0681: "Gravity Wells"

[aliceone]

It is because of the Sirens of Titan reference that I found and joined the forum. One of the best books I've ever read. *sniff*

[eaglef2]

I'm surprised the blogosphere got no coverage. I mean, if you include the gps satellites the blogosphere should be there too.

[DrChoc]

I do not usually post on forums, but I wanted to provide some interesting fodder for your brains.

This poster creates the depth of the well based on the amount of energy it would take for something on earth to escape that well and setting it equal to escaping the planets gravitational field. This was given.

At sea level g (acceleration due to gravity) on earth is ~9.8 m/(s^2), but as you go deeper the gravity decreases. To find the gravity at a certain depth beneath the earth (a well would be an example of this) gauss' law would have to be used. Needless to say (proof would be superfluous ) the gravity on a point mass inside the earth is ~r*g where r is the ratio of the radius of the point mass and the center of the earth to the ratio of earth.

Layman's terms: the lower you go in the earth the less gravity you experience. Therefore the calculations for the depth are off.

That and the well for Jupiter would be greater than the diameter of 5 earths and then some.

My dream: Build a lightSaber, drop it into the earth, make a tunnel straight through the earth, and have the ultimate oscillating free fall!!!

[gstaniak]

So many letters and no-one has spotted the Sirens on Titan yet? Shame on you! Go back to your rooms and read some Vonnegut!

[skeptical scientist]

Someone needs to hurry up and integrate the threads.

Integrating the threads is not in the moderators' job descriptions, so far as I know, but replying only to the first thread posted is in yours.

I only said "someone" (as in someone with more thread skill than me), not "the moderators". Don't assume, as that can lead to being the first three letters. And anyway, the moderators general job so far as I know, without checking anywhere, is to keep the threads and boards clean. I'd guess that does include getting rid of duplicate threads.

Thread skill? I thought you meant merging the threads, which requires moderator privileges. I have no idea what else you might mean by integrating threads.

but replying only to the first thread posted is in yours.

Maybe you didn't pick it up from

But I'll concede defeat (this time, Gadget!) and kill mine.

, but I DID create the FIRST thread.

My apologies. It's impossible to tell that when the time stamps are in minutes, as is board default, so I assumed the popular thread was the first one, with no evidence to the contrary.

Could someone explain why my "There are NINE planets" post was deleted? Did it contravene a rule about images or some such?

It wasn't deleted; it's in the other thread. I know, I know, having multiple threads with the same title in the same forum active at the same time can get confusing.

[Quizatzhaderac]

Are these numbers from the center of planets or from the surfaces? If from the surfaces how're we defining that for the gassy planets like Uranus and Urmom?

As to the Doom guy's mass: You don't want to carry more then 30% of you WIEGHT (earth standard) on your back for extended time. Provided you can balance a larger mass wouldn't be a problem.

Another thing I've wondering. I can figure out how little gravity would give me relative super strength, but how little would be necessary to give one heat vision?

[vlyd]

I'd like to nitpick a mistake in the comic: the assertion that the Moon's position in the Earth's gravity well is the reason it took a bigger rocket to get there than to get back.

The comparison between getting to the moon and launching something 6000km up in constant gravity is valid. However, it would take that same amount of work to descend into Earth's gravity well and make a soft landing. If you add the requirement that the landing be soft, you have to look at the total energy. Jumping into a well doesn't change your total energy; it only turns the potential into kinetic. If you want to have zero velocity at the surface, you have to decrease your total energy, which means doing negative work. The reason Apollo had a smaller rocket for return is the atmosphere. If the Earth had no atmosphere, it would have taken the exact same rocket to slow down for landing as it did to launch.

Still, the comparison between a gravity well and a physical well remains valid. A jet-pack that could launch you out of a well would also allow you land in it. But the point remains: you must do negative work to get into a well and stay there. The work can be done by rocket engines, the atmosphere, or an inelastic collision with the surface. If you had neither of those things (including the surface), you would not stop at the bottom of a gravity well: you would keep going until you escaped again on the other side.

[Hawb]

"My theory is that your cat is not lost, but that his waveform has temporarily collapsed." --Dirk Gently

That might be favorite book ever. Douglas Adams is the coolest.

[Keith8290]

There was no Pluto, and this makes me very sad, most of my life it was a planet. Give it the respect it deserves! Very well made chart though.

[ABoyle]

Very cool, but if (when?) I get the poster, I'll add little divots for Ceres, Pluto and Eris. If the moon's "well" is 288 kilometers, then Pluto's would be about a quarter as deep, at 75 kilometers. I figure that Eris' well would be a little bigger, at 87 kilometers. And Ceres would have a little 13-kilometer-deep notch. Please let me know if my figures are off.

[RedOswald]

best comic in a while, and the botched Sagan quote still brought warmth to my tummy.

[dennisw]

Awesome work there Randall.
I wonder how many professors are going to use this in their lectures. (They had better give you credit.)

I know my dad (EE-PhD), my son (working on BSEE) and I will have a fun time with the chart.
My daughter (BA-Music) will just sit in the corner an pout.

Perhaps she can be consoled by listening to Holst's The Planets.

For those who decry the misquote of Sagan, there's a tradition of it: "Billions and Billions" versus "Billions upon Billions".

[BioTube]

The reason Apollo had a smaller rocket for return is the atmosphere. If the Earth had no atmosphere, it would have taken the exact same rocket to slow down for landing as it did to launch.

I'd like to nitpick your post: the Apollo missions didn't make soft landings(they hit very hard). Also, since the return system consisted of only the service and command modules, the fuel requirements for the brake are much lower even assuming away friction.

[Möbius]

At sea level g (acceleration due to gravity) on earth is ~9.8 m/(s^2), but as you go deeper the gravity decreases.

That would be true if the Earth were a uniform, spherical, homogeneous cow. In general, gravitational acceleration increases as you approach the surface of the outer core, then decreases from there.

To find the gravity at a certain depth beneath the earth (a well would be an example of this) gauss' law would have to be used.

Why Gauss's law? As far as I know, to find the acceleration at any depth you just integrate the radial density function from 0 to the radius you're at to find the mass "below" you and call it good. Your point is valid nonetheless: it's still very roughly what you'd get from a uniform density... but the difference was surprising to me: g is almost 11 m/s^2 at the bottom of a 3,000 km deep hole.

I did an analysis of this last year.
short version:
http://www.typnet.net/Essays/EarthGravGraphics/Plot3.png

long version:
http://www.typnet.net/Essays/EarthGrav.htm

My dream: Build a lightSaber, drop it into the earth, make a tunnel straight through the earth, and have the ultimate oscillating free fall!!!

Coriolis says you better watch out for a severe case of rug burn on your way through.

--
Möbius

[wigglyworm91]

(...snip...)
Also I'm having trouble thinking of how to explain this in layman's terms, since it requires some hypotheticals. "If you were in a place where gravity does not decrease as you go upward, the amount of energy it would take to go 6000km (or whatever the proper figure is) straight up there is the same amount it takes to break Earth's gravitational pull." It might work, but I think some people would be confused by the theoretical place.

Pro tip: Most laymen don't realize that gravity decreases as you get farther away, or at least are willing to suspend their knowledge for "small distances" such as those seemingly pictured in the comic.

On another note, most laymen wouldn't think this comic was particularly funny.

[The Old Wolf]

It wasn't deleted; it's in the other thread. I know, I know, having multiple threads with the same title in the same forum active at the same time can get confusing.

Many thanks. I was afraid I had stepped into deep tapioca without even knowing it.

[Snow02]

To bring together a couple of posts from the first page... the "your mom" joke is both an acquired taste and a difficult trick to pull off without coming across like a jackass. When executed properly it is of enormous comical value. For example, when someone says "you sound like a jackass", to which you reply "your mom". You do indeed sound like a jackass. However, when someone says "your face" to which you reply, "your mom", that is comedy genius. So when the maximum depth of an imparted gravity well is represented by your mom, knowing that gravity well depth is (I assume?) partially dependant upon mass, I laugh. Hard.

[metaphysicist]

: Build a lightSaber, drop it into the earth, make a tunnel straight through the earth, and have the ultimate oscillating free fall!!!

Oh man, I've always dreamed of this too. Although I figured eventually I would come to a virtual weightlessness at the core when all of the forces were equal on all sides of me.

[svk]

I feel like there was some writer's block going on and someone just decided to make a very elaborate "your mom" joke...

Then I daresay, that was the most elaborate "your mom" joke I have ever seen!

[wigglyworm91]

I feel like there was some writer's block going on and someone just decided to make a very elaborate "your mom" joke...

Then I daresay, that was the most elaborate "your mom" joke I have ever seen!

Comes close to the backstory of this strip.

[diello]

A STILL MORE glorious dawn awaits. Not a sunrise, but a galaxy-rise. A morning filled with four hundred billion stars... the rising of the Milky Way ;)

[K^2]

I have a question on the peaks between the planets.

These peaks vary in height on the poster from jupiter to the left (ie, it is easier to go to venus, than return). But they are all at the same height from jupiter to the right. It seems like this variation is due to the sun's gravity well. Is the sun's gravity well really relatively flat on the right half of the comic (from jupiter to saturn to urnaus to neptune), incomparison to the the left?

The force of sun's gravity goes down with 1/ (r^2) so I guess it could be pretty flat out past jupiter? I'll believe it, but I was wondering if it was drawn this way just to fit it in a good size comic. because if saturn, urnanus and netpune kept going up to the right, there would be a lot more white space in a rectangular comic.

It's about potential, which goes as 1/R, rather than field itself. But same idea. It appears flat here, because on the scale set by terrestrial planets and gas giants, the Sun's potential near Uranus and Neptune is effectively zero.

Why Gauss's law?

Because that and spherical symmetry means that you can throw out two of the three integrals, and all you have to do is integrate over spherical shells. Makes derivation of grav potentials inside spherically symmetric body a lot easier.

[Max2009]

So, did everybody miss the Arthur C. Clark reference?

[Ubik]

Do you mean that text about making Jupiter a star?

[neoliminal]

: Build a lightSaber, drop it into the earth, make a tunnel straight through the earth, and have the ultimate oscillating free fall!!!

Oh man, I've always dreamed of this too. Although I figured eventually I would come to a virtual weightlessness at the core when all of the forces were equal on all sides of me.

I've always wondered about the weight distribution of a Light Sabre. When it's "on", it is heavier at the "blade"? That would be required for oscillating free fall. Otherwise it would end up landing at some random angel and bounce (or worse break.)

Any Star Wars geeks have enough knowledge to answer this one?

[bgriff]

Okay, I love this, I really do, but YOU FORGOT PLUTO (forum readers: ..."but wait I must explain!" ). No matter how many people claim that its not a planet, I refuse to accept this denial. It just makes sense, 9 planets, mathematically and aesthetically is logical. The problem is a combination of bureaucratic and artistically lacking scientist. Pluto was already considered a planet, it was awesome, had a dog named after it, god of the underworld, etc... It also orbits closer than Neptune every so often. 9 planets has a square root of 3, and can be broken into perfect symmetry, plus, adding the sun makes 10, the ideal multiple. I could probably go on all day with this, but please, remember Pluto, it feels rejected

But awesome diagram, one of my favorites (I do support a request for a reprint with pluto, and a Uranus joke). Also the comment, I believe that is somewhat unnecessary (correct me otherwise), in the fact that orbital motion need not be added simply, do to the fact that it is a separate factor from the initial gravity, in other words, another variable that would instead add to the propulsion of the object attempting to reach escape velocity, as motion is specific to the object rather than the mass of the planet.

Calling 10 the ideal multiple is a very small-minded way of thinking, since it depends on the accident of our 10 fingers that we prefer a base-10 counting system. I don't know what the ideal multiple would be in a more universal sense, but 8 as the cube of 2 and a nice neat 1000 in binary doesn't seem so bad to me.

[neoliminal]

Calling 10 the ideal multiple is a very small-minded way of thinking, since it depends on the accident of our 10 fingers that we prefer a base-10 counting system. I don't know what the ideal multiple would be in a more universal sense, but 8 as the cube of 2 and a nice neat 1000 in binary doesn't seem so bad to me.

12 is the ideal number.

[darthbyu]

I am a bit curious why the full version links to an HTML page with nothing but an embedded image, instead of directly to the image. O.o This prevents Firefox from being able to scale it to the window size.

Right-click image*, select "View Image"
*The large version that doesn't scale in Firefox, not the small one on the comic page

[scikidus]

Excuse me, I demand to see Nibiru on this chart! If it's going to destroy the earth in 2012, we might as well know its gravity well so we can use the slingshot effect to circumvent total apocalypse! Graah!

[functionally_stupid]

I am here to jump on the "hee hee, Sirens of Titan!" bandwagon.

Hee hee! 'Sirens of Titan'!

[Schelle]

A STILL MORE glorious dawn awaits. Not a sunrise, but a galaxy-rise. A morning filled with four hundred billion stars... the rising of the Milky Way

I believe it's four hundred billion suns, not stars.

[littlelj]

I am not a physicist, astro- or otherwise.

So I REALLY enjoyed this comic. I got the "your mom" joke and learned something too. I was also pleased to have checked that Pluto was omitted.

I love the "full size" comics. They kick arse.

[gravityhomer]

I have a question on the peaks between the planets.

These peaks vary in height on the poster from jupiter to the left (ie, it is easier to go to venus, than return). But they are all at the same height from jupiter to the right. It seems like this variation is due to the sun's gravity well. Is the sun's gravity well really relatively flat on the right half of the comic (from jupiter to saturn to urnaus to neptune), incomparison to the the left?

The force of sun's gravity goes down with 1/ (r^2) so I guess it could be pretty flat out past jupiter? I'll believe it, but I was wondering if it was drawn this way just to fit it in a good size comic. because if saturn, urnanus and netpune kept going up to the right, there would be a lot more white space in a rectangular comic.

oh and by the way, I think it is an awesome comic. I love these large blow up ones.

Kind of... I believe what you're noticing is mostly the big gap between the terrestrial planets and the gas giants. There isn't a property of the gravity well that incidentally makes it get much flatter past jupiter, it's just the large amount of space between Mars and Jupiter, and then all the space between the different gas giants that makes it appear that way.

Okay, so I agree horizontal distance does not have any meaning on the poster. But the height of peaks between the planets indicates how difficult it is to leave the planet. I was just thinking, for every single planet, shouldn't it be slightly more easy to leave the planet in the direction toward the sun, and slightly more difficult to leave the planet in the direction away from the sun (becuase you are also climbing further out of the sun's gravity well). But I'm now pretty confused about it. And am starting to think that the peak heights between the planets, don't have a relative meaning toward eachother.

[rthomas2]

It's from something Sagan said in a 1980s TV series called "Cosmos," in episode 9, "The Lives of the Stars."

Here's a video link to the quote, spoken around 6 min 20 sec:
http://www.youtube.com/watch?v=aXsrff9Z9eY

And the quote transcripted:
http://davis--237834.deviantart.com/art ... -138369531

And the whole series, hosted on Hulu:
http://www.hulu.com/cosmos

[gravityhomer]

I have a question on the peaks between the planets.

These peaks vary in height on the poster from jupiter to the left (ie, it is easier to go to venus, than return). But they are all at the same height from jupiter to the right. It seems like this variation is due to the sun's gravity well. Is the sun's gravity well really relatively flat on the right half of the comic (from jupiter to saturn to urnaus to neptune), incomparison to the the left?

The force of sun's gravity goes down with 1/ (r^2) so I guess it could be pretty flat out past jupiter? I'll believe it, but I was wondering if it was drawn this way just to fit it in a good size comic. because if saturn, urnanus and netpune kept going up to the right, there would be a lot more white space in a rectangular comic.

It's about potential, which goes as 1/R, rather than field itself. But same idea. It appears flat here, because on the scale set by terrestrial planets and gas giants, the Sun's potential near Uranus and Neptune is effectively zero.

okay, I see this. Is this the right way to picture it? Create the well for the sun. and then in that well push down the various wells for the planets, and then squish them all together so they are easily seen together, and not ridiculously spread out. The sun gravity well, is like the "background" that the other planet wells sit in.

[SpringLoaded12]

Awesome. However, it is my belief that no chart, graph, or diagram should be so complex that it requires a short essay and several other diagrams just to explain how to read it.

Another belief of mine, that goes with the group of things that I believe are true no matter how often the majority of people deny them... PLUTO IS A MOTHERFUCKING PLANET GODDAMMIT. Oh, and tomatoes are vegetables.

A STILL MORE glorious dawn awaits. Not a sunrise, but a galaxy-rise. A morning filled with four hundred billion stars... the rising of the Milky Way

I believe it's four hundred billion suns, not stars.

Suns are stars. Unless that's a quote and you're correcting diello on his wording.
I wish phpBB had a facepalm emoticon.

[rpgamer]

I have a question on the peaks between the planets.

These peaks vary in height on the poster from jupiter to the left (ie, it is easier to go to venus, than return). But they are all at the same height from jupiter to the right. It seems like this variation is due to the sun's gravity well. Is the sun's gravity well really relatively flat on the right half of the comic (from jupiter to saturn to urnaus to neptune), incomparison to the the left?

The force of sun's gravity goes down with 1/ (r^2) so I guess it could be pretty flat out past jupiter? I'll believe it, but I was wondering if it was drawn this way just to fit it in a good size comic. because if saturn, urnanus and netpune kept going up to the right, there would be a lot more white space in a rectangular comic.

It's about potential, which goes as 1/R, rather than field itself. But same idea. It appears flat here, because on the scale set by terrestrial planets and gas giants, the Sun's potential near Uranus and Neptune is effectively zero.

okay, I see this. Is this the right way to picture it? Create the well for the sun. and then in that well push down the various wells for the planets, and then squish them all together so they are easily seen together, and not ridiculously spread out. The sun gravity well, is like the "background" that the other planet wells sit in.

That seems to be pretty much it. Similar to how Jupiter's moons are within Jupiter's well.

[BurnTheOrange]

This comic seems like something you would find on Wikipedia... if (when) Randall controlled the Internet.

Sadly the things you should find on Wikipedia are rarely the things you do find there.

Personally, I was quite amused by the combination of something so massively science-y and instructional with a Your Mom joke. I was quite impressed with the useful and simply put science, then I read the things about mars' moons and chuckled. Then I saw your mom's gravity well and was burnt by the cheese.

[morgan in austin]

So, did everybody miss the Arthur C. Clark reference?

I did. Please elaborate.

[BioTube]

Spoiler:

2001 A Space Odyssey had Jupiter turned into a second sun at the end.