You explained in 6 minutes and with no experience required what took Wikipedia 12 pages and a bachelors in Astronomy and theoretical physics highly recommended to explain.
I remember reading a series of science fiction short stories about a space relay station in the L4 Lagrange point. The space station was called Venus Equilateral. It would relay radio signals between Earth and the human colonies on Venus and Mars. Of course there was an emergency in every story that the people on the space station needed to solve. The one thing I remember was that the station's only restaurant kept losing their cloth napkins and table cloths to the engineers.
If the two objects are more massive or less massive, or the ratio between their masses is different, will the LaGrange Points become bigger or stronger?
@vampiracy Just a conjecture here, but he said that the Lagrange points are a region of metastability between two bodies, so I'm inclined to believe that if the ratios differ by some amount the particle poised between those bodies would fall to the body with greater gravity (greater mass) if a perturbation were to occur to the particle. In essence I say the mechanics are similar to balancing a pen on your finger, if you barely tap it, it will fall in the direction of the force applied.
I heard about Lagrange points for the very first time today... while looking up an old Nintendo game called Lagrange Point. ... I'm glad I found this vid to explain them. I don't know what's more impressive, that Lagrange figured all this out or that someone made a video game named after his theorem.
This may be coming out of nowhere, but I must thank you for posting this! I am participating in NaNoWriMo 2010 and my novel takes place in Lagrange point colonies. This really helped me put a loose concept into a concrete theory for me to work with - so thank you!
Belive it or not Free energy is real,But there are very powerfull forces that want to supress the technology,if you want a real Free energy Magnet Motor, get the blueprints at LT-MAGNET-MOTORdotCOM ,take part in the revolution!
This is how we will be able to re-supply the missions to Mars and beyond! We will place container like vehicles filled with food, water and other necessary items for the crews to meet up/dock with on the way to Mars and back!
This is how we will be able to re-supply the missions to Mars and beyond! We will place container like vehicles filled with food, water and other necessary items for the crews to meet up/dock with on the way to Mars.
@Mahruful First of all, I am no expert, but I did speak to someone at NASA last week and he told me about this. No, I was just stating that Lagrange points will be used for our trips to Mars and beyond. Because of the cost of weight when we launch from Earth (roughly $1Mdollars/lb to Mars), we will have to launch these container vessels prior to the launch of our astronauts, and with the discovery of water on the moon, we will probably launch them from there.
I sorta get why L4 and L5 would work, but could someone explain L2 and L3? I would think at those points, the gravity of the two objects would add to eachother.
The 1980 SPS summer study by DOE discussed the uses of these! You are the first person in a long time to mention L5 society and this stuff that was going on in reaction to the Oil Embargoes, but also trying to get the space programs running again.
Plait is the man.. he doesn't come on to you as a know it all scientist.. its more like "hey let me explain how things work and enjoy my quirkiness".. he sounds as much the same as he did in his "death from the skies" book.. Freaking Ace!
Really interesting stuff even if bit complicated at times for normal dummy like me. I don't really understand much about astronomy, science, space or stuff like that but I still find your videos very entertaining, fun and joy to watch.
"Wheres my squishy earth ball? Of well, too far to find" -Phil Plait
@solalito : Not exactly, a L.p. have no mass and so can not support a real orbit, but you can have orbits that use the interaction between for example the sun and the earth, and these are centered on the L.p. since it is the same equalibrium effect they use; halo or lissajous orbits. For example SOHO near L1. and the Planck and Herschel observatories close to L2 These orbits tend to be unstable, so active means are needed to stabilize them.
@Mahruful : I expect so, you could place stations in orbit at them, the Earth-Moon L1 point would be a candidate, but most of them would be more valuable for special applications(observatories of different sorts) rather than direct settlement. L.ps do offer low energy transfer orbits(Like the Interplanetary transport network). Probably not suited for manned craft, but for cargo that doesn't need to get there quickly, the relatively low cost may make supplying bases and stations less costly.
i mean, if it does wrap back on itself like the surface of an expanding balloon, i can understand that, but i find it confusing how something can expand to infinite size, given 13.7 billion years, or given forever
i think its infinite in the sense that we can never be fast enough to reach or even see the infinitly expanding edge. basically something that can never be proven, maybe disproven one day.
I'd always thought that the big bang, and the universe being infinite in size, were conflicting theories,
but the spectacular Professor Muller in the physics lectures ive been watching (search Physics 10) says they are both the current accepted model, together
can you help my confusion and bridge my understanding of an infinite universe, with one which was once (briefly) very small in size?
Thanks, that was informative and fun. I am just a dilettante in matters astronomical, so this explanation was great.
Isn't your opinion on centrifugal "force" controversial. I laughed because I remember reading another scientist who insisted that such a force was an illusion.
Yes, the L2 point in the earth-sun system is continually shadowed by the earth. So if you use solar panels you have to go into a "halo" orbit around the L2 point instead of being exactly at it. From the spacecraft the earth would appear to closely circle the sun. There's an L2 point in the earth-moon system too. Ideal for a communications relay from the far side.
I take that back. The L2 point in the earth-sun system is far enough from the earth to be just outside its umbra, meaning that the sun would not be completely covered. It would appear like an annular eclipse. You'd probably still want a halo orbit around it to maximize solar power production.
This was definitely interesting. Up until that point, I thought L1 was found simply by drawing diagonals between two orbiting bodies. Forgot to account for centrifugal forces.
I wasn't disputing the existence of centrifugal forces so much as I just it was funny that Phil is saying one thing and my teacher another. I didn't mean to come across as playing one against the other.
maybe there would be a red halo around the earth? The lagrange pt is at the limit of the umbra, but the earth atmosphere makes earth a convex lens, like for a lunar eclipse.
If, for example, you have a ball on a string, and you spin it around, the only force in action is the tention of the string as it pulls it into the circular "orbit" (it would go straight along the tangent without the tention).
So there is no centriFUGAL force; no force pushing the ball outwards.
exactly! if you have newtons laws in mind, you will quickly come to the conclusion that a stationary circular motion is in fact an accelerated motion. therefore the direction of acceleration must obviously always point towards the center of the circle ("pushing it inwards", because it always wants to "fly off tangentially (inertia)") - so the direction of the force is set!
of course one now might argue: "but if i'm sitting in a roller coaster, clearly i feel a force pushing me in the other direction!"
yes, of course it feels like it - newton, again: "every action has an equal and opposite reaction". so its rather the roller coaster, which presses you towards the center of the circle, than you pushing outwards....
...of course it is to some extent a bit of a philosophical question, otherwise physicists would not argue about it! ;) but anyway, i think its very important to discuss accelerating reference frames with great care - and usually, when you start calculations with a zentrifugal force, things mess up...badly!
its much easier to set up the equations of momentum in the accelerated ref. frame, then to all the backtransformations to an inertial-system using euler-derivatives etc. and get all the ugly and messy zentripetal and coriolis-terms "for free" and you are sure to get the physics right.
sorry for the long talk, but i just felt like talking about this! :)
The sentrifugal force is not a fundamental "real" force, it's an effect of the movement versus what is called inertia, that objects tend to want to keep going in the same direction with the same speed and so on, it really should be called the sentrifugal effect
Centrifugal pumps? Err... inertia? Look, I'm not saying that the centrifugal effect doesn't exist, I'm just saying that the centrifugal force is a fictitious one, ie. it doesn't originate from physical interaction between objects. I cited wikipedia as a source since it's easy for anyone to check, I don't expect people to go out and buy a physics book just to make sure I'm not making it up.
The "centrifugal force" is just the liquid being pumped trying to go in a straight line because of its inertia. Essentially it comes down to how you define things. I think understanding the fictional nature of centrifugal force is an important step in realizing that any change in velocity, including a change in direction that doesn't change the speed, is an acceleration.
While I understand the concept of Lagrage points I still have problems with L3 and L2. But if I understand right those two lagrange points can only exist in a dynamic system, right?
Great explanation Phil! If you found this video informative, please support science and Phil this October and pick up his book 'Death from the Skies'.
some really good stuff here
msjessypp 1 week ago
thanks you did a very good job
cavhoki 2 months ago
You explained in 6 minutes and with no experience required what took Wikipedia 12 pages and a bachelors in Astronomy and theoretical physics highly recommended to explain.
REA00002 2 months ago 2
What's your take on the theory to move matter around a vessel in order to sprint through space/time. I hear it's shockingly possible.
Momentimum 3 months ago
i don't get why L2 and L3 are stable, both earth and sun's gravity pull in the same direction, so it's just like orbiting a bigger object
b0gdanB 4 months ago
@b0gdanB These points are stable, because there gravity force and centrifugal force are equal.
Loewenhertz3 3 months ago
Comment removed
b0gdanB 4 months ago
highly doubt that man will abandon earth for lagrangian colonization
chrisconwaypeters 4 months ago
I remember reading a series of science fiction short stories about a space relay station in the L4 Lagrange point. The space station was called Venus Equilateral. It would relay radio signals between Earth and the human colonies on Venus and Mars. Of course there was an emergency in every story that the people on the space station needed to solve. The one thing I remember was that the station's only restaurant kept losing their cloth napkins and table cloths to the engineers.
Klendathue 6 months ago
unstable equilibrium
1337paladin 8 months ago
I have a question:
If the two objects are more massive or less massive, or the ratio between their masses is different, will the LaGrange Points become bigger or stronger?
vampiracy 9 months ago
@vampiracy Just a conjecture here, but he said that the Lagrange points are a region of metastability between two bodies, so I'm inclined to believe that if the ratios differ by some amount the particle poised between those bodies would fall to the body with greater gravity (greater mass) if a perturbation were to occur to the particle. In essence I say the mechanics are similar to balancing a pen on your finger, if you barely tap it, it will fall in the direction of the force applied.
VIR092 8 months ago
I heard about Lagrange points for the very first time today... while looking up an old Nintendo game called Lagrange Point. ... I'm glad I found this vid to explain them. I don't know what's more impressive, that Lagrange figured all this out or that someone made a video game named after his theorem.
Great explanation vid. Thank you.
TheouAegis 9 months ago
Thanks for explaining too. :)
susedovie 9 months ago
centrifugal is just kinetic energy.....
chibraxial 9 months ago
Thanks for explaining!
QueenSemiramis 10 months ago
I never knew this...It's amazing! I love science.
UOYxSSIMxI 11 months ago
ur username should be badasstronomer
Ivin3690 1 year ago 8
You're a good astronomer badastronomer, why'd I not subscribed to your channel earlier.
muzammilali007 1 year ago
This may be coming out of nowhere, but I must thank you for posting this! I am participating in NaNoWriMo 2010 and my novel takes place in Lagrange point colonies. This really helped me put a loose concept into a concrete theory for me to work with - so thank you!
danipalmtree 1 year ago
Wonderfully executed! Thank you!
cipher2 1 year ago
This has been flagged as spam show
Belive it or not Free energy is real,But there are very powerfull forces that want to supress the technology,if you want a real Free energy Magnet Motor, get the blueprints at LT-MAGNET-MOTORdotCOM ,take part in the revolution!
ivylsp 1 year ago
Absolutely incredible explanation Phil!
oisiaa 1 year ago
This has been flagged as spam show
This is how we will be able to re-supply the missions to Mars and beyond! We will place container like vehicles filled with food, water and other necessary items for the crews to meet up/dock with on the way to Mars and back!
gnarlyharley71 1 year ago
This is how we will be able to re-supply the missions to Mars and beyond! We will place container like vehicles filled with food, water and other necessary items for the crews to meet up/dock with on the way to Mars.
gnarlyharley71 1 year ago
@gnarlyharley71
So is that the basic use that can be made of the langrange points? for space settlements?
Mahruful 1 year ago
@Mahruful First of all, I am no expert, but I did speak to someone at NASA last week and he told me about this. No, I was just stating that Lagrange points will be used for our trips to Mars and beyond. Because of the cost of weight when we launch from Earth (roughly $1Mdollars/lb to Mars), we will have to launch these container vessels prior to the launch of our astronauts, and with the discovery of water on the moon, we will probably launch them from there.
gnarlyharley71 1 year ago
This has been flagged as spam show
@gnarlyharley71 Thanks :)
Mahruful 1 year ago
phil plait only famous because TPTB needs a puppet to do their dirty work. BTw phil are you phage on abovetopsecret com?
dragnet53 1 year ago
I sorta get why L4 and L5 would work, but could someone explain L2 and L3? I would think at those points, the gravity of the two objects would add to eachother.
itchykami 1 year ago
@itchykami you have to consider the motions of the objects in addition to their gravitational fields.
Veteran4Peace 1 year ago
The 1980 SPS summer study by DOE discussed the uses of these! You are the first person in a long time to mention L5 society and this stuff that was going on in reaction to the Oil Embargoes, but also trying to get the space programs running again.
bmecher 1 year ago
Phil Plait rules.
sleepcity 1 year ago
dude dont you ever change that shirt!? ewwww :))))
GShock112 1 year ago
pseudo force : P
slapthatmech 1 year ago
wooooow u nailed it - made it more easier to understand - thanks a lot for the upload...
sasamuraki 1 year ago
Plait is the man.. he doesn't come on to you as a know it all scientist.. its more like "hey let me explain how things work and enjoy my quirkiness".. he sounds as much the same as he did in his "death from the skies" book.. Freaking Ace!
mmmodafoca 1 year ago
word
Tripo1iSamson 1 year ago
this guy knows what he´s talking about ;D
The1337Player 1 year ago
It's a real force, get over it! :D
ParaglidingManiac 1 year ago 3
Really interesting stuff even if bit complicated at times for normal dummy like me. I don't really understand much about astronomy, science, space or stuff like that but I still find your videos very entertaining, fun and joy to watch.
"Wheres my squishy earth ball? Of well, too far to find" -Phil Plait
Mii85 2 years ago 2
can satellites (small mass) orbit these lagrange points? or will they just tend to approach the exact lagrange points?
solalito 2 years ago
@solalito : Not exactly, a L.p. have no mass and so can not support a real orbit, but you can have orbits that use the interaction between for example the sun and the earth, and these are centered on the L.p. since it is the same equalibrium effect they use; halo or lissajous orbits. For example SOHO near L1. and the Planck and Herschel observatories close to L2 These orbits tend to be unstable, so active means are needed to stabilize them.
tr41 1 year ago
@tr41 Can langrange points be any help to space settlements?
Mahruful 1 year ago
@Mahruful : I expect so, you could place stations in orbit at them, the Earth-Moon L1 point would be a candidate, but most of them would be more valuable for special applications(observatories of different sorts) rather than direct settlement. L.ps do offer low energy transfer orbits(Like the Interplanetary transport network). Probably not suited for manned craft, but for cargo that doesn't need to get there quickly, the relatively low cost may make supplying bases and stations less costly.
tr41 1 year ago
@tr41 Ok thanks
Mahruful 1 year ago
i mean, if it does wrap back on itself like the surface of an expanding balloon, i can understand that, but i find it confusing how something can expand to infinite size, given 13.7 billion years, or given forever
HeyHeyHarmonicaLuke 2 years ago
i think its infinite in the sense that we can never be fast enough to reach or even see the infinitly expanding edge. basically something that can never be proven, maybe disproven one day.
kenny8331 1 year ago
I'd always thought that the big bang, and the universe being infinite in size, were conflicting theories,
but the spectacular Professor Muller in the physics lectures ive been watching (search Physics 10) says they are both the current accepted model, together
can you help my confusion and bridge my understanding of an infinite universe, with one which was once (briefly) very small in size?
HeyHeyHarmonicaLuke 2 years ago
Thanks, that was informative and fun. I am just a dilettante in matters astronomical, so this explanation was great.
Isn't your opinion on centrifugal "force" controversial. I laughed because I remember reading another scientist who insisted that such a force was an illusion.
tagginos 2 years ago
great and a very easy explanation =)
ty
UlrichVIII 2 years ago
This comment has received too many negative votes show
pervert
ojedajuanpablo 2 years ago
This comment has received too many negative votes show
You're a pervert for thinking like that, pervert.
GunzFTW99 2 years ago
3:29 "oh, where's my SQUISHY earth BALL? oh well, its too far."
ojedajuanpablo 2 years ago 19
Ok, is the L2 in permanent shadow? Is L2, earth and sol always colinear?
I guess one has to know how far the Earth's penumbra extends.
kurtu5 2 years ago
Yes, the L2 point in the earth-sun system is continually shadowed by the earth. So if you use solar panels you have to go into a "halo" orbit around the L2 point instead of being exactly at it. From the spacecraft the earth would appear to closely circle the sun. There's an L2 point in the earth-moon system too. Ideal for a communications relay from the far side.
philkarn 2 years ago
I take that back. The L2 point in the earth-sun system is far enough from the earth to be just outside its umbra, meaning that the sun would not be completely covered. It would appear like an annular eclipse. You'd probably still want a halo orbit around it to maximize solar power production.
philkarn 2 years ago
that was definetly interesting , never heard of that before but WOW !!
DonEddy89 2 years ago
This was definitely interesting. Up until that point, I thought L1 was found simply by drawing diagonals between two orbiting bodies. Forgot to account for centrifugal forces.
FenristheRedWolf 2 years ago
Obviously I need to explain a few things.
I wasn't disputing the existence of centrifugal forces so much as I just it was funny that Phil is saying one thing and my teacher another. I didn't mean to come across as playing one against the other.
InfidelAvenger 2 years ago
The centrifugal force comment was a lol. I specifically remember my astronomy teacher specifically saying that centrifugal forces don't exist.
The fact is, all forces come in pairs, so if there is a force outward, there is an equal force inward as well.
InfidelAvenger 2 years ago
Yes because teachers know it all.
Prodigyexam12 2 years ago
A follow-on from LaGrange points must surely be horseshoe orbits. :)
bdf2718 3 years ago
"Back to the sun" at L2? Ummm, surely the point is that a significant portion (all?) of the sun is blocked by the earth.
bdf2718 3 years ago
maybe there would be a red halo around the earth? The lagrange pt is at the limit of the umbra, but the earth atmosphere makes earth a convex lens, like for a lunar eclipse.
dobozzene 2 years ago
so that's what people did before television
TherealNDE 3 years ago
There is no such thing as a centrifugal force.
If, for example, you have a ball on a string, and you spin it around, the only force in action is the tention of the string as it pulls it into the circular "orbit" (it would go straight along the tangent without the tention).
So there is no centriFUGAL force; no force pushing the ball outwards.
fatmanprime 3 years ago
that outward force IS centrifugal
KingKongRules001 2 years ago
No, it isn't.
The only force acting on the object is the force pulling it inwards - the centripetal force.
There's no such thing as a centrifugal force.
fatmanprime 2 years ago
exactly! if you have newtons laws in mind, you will quickly come to the conclusion that a stationary circular motion is in fact an accelerated motion. therefore the direction of acceleration must obviously always point towards the center of the circle ("pushing it inwards", because it always wants to "fly off tangentially (inertia)") - so the direction of the force is set!
kaylon99 2 years ago
of course one now might argue: "but if i'm sitting in a roller coaster, clearly i feel a force pushing me in the other direction!"
yes, of course it feels like it - newton, again: "every action has an equal and opposite reaction". so its rather the roller coaster, which presses you towards the center of the circle, than you pushing outwards....
kaylon99 2 years ago
...of course it is to some extent a bit of a philosophical question, otherwise physicists would not argue about it! ;) but anyway, i think its very important to discuss accelerating reference frames with great care - and usually, when you start calculations with a zentrifugal force, things mess up...badly!
kaylon99 2 years ago
its much easier to set up the equations of momentum in the accelerated ref. frame, then to all the backtransformations to an inertial-system using euler-derivatives etc. and get all the ugly and messy zentripetal and coriolis-terms "for free" and you are sure to get the physics right.
sorry for the long talk, but i just felt like talking about this! :)
greetz from switzerland
kaylon99 2 years ago
Yes, that truly would be awesome.
Newly subscribed to your vids. Got the tip from AndromedasWake.
You have a special skill and really enjoy your videos.
Thanks.
forthreisch 3 years ago
Yay, mintie!
doloafing 3 years ago
yes, I really think it would be awesome
whisperelmwood 3 years ago
i dont get it
gul11and 3 years ago
"wouldn't that be awesome"
YES IT WOULD
TheReasonWhyGuy 3 years ago 3
The sentrifugal force is not a fundamental "real" force, it's an effect of the movement versus what is called inertia, that objects tend to want to keep going in the same direction with the same speed and so on, it really should be called the sentrifugal effect
dagsteer 3 years ago
What Phil is talking about is the reactive centrifugal force, a REAL force which opposes centripetal force.
Remember, he's talking about astronomy, not mechanics. Centrifugal Force is a slightly different thing in both of them.
Cockwallet 3 years ago 3
YEah, and in more of a physics class term, the centrifugal force is just a normal force as a result of the centripetal force. I agree.
TheOz91 3 years ago
Can you please explain more about the reactive centrifugal force? My fuses are burning out all the time... ;-)
tomaselvis 3 years ago
my wonderful australian candy minty of science lol roflmao
crazyhippy94 3 years ago
you were on apod on sunday
and you havnt aswerd my question
1. what does centripedal mean?
2. what's opposite of the word and can you tell me what it means, (q1)?
3. why does clouds stop that orbit aroung the earth again?
4. when the suns blazed collide thats when flare happen then in a few hours time does it forme to a promince
5. when supernova happens the universe expands because it's hot, well if it was cold would the universe shrink.
6. what is the dark matter
gul11and 3 years ago
yes centrifugale , its a real force , get over it!!
LOL
system0system 3 years ago
If it's a 'real' force how come its magnitude depends on the mass and it disappears in an inertial frame?
furby100 3 years ago 2
Thanks for making this video, it's very interesting. But I'm confused, wouldn't the gravity from the moon disturb the L4 and L5 points?
usefkl05 3 years ago
"Wheres my squishy earth ball", hehe, were taking leaps and bounds towards smashing the stereotype of the mad physicist here :P . Great video!
SimonRoberts0204 3 years ago
Centrifugal pumps? Err... inertia? Look, I'm not saying that the centrifugal effect doesn't exist, I'm just saying that the centrifugal force is a fictitious one, ie. it doesn't originate from physical interaction between objects. I cited wikipedia as a source since it's easy for anyone to check, I don't expect people to go out and buy a physics book just to make sure I'm not making it up.
JKnKosto 3 years ago 2
Unless by "real force" you mean "fictitious force", Wikipedia disagrees with you, Phil. Sorry, I just can't get over it :(
Loved the video, though, very informative.
JKnKosto 3 years ago
Wikipedia, pffft. wikipedia is maintained by its users (anyone with an account that is), and users are occasionally wrong too.
my question to you is, if centrifugal force doesn't exist, how do you explain centrifugal pumps?
inversionjaybomb 3 years ago
The "centrifugal force" is just the liquid being pumped trying to go in a straight line because of its inertia. Essentially it comes down to how you define things. I think understanding the fictional nature of centrifugal force is an important step in realizing that any change in velocity, including a change in direction that doesn't change the speed, is an acceleration.
furby100 3 years ago 2
"Theres the Centrifugal force to the outside, and yes, centrifugal, it is a real force, get over it!" rofl
fuocochan 3 years ago
Space stations on the L4 and L5 points? I guess the people who lived there would have to sing "Home on Lagrange..."
Sorry, but someone had to say it.
gyrogeerloose 3 years ago
DUDE I LOVE YOUR SHIRT!!!
erikdude666 3 years ago
pause in 0:29 hehe
gul11and 3 years ago
While I understand the concept of Lagrage points I still have problems with L3 and L2. But if I understand right those two lagrange points can only exist in a dynamic system, right?
MrCalhoun 3 years ago
Great explanations, thanks!
vecter 3 years ago
He should have his own educational TV show on astronomy.
kablamo9999 3 years ago 2
Phil is Awesome. With a capital "A".
Fjarhultian 3 years ago 14
'And yes it's a force, get over it' Haha i love that!
373724 3 years ago 3
yea he kicked my ass with his knowledge, over and over again
stjoh002 3 years ago 2
How did you get so smart?
Richardgwm 3 years ago
It's just natural really. I can't help it.
... oh wait ... were you replying to me?
IRONMANAustralia 3 years ago
So what part do these points play in theories of planetary formation?
Like, do you have large Jovian planets forming, and effectively "creating" other smaller planets concurrently?
Is it unlikely that you would find a single gas giant orbiting a star due to this effect?
If so, wouldn't that mean some of those large planets we have observed practically MUST have smaller planets in their system?
Could you use this to calculate a probable relative mass difference?
IRONMANAustralia 3 years ago 2
A bit of an obsurity; the late Arthur C Clarke made references to the L-points of Jupiter and Io in his novel "2010".
A bit of a reference is given in the movie as well.
thirdclass2006 3 years ago
Great explanation Phil! If you found this video informative, please support science and Phil this October and pick up his book 'Death from the Skies'.
knight2255 3 years ago
How many angels can dance on the head of a pin? ;-)
negativeheatcapacity 3 years ago
This is sweet! Thanks Phil! :)
kerryhall 3 years ago
Interesting stuff :)
Whysely 3 years ago