In The Lightning Thief, Luke, resident douchebro of the series, gives Percy winged shoes gifted to him from Hermes to "help" on the first quest. Actually, Luke wants Percy to wear them so when they go to the underworld, Kronos can use the curse on the shoes to suck Percy into Tartarus and claim the Master Bolt which Percy is carrying. But Percy can't fly because Zeus is a prissy bitch, so he gives the shoes to Grover the satyr. When the time comes that Kronos does try to suck them into Tartarus, Grover's hooves slip out and Kronos gets a few empty sneakers, much to his chagrin.
Annabeth's first line in HoH says she and Percy fell for nine days before reaching ground. Both of them describe Tartarus to be a vacuum, which I took literally, but Annabeth says wind rushes in her ears on the way down, so there's air resistance. That means I have to use maximum velocity for their fall.
Now, calculating their maximum velocity would be tedious, but thankfully I can use recorded data for skydivers.
http://hypertextbook.com/facts/JianHuang.shtml
Scroll down and you'll see several higher values than the first few, the latter of which are probably for higher altitude skydiving. Percy and Annabeth were huddled together quite intimately the entire way down. I'd think 200mph, or about 89m/s, would be safe to use.
So nine days give or take at a velocity of 89m/s.
89(60*60*24*9)=69,206,400m
And, actually, the gravity in Tartarus is much greater than Earth's gravitational constant...
Well, whatever :distracted
So the mouth of Tartarus extends for roughly 70,000km. That might sound weird, but Tartarus actually leads to the abyss that is Chaos so I don't think it really cares how big the Earth is.
Anyway.
So in The Lightning Thief, Grover almost gets sucked into Tartarus due to Kronos's curse. When the titan sees the shoes are empty, he gets mad and tries to pull the demigods in. The entire conversation quite generously takes a minute (I timed myself reciting it with several...several second pauses).
This means the shoes had to traverse the entire length of Tartarus in that minute for Kronos to see they were empty.
69206400/60=1153440m/s
or about mach 3392.5.
That isn't to say that they could achieve these speeds while carrying Grover, but given that they're defective replicas of Hermes's sandals...
Annabeth's first line in HoH says she and Percy fell for nine days before reaching ground. Both of them describe Tartarus to be a vacuum, which I took literally, but Annabeth says wind rushes in her ears on the way down, so there's air resistance. That means I have to use maximum velocity for their fall.
Now, calculating their maximum velocity would be tedious, but thankfully I can use recorded data for skydivers.
http://hypertextbook.com/facts/JianHuang.shtml
Scroll down and you'll see several higher values than the first few, the latter of which are probably for higher altitude skydiving. Percy and Annabeth were huddled together quite intimately the entire way down. I'd think 200mph, or about 89m/s, would be safe to use.
So nine days give or take at a velocity of 89m/s.
89(60*60*24*9)=69,206,400m
And, actually, the gravity in Tartarus is much greater than Earth's gravitational constant...
Well, whatever :distracted
So the mouth of Tartarus extends for roughly 70,000km. That might sound weird, but Tartarus actually leads to the abyss that is Chaos so I don't think it really cares how big the Earth is.
Anyway.
So in The Lightning Thief, Grover almost gets sucked into Tartarus due to Kronos's curse. When the titan sees the shoes are empty, he gets mad and tries to pull the demigods in. The entire conversation quite generously takes a minute (I timed myself reciting it with several...several second pauses).
This means the shoes had to traverse the entire length of Tartarus in that minute for Kronos to see they were empty.
69206400/60=1153440m/s
or about mach 3392.5.
That isn't to say that they could achieve these speeds while carrying Grover, but given that they're defective replicas of Hermes's sandals...
