The ARK in Sonic the Hedgehog

ARK diameter = 83.01 px

Earth diameter = 1513 px

Earth diameter = 12,742,000 meters

ARK diameter = (83.01/1513) * 12,742,000 = 699,083.555849 meters

Let's get the approximate volume this thing's shape via modelling it as a hemisphere and ignoring the extra volume of parts sticking out of its shape.

Hemisphere volume = (2/3)*pi*((699,083.555849/2)^3) = 8.9444963E16 m^3

Will be assuming that the ARK is 80% hollow as a living structure.

Volume = 8.9444963E16 * .2 = 1.7888993E16 m^3

Going to reasonably assume a composition of 80% steel and 20% plastic.

https://amesweb.info/Materials/Density_of_Steel.aspx

Density of steel is 7870 kg/m^3

1.7888993E16 * .8 * 7870 = 1.126291E20 kg

https://www.sciencedirect.com/topics/engineering/density-polyethylene

Density of plastic is 910 kg/m^3

1.7888993E16 * .2 * 910 = 3.2557967E18 kg

Mass of ARK = 3.2557967E18 + 1.126291E20 = 1.158849E20 kg

http://www.watchframebyframe.com/watch/yt/zum3oVY9Rhg

https://imgur.com/V3nKfeA

Screen Height = 552 px

ARK diameter = 699,083.555849 meters = 70 px

2atan(tan(70deg/2)*[70/552]) = 10.148476787291 degrees

Size = 699,083.555849 (meters)

https://www.1728.org/angsize.htm

Distance to screen = 3.9365E6 meters

https://imgur.com/a5J5ZhV

Screen Height = 552 px

ARK diameter = 64 px

2atan(tan(70deg/2)*[64/552]) = 9.282584464523 degrees

Size = 699,083.555849 (meters)

https://www.1728.org/angsize.htm

Distance to screen = 4.3056E6 meters

This happens in 1 frame at 60 fps

ARK Velocity = (4.3056E6-3.9365E6) * (60/1) = 22,146,000 m/s

Kinetic Energy of ARK = .5*(1.158849E20)*(22,146,000^2) = 2.8417603E34 joules or 5-A

This result scales to Ultimate Emerl, Final Hazard, and Perfect Chaos as this was done uber casually by the raw energy of the 7 Chaos Emeralds transferred to the ARK's engines to move the ARK at an "incredible velocity" that would destroy the Earth once it crashed as per Gerald Robotnik's plan for revenge.