Let's discuss Mathematics

[sanabas]

Umm, are you sure? The Earth's rotation is 24 hours, so at the equator, nights are only 12 hours, and since the plane is at the equator, and is going WITH the Earth's rotation, not against it, I'd think it would cross the terminator again in less than 12, 13 hours.

It'd work better if I used the earth's circumference, not diameter, and had the terminator moving the right way.

 

[PlutonianEmpire]

Lolllllllllllll.....

I had a really hard time figuring out the equations, so because of that, all my planes were going way too fast, but I knew I was missing something.

I googled how to get the circumference of a world, and it turned out I was neglecting to multiply by 2. Then your posts made sense.

Thanks guys.

 

[Ajidica]

This is pretty easy, but I can't remember how to do it.
How do I remove the denominator from -5/(7x^2)?
I know if the 7 wasn't there I could shift the x^2 up to the numerator and have the answer be -5x^-2 but I can't remember how to handle the seven.

(If it is any help I'm doing derivatives and I started with f(x)=5/7x.)

 

[sanabas]

This is pretty easy, but I can't remember how to do it.
How do I remove the denominator from -5/(7x^2)?
I know if the 7 wasn't there I could shift the x^2 up to the numerator and have the answer be -5x^-2 but I can't remember how to handle the seven.

(If it is any help I'm doing derivatives and I started with f(x)=5/7x.)

You've already got it. You can't change the -5/7 part, you can put the x^2 on top or bottom by changing the sign. The answer's (-5/7)x^-2, or -5x^-2/7, or -5/(7x^2), depending how you want to write it.

 

[Ajidica]

Thanks. I was always terrible at exponents.

 

[PlutonianEmpire]

How do I calculate the oblateness of a particular gas giant, real or fictional?

An explanation of the formula/equation would be welcome.

 

[dutchfire]

This http://en.wikipedia.org/wiki/Oblate_spheroid ?

 

[ParadigmShifter]

I think he wants to be able to calculate how oblate a gas giant would be given its properties.

I'm guessing things that would influence it would be rotational speed, wind speed, density, drag, gravity in the region, etc.

I don't know much about astrophysics though.

Truronian might know something about it he did fluid mechanics IIRC.

 

[Truronian]

Unfortunately I didn't do anything like that. I wouldn't have thought it would be too hard to find an equation for it though, it should only depend on the mass and rotational velocity. I think.

A quick google turned up this thread from another forum...

EDIT: Or if you fancy something slightly heavier... http://www.barnesos.net/publications/papers/Oblateness.pdf

 

[PlutonianEmpire]

Unfortunately I didn't do anything like that. I wouldn't have thought it would be too hard to find an equation for it though, it should only depend on the mass and rotational velocity. I think.

A quick google turned up this thread from another forum...

EDIT: Or if you fancy something slightly heavier... http://www.barnesos.net/publications/papers/Oblateness.pdf

I visit that other forum on a regular basis. It's the support forum for Celestia, the astronomy program I use for my worldbuilding. A quick search should reveal my presence there.

Thank you for the help.

 

[Gigaz]

I had a course lately which approached the problem for liquid drops, it is usually too difficult to calculate it by hand. For a gas giant it is a different problem because:
1. gravity is a long range interaction unlike the dipole or Van-der-Waals forces between molecules.
2. A big planet can not be modelled as composed of incompressible units. Compression energy becomes important.
You'd have to find the minimum of the sum of E(compression), E(rotation) and E(gravitation) depending on the eccentricity of the ellipsoid to determine the equilibrium state.

 

[PlutonianEmpire]

Ok, here's a new one.

Lilith and Hades orbit each other every 10.02 Earth days.

Belle Hades' sidereal rotation period is 26.4483 Earth hours. Its year is 7196 Earth hours, or 299.83 Earth days.

Based on just these numbers, how many Belle Hadean SOLAR (not sidereal, based on when the Lilith/Hades barycenter reaches zenith, and Belle Hades orbits the barycenter too, since it is circumbinary) days does it take for Lilith and Hades to complete their revolution around each other, as observed by a Belle Hadean?

And how did you calculate that number?

 

[Gigaz]

I think this problem is rather ill-posed. But I'll assume that the three bodies are in a plane.
The problem is composed of two seperate problems:

First one: How much time passes for a Belle Hadean until the Lilith/Hades Barycenter is at the same position again? This is the Belle Hadean Solar.
Second one: How much time passes for a Belle Hadean between two Hades-Lilith-Belle Hades linear events? This is the revolution as observed by the Belle Hadean.

Observed revolution expressed in Belle Hadean Solar is the final solution to the problem.

 

[dutchfire]

But I'll assume that the three bodies are in a plane.

Any three bodies lie in a plane.

 

[ParadigmShifter]

At a specific point in time

Not necessarily the same plane as time goes on...

 

[Atticus]

I don't think planes are very useful for moving bodies. They make much noise and attract unwanted attention.

 

[Petek]

Many long-standing conjectures, such as the Riemann Hypothesis and the Goldbach conjecture, have been verified by computer for numbers into the hundreds of millions, if not even higher. These computer tests will never prove the conjectures, but they might discover a counterexample. My question: Has a computer ever actually found a counterexample to some long-standing conjecture?

 

[sanabas]

I think I remember there being one. I'll see what I can find.

 

[sanabas]

Not necessarily found with computers, but examples of a large counter-example proving a conjecture false:

http://en.wikipedia.org/wiki/Pólya_conjecture
http://en.wikipedia.org/wiki/Euler's_sum_of_powers_conjecture

 

[Petek]

The Wikipedia links for the Polya conjecture appear to show that the counterexamples were indeed found by computers. Just what I was looking for. Thanks!