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Measuring objects in Sonic CD for science!! (Things got updated, check latest post)


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Gotta say I love topics like these! We may be wrong when trying to measure/quantify or qualify elements from games, but it's still fun to speculate. ^_^

I'll read more carefully when I've got more time on my hands. But thanks for bringing this to other fans' attention!

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Hm, the metal chain is slack. Force exerted on planet by chain would be zero. Hence, chain does not hold planet. The Earth is. If we consider the physics of circular motion and gravitation, the planet would be in geostationary orbit.

M is earth mass. m is little planet's mass. r is distance from the centres of the planets. w is angular velocity which is 2pi/1day. G is gravitational constant

mrw^2=GMm/r^2

r^3 x w^2= GM

r^3 x (2pi/(24 x 3600))^2=6.67x10^-11 x 5.972x10^24

r^3= 7.532 x10^22 

r= 4.22 x10^7

take this value minus the radius of the earth (6371km = 6.371 x10^6) and radius of little planet to get the  shortest distance from little planet and earth

whic means sonic still has to run 3.6 x10^7m to get to little planet. To put things in perspective, speed of sound is 330m/s and speed of light is 3x10^8m/s.

disclaimer i never played sonic cd.

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9 hours ago, caseykz said:

Hm, the metal chain is slack. Force exerted on planet by chain would be zero. Hence, chain does not hold planet. The Earth is. If we consider the physics of circular motion and gravitation, the planet would be in geostationary orbit.

M is earth mass. m is little planet's mass. r is distance from the centres of the planets. w is angular velocity which is 2pi/1day. G is gravitational constant

mrw^2=GMm/r^2

r^3 x w^2= GM

r^3 x 2pi/(24 x 3600)=6.67x10^-11 x 5.972x10^24

r=4.226x10^11 m

take this value minus the radius of the earth (6371m) and radius of little planet to get the  shortest distance from little planet and earth

whic means sonic still has to run 4x10^11m to get to little planet. To put things in perspective, speed of sound is 330m/s and speed of light is 3x10^8m/s.

disclaimer i never played sonic cd.

That is a good calculation given the numbers you were using, but it is not applicable in this situation. A geostationary orbit by definition is an orbit that takes place at about 35,786 km above the Earth's equator because for an object to stay at a fixed point above the Earth needs to be about that distance away while Little Planet is not nearly that high. Little Planet is just about 1227 feet above the Earth based on what I could measure. And I'm not counting it being chained down at the moment of Sonic CD as being naturally fixed in the same spot over Earth's surface. But thanks anyway dude. I appreciate you putting in that work for this. 

But anyway: 

UPDATE. 

I redid some of the numbers so I will place them here. Refer to here if you want the current numbers. 

The width of the mountain Sonic stands on is 895.3560974 ft 

The height of the mountain little planet is chained to is 1317.385332 ft 

The width of the mountain little planet is chained to is 1368.545928 ft 

The height at which the chain starts is 434.8650606 ft 

The diameter of Little Planet is 2226.322122 ft 

The surface area of Little Planet is 15571336 ft^2 

The circumference of Little Planet is 6994.194389 ft 

The Length of Never Lake is 4563.427852 ft 

The distance Little Planet is from the mountain it is chained to is 2406.185123 ft 

The height Little Planet is from the ground is 1227.85421 ft 

The length of an individual chain link is 8.3925438582877 ft 

The width of an individual chain link is 6.54222088 ft 

The change in height of the chain is 792.9892304 ft 

The length of the whole chain is 2778.425 ft (This required a slight assumption as I have not had the experience of taking a calculus class yet, I do not have the skills for finding the length of a catenary the formal way so I found a "hammock calculator" that could crudely figure out the propable length of what the chain could be in length. Keep this in mind.) 

I also had to assume Sonic lands a bit less than halfway up the chain (I don't think there will ever be a way of 100% finding exactly where he lands) at about .4375 the distance of the chain. Like I said, this is just an assumption. 

I then timed the time it takes Sonic from roughly starting the peel out move on the chain up to roughly where he lands on the Little Planet. I took 10 different times and got the average of them. I got 1.249 seconds. 

Since Sonic landed about .4375 the distance of the chain he had to run about 1562.864063 feet. 

Now we just divide velocity by time, and convert feet per second to miles per hour and it comes out to 853.15853 miles per hour. This means Sonic has a kinetic energy of 2545572714 Joules at this speed which is more than twice the energy of a lightning bolt. 

I think THIS is probably the best estimates I can give everything. 

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1 hour ago, ShroomZ said:

That is a good calculation given the numbers you were using, but it is not applicable in this situation. A geostationary orbit by definition is an orbit that takes place at about 35,786 km above the Earth's equator because for an object to stay at a fixed point above the Earth needs to be about that distance away while Little Planet is not nearly that high. Little Planet is just about 1227 feet above the Earth based on what I could measure. And I'm not counting it being chained down at the moment of Sonic CD as being naturally fixed in the same spot over Earth's surface. But thanks anyway dude. I appreciate you putting in that work for this. 

But anyway: 

UPDATE. 

I redid some of the numbers so I will place them here. Refer to here if you want the current numbers. 

The width of the mountain Sonic stands on is 895.3560974 ft 

The height of the mountain little planet is chained to is 1317.385332 ft 

The width of the mountain little planet is chained to is 1368.545928 ft 

The height at which the chain starts is 434.8650606 ft 

The diameter of Little Planet is 2226.322122 ft 

The surface area of Little Planet is 15571336 ft^2 

The circumference of Little Planet is 6994.194389 ft 

The Length of Never Lake is 4563.427852 ft 

The distance Little Planet is from the mountain it is chained to is 2406.185123 ft 

The height Little Planet is from the ground is 1227.85421 ft 

The length of an individual chain link is 8.3925438582877 ft 

The width of an individual chain link is 6.54222088 ft 

The change in height of the chain is 792.9892304 ft 

The length of the whole chain is 2778.425 ft (This required a slight assumption as I have not had the experience of taking a calculus class yet, I do not have the skills for finding the length of a catenary the formal way so I found a "hammock calculator" that could crudely figure out the propable length of what the chain could be in length. Keep this in mind.) 

I also had to assume Sonic lands a bit less than halfway up the chain (I don't think there will ever be a way of 100% finding exactly where he lands) at about .4375 the distance of the chain. Like I said, this is just an assumption. 

I then timed the time it takes Sonic from roughly starting the peel out move on the chain up to roughly where he lands on the Little Planet. I took 10 different times and got the average of them. I got 1.249 seconds. 

Since Sonic landed about .4375 the distance of the chain he had to run about 1562.864063 feet. 

Now we just divide velocity by time, and convert feet per second to miles per hour and it comes out to 853.15853 miles per hour. This means Sonic has a kinetic energy of 2545572714 Joules at this speed which is more than twice the energy of a lightning bolt. 

I think THIS is probably the best estimates I can give everything. 

thanks for cross-checking. i made serious calculation errors that night. Please take note of the edits.

anyway, you might be able to insert the angle the chain makes to the vertical and thus calculate the approx length of the chain, and then use your hammock calculator to calculate the chain if you wish to pursue the physics side of things. 

The value i calculated may be applied to the distance of Tropical Resort in Colours to Earth. So it might also be possible to calculate Sonic's speed via Terminal Velocity. Although not feasible since Sonic didn't run the whole length and wisps messing with gravity.

btw, can you convert everything to metric? It will be easier if we intend to apply formulas. 

wait, are you sure though? Airplane height is 39,000ft which is approx 10,000m. And 8ft is approx 2m, i seem to remember the chain link being longer. And physically, for a thing to stay in orbit for a long time, it must stay away from air resistance and thus has to be above the atmosphere, unless Eggman keeps supplying energy to keep it at that speed, which then makes my calculations void. 

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15 hours ago, caseykz said:

thanks for cross-checking. i made serious calculation errors that night. Please take note of the edits.

anyway, you might be able to insert the angle the chain makes to the vertical and thus calculate the approx length of the chain, and then use your hammock calculator to calculate the chain if you wish to pursue the physics side of things. 

The value i calculated may be applied to the distance of Tropical Resort in Colours to Earth. So it might also be possible to calculate Sonic's speed via Terminal Velocity. Although not feasible since Sonic didn't run the whole length and wisps messing with gravity.

btw, can you convert everything to metric? It will be easier if we intend to apply formulas. 

wait, are you sure though? Airplane height is 39,000ft which is approx 10,000m. And 8ft is approx 2m, i seem to remember the chain link being longer. And physically, for a thing to stay in orbit for a long time, it must stay away from air resistance and thus has to be above the atmosphere, unless Eggman keeps supplying energy to keep it at that speed, which then makes my calculations void. 

Right now I will answer your question about Little Planet's height. Remember that Eggman has it chained down at the moment so it is presently at that height. At the end of Sonic CD we see the chain be broken and Little Planet gets much higher above the Earth. But this just makes it more complicated as in the next scene we see Little Planet much lower again, similar to where it was in the intro cutscene. My assumption is that it can move to all sorts of heights and I guess the reason why it could naturally be that low is...magic, I honestly don't bloody know XP. You are correct about if you seriously want an object to stay in a stable orbit for it to be away from air resistance but there simply is no explanation for Little Planet being able to be that low, Like I said it seems to be able to move it's height above the Earth at will, and I was using it's present height in the intro cutscene to figure it out there so I could get it's size in reference to everything else. 

This is a point where we simply have to suspend our disbelief about the altitude where Little Planet usually naturally orbits because it's a mess here. XP 

 

Also, I will give the metric conversions to all of these amounts later. 

 

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