle to mars.
    i worked on the 2000 BBC series "the planets", i did about 20 shots of various satellites, proto planets forming, and a model of the solar system (although i tried to be accurate to reality, as this was just graphics for a show accuracy came in second place), so, i have a vague understanding of rocket science (i did graphics for ESA's SOHO project too, and a whole series about colonising asteroids) but you lost me at "velocity little us" as i am algebra blind - lol.
    another fascinating program though, keep them coming.
    (i have some of my tv stuff on my channel if you scroll back 20 years or so :) )

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      Thanks Harry! If i ever meet him, ill let him know you are waiting!
      Those are some cool guitars you have there, didnt quite find the space though

    • @HarryNicNicholas
      @HarryNicNicholas 18 днів тому

      @@SpaceMog it is 20 plus years ago, look for "'the planets' bbc tv documentary series"

  • @christopherwilson6527
    @christopherwilson6527 18 днів тому +1

    Finally I found a video that explains it properly. I knew how the assist works, but I didn’t know which passing direction did what (in front to slow, behind to speed up). Love your videos!

  • @johnlewis8664
    @johnlewis8664 18 днів тому +2

    Great video! Looks like we’ve got a bit of a wait on our hands… plenty of time for more maths!

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      Yes we do! Thanks :-)

  • @DavidBrant
    @DavidBrant 18 днів тому +2

    Reminds me to practice my gravitational assist 😮‍💨 😅
    It’s another one ☝🏼 great vid Doc! ❤

    • @SpaceMog
      @SpaceMog  18 днів тому

      what's that? 😆

  • @gregorymccoy6797
    @gregorymccoy6797 18 днів тому +1

    Wonderful bit of science you've shared with us. Finally joined your channel.

    • @SpaceMog
      @SpaceMog  18 днів тому

      Thanks and welcome

  • @samedwards6683
    @samedwards6683 17 днів тому +1

    Thanks for yet another educational and entertaining video. Keep it up.

    • @SpaceMog
      @SpaceMog  14 днів тому

      Thanks for watching!

  • @ARWest-bp4yb
    @ARWest-bp4yb 18 днів тому +3

    It sucks that it takes so long to reach the outer planets! I was twelve when the Voyagers launched and twenty four when Voyager 2 reached Neptune. I didn't seem that long back then, but I'll be retired by the time JUICE get to Jupiter and that seems like so much longer now.😄 Hopefully when Starship is operational we can get out there faster, it would be nice to re-visit Uranus and Neptune in my lifetime!🤞🤞 Thanks Dr. Maggie!👍👍

    • @SpaceMog
      @SpaceMog  18 днів тому

      Can't wait until Starship works too - i can't wait to take a trip myself - wouldn't you like to see those planets with your own eyes? :-)

    • @ARWest-bp4yb
      @ARWest-bp4yb 18 днів тому

      @@SpaceMog Sure, and I can get the senior discount by then!🤣

  • @donaldbohn3183
    @donaldbohn3183 17 днів тому +1

    Well explained. I've actually seen it shown in recent videos.

  • @TheBevo67
    @TheBevo67 18 днів тому

    Love your videos - always look forward to them and learning a little something about space exploration and the science behind it.

    • @SpaceMog
      @SpaceMog  18 днів тому

      Awesome, thank you!

  • @caseymead9399
    @caseymead9399 18 днів тому +2

    OOh I love me some Δ-V. More equations please!

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      Glad you liked it 🧮

  • @paulalexandredumasseauvan2357
    @paulalexandredumasseauvan2357 18 днів тому +1

    thanks for the explanation! enjoyed your video 👍☺

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      Glad you enjoyed it!

  • @Allan_aka_RocKITEman
    @Allan_aka_RocKITEman 18 днів тому +1

    Starting at about 06:39 in this video: Most of the math {up to that point in the video} went over my head. HOWEVER, Dr. Maggie mentioning the planet losing as much momentum as the spacecraft gains is something I first became aware of reading Arthur C. Clarke's _novelization_ of *2OO1: A SPACE ODYSSEY.*

  • @eeeXDeee
    @eeeXDeee 18 днів тому +1

    So informative! Nice video

  • @donaldbohn3183
    @donaldbohn3183 17 днів тому +1

    I love graphics of how the solar system actually moves in our galaxy!

    • @SpaceMog
      @SpaceMog  14 днів тому

      I was trying to find a royalty free version but didnt manage to and had no time to mock one up in blender but i completely agree, its mesmerising

  • @NobodyOfNote-qv5wh
    @NobodyOfNote-qv5wh 18 днів тому

    Great work, as usual really enjoying your explanations! 😊

  • @johnjoseph9823
    @johnjoseph9823 18 днів тому +1

    Brilliant as always. thank you

  • @narrator69
    @narrator69 18 днів тому

    Kerbal Space Program and the Real Solar System mod for the game taught me so much about rocketry.
    At first I couldn't even get to orbit but after a year I can easily get to any planet or moon in the system.

    • @SpaceMog
      @SpaceMog  18 днів тому

      I still suck at that game 😅

  • @matthewhenson2421
    @matthewhenson2421 18 днів тому +2

    The Lunar Earth Flyby images of the moon and the Earth are exactly surprising.

    • @SpaceMog
      @SpaceMog  18 днів тому

      I hope you liked them as much as i did :-)

  • @MrGaborseres
    @MrGaborseres 18 днів тому +1

    🤔❤️👍Thanks for the good video and explanation

    • @SpaceMog
      @SpaceMog  18 днів тому

      Thanks for watching

  • @treefarm3288
    @treefarm3288 16 днів тому +1

    Thanks for the video, but we had to wait till minute 10 to find out what the actual figures for JUICE were. Too bad I will be extra old by 2031, haha.

    • @SpaceMog
      @SpaceMog  14 днів тому

      You can wait 10minutes, you dont age that quickly :-)

  • @BZAKether
    @BZAKether 18 днів тому

    Thank you for the orbital assist explanation, I had wondered how it was possible to gain speed overall if the gained speed by the "fall" was being lost on the way out, I didn't think about the planet or object itself and its effect on the speed!

  • @EmmanuelBrito
    @EmmanuelBrito 15 днів тому

    I’m not sure if she’s cold but she appears to be and I find it compliments the space visuals in the background. It’s like not having yellow to appreciate but using that appreciation to fully appreciate the efforts of red and green to somehow stimulate a simulated intuitive instinctive intuitional instinct to mimic yellow for myself . 🤓

  • @jaimeduncan6167
    @jaimeduncan6167 18 днів тому

    Subscribed, 3th excellent video în a row. We need Nuclear thermal and Nuclear electric propulsion. I understand why Jupiter Icy Moons Orbiter was cancelled but the work on the nuclear reactor should have continued. We are still exploring the planets with an approach of the 80s (but with better computers to do even more fancy gravity assists). Clearly electric propulsion is not going to move the aircraft to Jupiter and then slowdown the spacecraft but Nuclear thermal will do (Yes SLS can do the job, but at 4 billion a pop to gain few years is too much)

  • @sectsan2471
    @sectsan2471 18 днів тому +5

  • @syclonusmusic
    @syclonusmusic 18 днів тому

    Hi 😊 could you show more orbital mechanics with algebra using real numbers? How could we show navigation using x, y, and z coordinate systems? Thanks 😊

  • @ptonpc
    @ptonpc 18 днів тому

    Nicely explained. Thank you :) A bit sad to think the chances are I will have expired long before JUICE gets there. Safe and successful flight to it.

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      🥲 you never know

    • @ptonpc
      @ptonpc 17 днів тому

      @@SpaceMog Without playing the world's smallest violin, the chances are pretty much nil. Thanks anyway, The most 'annoying' thing is all these great missions in the pipeline I'll never see.

  • @joelcorley3478
    @joelcorley3478 18 днів тому

    I would point out that gravity assists are not entirely free. You almost always need to do some kind of correction burn well ahead of the approach in order to nail the flyby corridor. The Oberth effect tends to dictate where in the orbit that correction burn ought to be.

  • @corychristensen5917
    @corychristensen5917 18 днів тому +5

    Can solar sails also be used as solar brakes? For decelerating interstellar travel or travel to Mercury and Venus

    • @flakcannon722
      @flakcannon722 18 днів тому +2

      Solar sails could be used to slow something down over a long time, if you were headed at the sun...

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      absolutely - changing the orientation of the sail, it could be quite effective!

  • @John-wd5cb
    @John-wd5cb 18 днів тому

    Amazing!
    You can build a craft fuselage that absorbs every particle emission and send it at a gravity network of routes around the Solar system with almost minimal propulsion adjustments and nobody will ever detect it!😮

    • @John-wd5cb
      @John-wd5cb 18 днів тому

      👽 alien 1: 🤯
      👽 alien 2: 🤔

  • @husk79
    @husk79 18 днів тому +1

    Was JUICE supposed to use the moon and Earth to accelerate and decelerate from the start or was it redirected because of the fuel loss from the wonky antenna jam?

    • @SpaceMog
      @SpaceMog  14 днів тому

      It was, although the exact calculations are always changing. JUICE was supposed to launch in 2022 and for that scenario it would have done 2 flybys of moon and Earth before Venus. The 1 year delay in launch meant they now have 1 flyby of moon and Earth before Venus but then 2 more after that

  • @ChrisM-hx9kv
    @ChrisM-hx9kv 18 днів тому

    Commenting to feed the complex equation of the algorithm. May it's increased mass provide a proper slingshot maneuver for more viewers to slow down and view this channel 🙃

    • @SpaceMog
      @SpaceMog  18 днів тому

      Thanks so much 😇

  • @WatchingUntiltheEnd
    @WatchingUntiltheEnd 17 днів тому

    7:24, it kinda does.

  • @HarryNicNicholas
    @HarryNicNicholas 18 днів тому

    okay, your homework: how do we know where and when moons will be? i mean okay it can be worked out from observation, but i assume there is an almanac or a directory of the positions of most if not all planetary objects? we have catalogues for stars and galaxies, so i assume there is an equivalent for the planets and moons? i suppose i could look it up. again thanks for a great insight.

    • @tonywells6990
      @tonywells6990 18 днів тому +1

      NASA's JPL (Jet Propulsion Laboratory in California) provides ephemeris (trajectories, basically a table of positions and velocities) of all the moons and planets and other objects in the solar system from observations. I'm sure other space agencies produce their own ephemerides but JPL is the most famous.

    • @John-wd5cb
      @John-wd5cb 18 днів тому +1

      Red-eye

    • @HarryNicNicholas
      @HarryNicNicholas 18 днів тому

      @@tonywells6990 ah, i suspected as much, but thanks for pointing me in the right direction.

  • @blacksmith67
    @blacksmith67 8 днів тому

    Can a Lagrange point be used for gravity assists?

  • @Privacityuser
    @Privacityuser 18 днів тому

    Most fast object records ? 💥

  • @alnilam2151
    @alnilam2151 18 днів тому +3

    I encountered my own; sudden, decelleration just yesterday & wow did gravity stop in its' path track orbit is literally unknown: no jury to be found on phys10s Achilles+Abruptor both equal disrupters in constant... Hip+Hap Less Battle: wanna know what is #Oxymoronic the #HumanBody its' own #StringOfTheory {/} ;x

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      That's sad to hear, i hope everything is going ok and you get better soon

    • @alnilam2151
      @alnilam2151 18 днів тому

      @@SpaceMog Well, it's not that I didn't see it coming; Atlas had it Leonardo drew it I guess I'll have 2 carry+manage it! #lifesucks {/} ;x

    • @alnilam2151
      @alnilam2151 18 днів тому

      @@SpaceMog And, ThankYou for the concern! 😘

  • @The1stDukeDroklar
    @The1stDukeDroklar 18 днів тому

    "This is basic rocket science people" - Ender's Game

  • @AndersWelander
    @AndersWelander 18 днів тому

    Icy moons made me think of a Cuban I met last night at a party. He said he wanted to have a wife from Iceland because then the kids would be ice-cubes.

  • @Vagabondo-fs6qu
    @Vagabondo-fs6qu 18 днів тому +1

    You lost me at the first derivative 😂

  • @coreymay918
    @coreymay918 18 днів тому

    Fighting urge to do math at home

  • @arnokosterman231
    @arnokosterman231 18 днів тому

    😍

    • @arnokosterman231
      @arnokosterman231 18 днів тому

      Diamagneticle closer to the planet the resistance of the planet resisst more thentional diverentional displacemends 😍 so from oll directions you reseave thentional diverentional displasmends partley bouncing of the craft and partley mantainence of the ciclesematic and colective cohesion so the behavieures can stay in existance jead close the planet youl reseave less thentional behavieures displasmends from the planet position ontil you get inside the space that is graventational counterd in orbit dinamics 🌹
      In a way in the right direction it could exelerate til the speed of the space that is dragging the spacecraft around against the rotational motion of the graventational countering youl are able to slow down😍 and find withs polarflux is stronger to move out with less felosety losses 🛸
      Look to the total interaction sharings in your face book😍
      It is cristal clear wat men see as atrecting behavieures is still there do to the bicker resistance that resists more from behind the resistance while you reseave from oll other directions more 😍🌹😍
      Is not gravety gravety is towart the kuiperbeld behind the rings of planets in the graventational countering zone of the cicles it is magneticley and diamagneticley pushed and in the less directional space and motion zones it is diamagneticle pushed thentional diverentional displasmends in to kinetic translations of directions🛸
      I make tomorrow a new video to show clearly just like the body was pushed down than with a craft is pushed towart aour in withs sone wat interaction tace over to ad to the behavieures of the trajectory💜
      It is funnie no one in space teghnolegys in the past dit not saw our manshenend it o yes one time in polarized sail satellites when the enter the meat plasmafilemental behavieures out the plasma philemental it is within chainces directions of cominications towart it total behavieures of existance towart the poseble behavieures of the medium transfer inside and as that plasma philemental behavieures (shaped translations)
      Look to the new Higgs field not bi long correct but there is awernes that if whe posebiletys of the cosmic translations chainces everything desolves in to new behavieures

    • @arnokosterman231
      @arnokosterman231 18 днів тому

      Planets except mercury rotates
      The rings around it orbits the sun like the kuiperbeld ourbits the galaxy yet the sun is contained somwhere in the position on the princeple feildflow and rings intergety structure and diamagneticle container and graventational countered metacontainer behind the coronal🛸

    • @arnokosterman231
      @arnokosterman231 18 днів тому

      Diamagneticle closer to the planet the resistance of the planet resisst more thentional diverentional displacemends 😍 so from oll directions you reseave thentional diverentional displasmends partley bouncing of the craft and partley mantainence of the ciclesematic and colective cohesion so the behavieures can stay in existance jead close the planet youl reseave less thentional behavieures displasmends from the planet position ontil you get inside the space that is graventational counterd in orbit dinamics 🌹
      In a way in the right direction it could exelerate til the speed of the space that is dragging the spacecraft around against the rotational motion of the graventational countering youl are able to slow down😍 and find withs polarflux is stronger to move out with less felosety losses 🛸
      Look to the total interaction sharings in your face book😍
      It is cristal clear wat men see as atrecting behavieures is still there do to the bicker resistance that resists more from behind the resistance while you reseave from oll other directions more 😍🌹😍
      Is not gravety gravety is towart the kuiperbeld behind the rings of planets in the graventational countering zone of the cicles it is magneticley and diamagneticley pushed and in the less directional space and motion zones it is diamagneticle pushed thentional diverentional displasmends in to kinetic translations of directions🛸
      I make tomorrow a new video to show clearly just like the body was pushed down than with a craft is pushed towart aour in withs sone wat interaction tace over to ad to the behavieures of the trajectory💜
      It is funnie no one in space teghnolegys in the past dit not saw our manshenend it o yes one time in polarized sail satellites when the enter the meat plasmafilemental behavieures out the plasma philemental it is within chainces directions of cominications towart it total behavieures of existance towart the poseble behavieures of the medium transfer inside and as that plasma philemental behavieures (shaped translations)
      Look to the new Higgs field not bi long correct but there is awernes that if whe posebiletys of the cosmic translations chainces everything desolves in to new behavieures

    • @arnokosterman231
      @arnokosterman231 18 днів тому

      So you see and say when ther air is cloudy our with misdisireble resistance eurths space time is slowing down a litle bit when you are inside the graventational countering zone you are equatorial resistance yet a notes and sout hemospheric conductor like our space debris is too😅

    • @arnokosterman231
      @arnokosterman231 18 днів тому

      Ah thay you are against the kuiper pull zone than you slow down do to that you move against the kuiper pull
      Tace a lower orbit to get in the graventational countering sone and youl speed up when you are afrond of the planet🐝🥰🎁🥰🐜

  • @flakcannon722
    @flakcannon722 18 днів тому +5

    Ridiculously difficult calculations made understandable by anyone.
    I'm pretty sure you could teach highschool kids.

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      I teach masters students ☺️

    • @flakcannon722
      @flakcannon722 18 днів тому +1

      @@SpaceMog I hope you don't have to simplify it that much for them lol

    • @SpaceMog
      @SpaceMog  18 днів тому +2

      @@flakcannon722 Considering the last 3 cohorts dont know how AA batteries work, I must admit its not far off :/

    • @flakcannon722
      @flakcannon722 18 днів тому

      @@SpaceMog that got a laugh out of me 😁
      Good luck with them

    • @erkinalp
      @erkinalp 17 днів тому

      @@SpaceMog easy, zinc and carbon elctrodes in a manganese solution gradually rip the battery off of the electrodes (ionisation in primary batteries is effectively irreversible) and generate an electric field in the process, causing an electrical tension measuring 1.5 volts when fresh

  • @HobieH3
    @HobieH3 18 днів тому

    Like for algorithm

  • @HarryNicNicholas
    @HarryNicNicholas 18 днів тому

    tricky question that i've asked on lots of science channels and never got a reply - why does squaring work? why ISN'T it E = MC almost squared or even E = MC not quite squared? how come squaring is a nice round figure? would squaring always work even if the speed of light was faster or slower? i do art, not maths dammit.

    • @tonywells6990
      @tonywells6990 18 днів тому +4

      You can trace it back to Pythagoras theorem, the sum of two squares of a right angled triangle (i.e. the lines are perpendicular to each other, or act in separate dimensions) is equal to another square. The areas of the two squares when added is equal to the area of another square. So when you take the square root of that new area you get the length of the new line.
      Equations like E=mc^2 are also based on geometry of lines, but also it can be equated as momentum times energy (p=mv and E=pc) so when you replace the p with mv you get E=mvc, then using v=c (velocity equals speed of light) you get E=mcc=mc^2.
      Also the branch of mathematics called calculus is based on geometry, and if you integrate a variable you raise its power by one. For example integrating x you get x^2/2, integrating x^2 you get x^3/3. Integrating momentum (mass times velocity) you get the kinetic energy of a mass: integrate p=mv -> E=1/2 mv^2.
      I recommend studying basic geometry, algebra and calculus if you want to understand the math.

    • @SpaceMog
      @SpaceMog  18 днів тому +1

      Exactly this. Thanks!

    • @HarryNicNicholas
      @HarryNicNicholas 18 днів тому

      @@tonywells6990 thank you so much, but you haven't answered the question, which is, why does it round out nicely?
      what i was getting at is, yes, or course there is a physical requirement for - say - light to fade according to the inverse square law, for every one inch travelled, it becomes "four times weaker", the question is why is it "four times" and not "3.99 times"
      I DO NOT DOUBT YOUR MATHS, what boggles me is that it's a ROUND NUMBER, as opposed to a not quite a round number.......
      and if i'm, being dumb, bear in mind i'm an artist not a mathematician.

    • @HarryNicNicholas
      @HarryNicNicholas 18 днів тому

      @@tonywells6990 PS good explanation. and trust me, it's not beyond me to realise i'm just being dumb - lol.
      i mean i can see that it's related to physical geometry, but what boggles me is that there is an exact ratio, rather than an "almost but not quite exact" ratios. do you at least see where i'm coming from?

    • @tonywells6990
      @tonywells6990 18 днів тому

      @@HarryNicNicholas It is a logical consequence of a conserved quantity as it is diluted through some geometry with straight lines. Just draw two lines from a point, then measure the area of a triangle made 5cm from the point, and another made 10cm from the point. You will find the 10cm triangle has 4 times the area of the 5cm triangle since the area is squared as you double the length. If the lines are not straight then you would find another ratio.

  • @ROBOTRIX_eu
    @ROBOTRIX_eu 18 днів тому +1

    • @SpaceMog
      @SpaceMog  18 днів тому

      How did you do that? so cool!