Posts by Gregory Thomas

A quick tweak to Kepler's third law

Hey everyone,

So, I found this specific correction for Kepler's third law that ends up being almost identical to the "official" version we usually talk about.

The official correction is here:

https://en.wikipedia.org/wiki/Two-body_problem

If you run the numbers and compare these two corrections, you get this expression:

[G/(4*π *π )]/[ln( 2 * e ) / ( 10 ^ 12 )]= ?

So, what's the value of "?"

If "?" turns out to be roughly 1, then both corrections are basically the same thing.

Let's crunch the numbers!!

G/(4*π *π )=6,67428 × 10^(−11)/(4*π *π )=1,69061 × 10^(−12)

ln( 2 * e ) / ( 10 ^ 12 )=[ln(2) + 1] × 10^(−12)=1,69315 × 10^(−12)

-----------------------------------------------------------------------------------------

1,69061 / 1,69315 = 0,998

This math pretty much proves that the difference between these two corrections is less than 1%.

Since the guy behind this new version of Kepler's third law is Silvio Sponza, I'd suggest you guys unban him.

Best,

Gregory Thomas

Hey Casey Bennett,

I’ve honestly tried everything in my power to get myself banned from here, but I just can't seem to make it happen.
Since you were such a lifesaver when you helped me switch up my username, I was hoping you might be a total legend and just hit me with the Ban too.

(Seriously though, I really need this! If I’m actually going to crush my finals and graduate on time, I can't be wasting all my energy scrolling through this forum.)

Best,

Gregory Thomas

silverwolf88 said:Gregory Thomas, you honestly think the data in those links isn't legit?
I was just sitting here thinking about how much we take for granted when it comes to the sheer scale of things out there in space. You know, I was reading up on some old physics theories—the kind of stuff that makes your head spin if you stare at it too long—and it really puts our little corner of the universe into perspective. It’s wild to think about the math behind it all, especially when you start looking at the relationship between gravity and planetary bodies. It actually reminds me of this one time I was driving through the Midwest, just staring out at those endless cornfields under a massive sky, feeling incredibly small. That’s exactly what happens when you start diving into the mass calculations for a giant like Jupiter. When you look at the formula where the Mass of Jupiter = A3 / p2 Mass of Jupiter, it’s not just numbers on a page; it’s the literal blueprint of how these giants hold everything together. It’s heavy stuff, literally and figuratively! Anyway, just a random thought that popped into my head while I was grabbing my morning coffee. Hope everyone's having a killer day!
Which correction actually makes the math for Earth and the Moon more accurate?

If you're absolutely certain those bills I showed you aren't accurate, then why on earth aren't you giving me a 1 (insufficient)?

Didn't I already mention that your tweak to Kepler's third law is pretty much on par with the "official correction"?
Isn't that a pretty solid grade, though?

silverwolf88 said:Some people out there swear you can't actually calculate the mass of a planet if it doesn't have its own Moon orbiting it, so a ton of folks just give up on trying to find a solution altogether.
..

Understood. I'm ready to go. Just send over the content you need me to rework, and I'll get to work crafting those fresh, Americanized posts while keeping the original voice intact.
If I’m following you correctly, your tweak to Kepler's third law actually gives us way better precision when we're trying to pin down the mass of a celestial body that doesn't have its own moon orbiting it.

So, if I’m following the logic here correctly, we basically use artificial satellites to get a more precise read on the mass of a celestial body that doesn't have any natural moons orbiting it.
If I caught that right!

Here’s a quick breakdown of how you’d calculate the mass for a planet like Jupiter that’s got its own natural satellites:

So, if you're looking at the math, we've got a = Callisto’s mean distance = 4.898 lunar.

p = Callisto’s orbital period = 0.611 Moon cycles

Just pop those figures right into the equation down here, and boom—there you go! WE have Jupiter ’ expressed in Earth masses.

Mass of Jupiter = A3 / p2 Mass of Jupiter
Mass of Jupiter = A3 / p2 Mass of Jupiter
So, I was sitting around crunching some numbers earlier, thinking about how massive things actually get out in space, and I landed on this: Mass of Jupiter = A3 / p2 Mass of Jupiter. It’s wild when you really start looking at the math behind it.
The mass of Jupiter equals about 314.756 Earth-masses.

Ever wonder how we actually pin down the mass of a giant like Jupiter? It’s not like we can just toss it on a scale in a lab somewhere. Honestly, figuring out the weight of a gas giant is one of those things that sounds simple until you realize you're dealing with a massive ball of swirling storms floating millions of miles away. The whole thing really boils down to some classic orbital mechanics—stuff you probably remember from high school physics, though maybe not quite this applied. We basically look at how Jupiter tugs on other things. Think about it like this: if you're spinning a heavy weight on a string, you can feel that pull. In space, we watch how Jupiter's gravity messes with the orbits of its moons or even how it nudges the Sun. By measuring that gravitational "tug," we can work backward using math to figure out exactly how much mass is doing the pulling. It’s pretty wild when you think about it. We aren't physically touching the planet, yet through pure observation and some heavy-duty calculations, we know its heft. It’s all about that relationship between distance, speed, and gravity. If you've ever played around with Newton's laws, you know that once you have the orbital period and the distance, the rest is just solving for the variable. It makes you realize how much we can truly understand about the universe just by watching how things move.

EDIT
I ended up cutting out that whole section about the rough estimate for the Moon's mass.

Alexander Thompson said:Newton, Bato, Newton.

Henry Cavendish?
Since I ended up deleting my previous post, I feel like I owe it to you guys to clarify that we’re basically debating the massive leap between the seventeenth and eighteenth centuries.

EDIT

DELETED POST:
The seventeenth century?
Long story short, just look this up:
https://en.wikipedia.org/wiki/Henry_Cavendish

P. S.
It doesn't really change the debate, but I should probably mention that my name isn't Bato magarac.
I'm actually Gregory Thomas, though honestly, you can just call me Pi since remembering the value of e is always a bit of a struggle for me!

silverwolf88's take on the 3rd Kepler's law correction actually differs from the "official" version by less than 1%.

silverwolf88 said:Can you look at these two expressions I've laid out and tell me if putting a period on one side of the equals sign makes sense?

The constant equality as measured in the Henry Cavendish experiment:
6.6740831 / ( ( ( 2 * pi ) ^ 2 ) * ( 10 ^ 11 ) ) = ( ( R + r ) ^ 3 ) / ( ( T ^ 2 ) * ( M + m ) )

The constant equality using my own correction:
ln( 2 * e ) / ( 10 ^ 12 ) = ( ( R + r ) ^ 3 ) / ( ( T ^ 2 ) * ( M + m ) )

It's just basic math, really.

silverwolf88 said:( ( R + r ) ^ 3 ) / ( ( T ^ 2 ) * ( M + m ) ) = ln( 2 * e ) / ( 10 ^ 12 )

The official correction for Kepler's 3rd law:


https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

Casey Bennett said:I’m afraid not. A handle like that is just way too long. Unfortunately, you picked a nickname right out of the gate that leaves you absolutely zero room to maneuver.

Fair enough.

Can I snag the handle "e is"?
(If I add "natural logarithm" to the word "base," the length stays about the same.)

Sure thing. Just hit up Nica 🙂

Casey Bennett said:Sorry for the wait. A change isn't possible here; I’d kindly ask that you take a moment to actually read the guidelines laid out in the opening post.

Thanks for getting back to me.
If I write "e is the base" instead of just "e is the base," would there be any chance—maybe?—of changing my handle?

Hey Duba,

Any chance I could swap my nickname over to "Euler number"?

P. S.
Is there a way to make my signature pop up on every single one of my posts?

Joseph Bailey41 said:Yeah, thanks! 👍

You're welcome, though I feel like we should probably be giving the thanks to the poet instead.

Your take might actually be right if Paliti was some kind of poet.

(Just using the word "maybe" here since I haven't actually read the work myself.)

Joseph Bailey41 said:Maybe one day your perspective will finally align with what's actually happening in reality. 👍

I honestly don't see a reason for that—not really a purpose, unless I try too hard to force the idea that "everything happens for a reason."

That doesn't have anything to do with modern societal decay—people have always looked for external miracles. As for the internal stuff, it's a miracle we're still breathing after everything. It’s a miracle how easy it is to just exist. It's a miracle I'm even typing this post. And poets? They're the real wonders of this world. ☕

Poets really are wonders in this world.

Is there any way to write one message about deleting several messages?

Is there any way to draft one message about deleting several messages?

Alright.
Is there any way I could just write one single message to handle deleting messages?

Harold Taylor6 said:That just isn't an option.

The mods have the power to delete a post and simply write—"a message was here, but it has been deleted"—right within the original author's thread, but honestly? I don't see why they would go through all that extra trouble! Especially since posts that get flagged often lead to a strike, and once that happens, the specific record of why the strike was issued usually gets wiped away—particularly during the appeals process.

Thanks for getting back to me.

If we had a feature for "deleting messages" alongside an option for "deleting messages and posting a deletion notice," then the mods wouldn't even have to manually type out notices—the software would just handle the whole thing automatically.

Harold Taylor6 said:That just isn't an option.

The mods have the power to delete a post and simply write—"a message was here, but it has been deleted"—right within the original author's thread, but honestly? I don't see why they would go through all that extra trouble! Especially since posts that get flagged often lead to a strike, and once that happens, the specific record of why the strike was issued usually gets wiped away—particularly during the appeals process.

Is there any way for moderators to post a notification about deleting messages if a user specifically asks them to?

Like, if I were to ask you guys to post a heads-up that one or more posts have been taken down, would that be something you could actually do?

Is there any way for an admin to leave a little note where a deleted message used to be, just to let everyone know it was removed?

If that’s not currently an option, would it be possible to have one of those notes added at the spot of a deleted message if a user actually asks for it?

Topic Wallpaper and posters Here’s an example of what I mean by merged threads.
You can see how it works via this link in the subforum where the thread was originally opened.

For some of those merged threads, though, there isn't a link available like that.

Is there any way we could actually add a link like that if a user asks for it?

While I've got your attention, I wanted to toss out a quick question about deleted posts.



Is it possible to have an automated system leave a note where a deleted message used to be, just stating that the admins cleared it out?

If that's not an option, could we maybe allow a user to request that such a note be left behind in place of their deleted content?

Lisa Jackson7 said:I think you're taking the whole "label" thing way too broad—like you're grouping every single social clique together.
As Aristotle put it, man is a "political animal," so anyone who is completely detached from that is either a god or a beast.
And as for not having an opinion... I already told you, we don't all need to have a take on everything.

That’s actually a pretty bad way to translate an Aristotelian claim.

The right way to put it is:

.. man is a zoon politikon, a social being ..

http://en.wikipedia.org/wiki/Politics_(Aristotle)

I honestly feel like I just wasted my life typing that whole message out.
Since I actually managed to get it posted in the right thread anyway, I ended up opening this one totally by accident.

Thanks for bearing with me.