Calc Borderlands - Troy phaselocks Elpis

Troy phaselocks Elpis. Note that Elpis gets progressively closer in later shots. This is Elpis before Troy phaselocked it...
...and this is after...
...and this is during the battle with Troy.
The map markers also note the moon is falling.
So yes, Elpis is definately getting closer. Unfortunately, we don't have a usable timeframe. Fortunately, we don't need one. Using the method I used previously in my Mom, Please Don't Come Adventuring With Me! calcs (and the method used in the calc here), where I calced the energy to move a planet out of orbit.

V = [GM(2/r - 1/a)]1/2

Click to expand...

V = velocity of the planet in its orbit
G = gravitational constant
M_sun = Sun's mass
r = current Sun-planet distance
a = Sun-planet distance over the entire orbit

Click to expand...

Although here, we'll replace the Sun's mass and orbital distance with those of the planet, and believe it or not, we're actually lucky enough to have the official orbital rotation speed of Elpis, along with it's size! Elpis has a radius of roughly 808 miles (meaning a diameter of 1616 miles, or 2600.6999km) and sits in an orbit of 87,000 miles (140012.928km) from Pandora, which it orbits every 15 days.
Ergo, we can find the circumference of it's orbit, and from there the speed.

C = 2πr
= 2 X π X 140012.928km
= 879727.172km

T = 60s X 60 X 24
= 86400s X 15
= 1296000s

T = 879727.172km/1296000s
= 678.80183m/s

So that's Elpis's initial velocity. Now we need to calculate the change in velocity needed to bring it closer to Pandora. To do that, we need Elpis's new distance to Pandora.

object degree size = 2*atan(Object_Size/(Panel_Height/tan(70/2)))

Click to expand...

= 2*atan(551/(1080/tan(70/2)))
= 0.474366376 rad
= 27.1791912877833255 degrees

We put this through the angscaler, and we can determine that Elpis is now 5379.3 (or 5379300m) away. To calculate the velocity of a similar satellite in an orbit of this distance. Luckily for us, we're also given a rough mass for Elpis too, weighing 'a few sextillion metric tons'!
One sextillion is equal to 10^21, and it says a few sextillion, as as a few is more than a couple, let's assume three sextillion tons.

T = 10^21 X 3
= 3.0e21 tons (2.99999999999999995e+24kg)

Using the method I used previously in my Mom, Please Don't Come Adventuring With Me! calcs (and the method used in the calc here), where I calced the energy to move a planet out of orbit.The gravitational constant of the Earth in ngs is 6.674×10^−8 (6.67400e-8)....

V = (GM(2/r - 1/a))^(1/2)
= ((6.674×10^−8) X (2.99999999999999995e+24)/(5379300))^(1/2))
= 192926.038m/s

All that's left now is to calculate the kinetic energy of both.

KE = (0.5)mv^2
= (0.5) X 2.99999999999999995e+24 X 678.80183^2
= 6.91157887e29 joules

KE = (0.5)mv^2
= (0.5) X 2.99999999999999995e+24 X 678.80183^2
= 5.58306842e34 joules

Lastly? We just subtract the energy, and that's the energy required to move Elpis!

E = 5.58306842e34 - 6.91157887e29
= 5.5829993e34 joules
= 13.343688575525813889 yottatons

However, the canon speed of Elpis is way slower than what I calced it. I'm still figuring out a way to correctly find the speed value, but until then, I'll just use the kinetic energy of Elpis in its initial rotation, that being 165.19069956978970026 exatons.

Final Results
Troy phaselocks Elpis (low end) = 165.191 exatons
Troy phaselocks Elpis (high end) = 13.344 yottatons

Well, calcing moving planets is way harder than I remembered. :defeat Anyway, even when cut off from his Eridium supply, Troy uses Tyreen's power, and the Vault Hunters defeat him.