nice one twilight!

@The Smiling Pony  
And…for the most part, even when I DO submit a question or say something…I get ignored.

@The Smiling Pony  
Tumblr keeps freezing up on me.

@HighRollerHydra  
You get a small chance of influencing a story starring your favourite characters / OCs that you find enjoyable, artists get a cache of ideas they can use for gags and a decent following.

I don’t get the appeal of all these “ask people tumblr” accounts.

@Evil DeC0Y  
You’re welcome!
 
Feel free to message me any time with questions. Derpibooru does have a PM system. I’m also Eagle1 Division on deviantart.

@Cirrus Light  
Thank you very much, I truly appreciate it :D!

@Evil DeC0Y  
Here’s some scribbles I made. Hers would probably look similar. In the box are all the relevant numbers I could remember off the top of my head.
 

 
I did use a calculator, however. But from her “Failure Success Song,” it’s been kinda canonized that her brain is a calculator.
 
As for figuring out the velocity shift because of the tilt on the Earth’s axis and all; I believe the orbital inclination of the moon off the Earth’s equator is… Either 25 degrees or 5? If she could magic in a telescope and look at the Earth, she could figure it out just by looking if she remembers where the equator is on the Earth’s surface relative to its landmasses (ie, looking at this globe: you can kinda guess what your tilt is with respect to Earth’s equator. She could do the same with a telescope, except the equator wouldn’t be marked as nicely; she’d have to remember where it is from memory and looking at the land masses (if she remembers it runs just north of New Guinie and through the Signapore Straight, then she could tell where it is from the land masses)).
 
Alternatively, she could figure it out very accurately instead of just “Eying it” by making observations of the Earth over the course of half a day or so.

@Cirrus Light  
In the next update Twilight will be writing the equation in the dirt, what would be a one for her to have written down?

@Cirrus Light
 

eheeeee

@Evil DeC0Y  
Yes! How dare you seek knowledge!
 
Loljk, ask away :p

@Cirrus Light  
You have just helped me quite a bit with the next update. Do you mind if I ask you a question(well two counting this one)?

@The Smiling Pony  
Hopefully she knows the truth, whatever it is, because teleporting into Earth’s atmosphere at some-odd 2,000 mph (roughly mach 3) won’t be good for her health, assuming she can’t take, oh, a few thousand degrees and air pressure equivalent to hitting a brick wall at 60 mph or something :p

@Cirrus Light
 
Oh, excuse me (wish I could edit), I forgot to mention that the integral
 

 
Should be with respect to dr. Since energy is force*distance, then taking an integral of a force equation with respect to distance amounts to finding the area under the curve of a graph of force vs distance, thus the energy.

Well, if she remembers that the force of gravity is F = GM1M2/r^{2, then she can derive it as follows:  
F = GM1M2/r}2  
E = GM1M2 * Integral(r^(2)) = GM1M2 * (-1/r| from r1 to r2 = GM1M2(1/r1 1/r2)  
The binding energy will be  
Eb = GM1M2 * lim(t->inf)(1/r1-1/t) = GM1M2/r1
 
Now to equate energy and velocity, we use kinetic energy of the orbiting body;  
KE = (0.5)M2v^{2 = GM1M2/r1  
v}2 = 2GM1/r1
 
For a circular orbit, though, we want half of the binding energy, so:
 
v = Sqrt(GM/r)
 
Where G is the gravitational constant: 6.67*10^(-11), M is the mass of the parent body, and r is the distance in-between the centers of the two bodies.
 
Getting those numbers won’t be easy if she doesn’t remember them…
 
Or, much more succinctly, if she recalls that centrifugal acceleration = V^{2/r, then she need only balance gravity and centrifugal acceleration:
 
v}2/r = GM/r^{2  
v}2 = GM/r  
v = Sqrt(GM/r)
 
Now accounting for the inclination of the moon’s orbit against the Earth’s equator just involves simple vectors…
 
Also, just teleporting in steps and adjusting her path in realtime might be easier and safer than trying to derive the r and M accurately enough to teleport straight to Earth.
 
Yeah, I’ve been having fun. :p

That Twilight face..

@Background Pony #7C25  
The speed of moonrise and sunrise on Equestria isn’t consistent with a steady angular rotation, so Celestia and Luna are probably tweaking things on a regular basis, effectively making the day (and night) length shorter than it would be otherwise.

@Background Pony #7C25  
Twilight might be in on how that’s all a ruse to keep the royals in power.

Hmmmm, doesn’t the fact that Celestia and Luna have to “move” the sun and moon themselves mean that Equestria doesn’t actually rotate…?