Originally Posted by AznDud333
didnt someone say we were going at 67,000mph relative to the sun? pretty sure that surpasses the escape velocity from ground which is 11,190 km/s
edit: ya, other sources say its around 30km/s...thats nearly 3 times the escape velocity..even if you add in gravity and air friction it's probably more than enough
edit 2: OHH...never mind failed unit conversion>.>
edit 3: but wait..if it stops orbiting doesnt it mean there is no rotation/no gravity? which means there wont be escape velocity..
Originally Posted by AznDud333
ya im a bit confused...cuz that other guy said 67000mph and i thought it was 67000mps
Originally Posted by lordikon
67,000 miles per second would be about 1/3rd the speed of light and would get you to the moon in about 4 seconds. It currently takes us 3 days to get to the moon, so we're definitely going much slower than 67,000 miles in one second.
If the Sun were to evaporate, it's gravitational pull would be nonexistent meaning we would no longer revolve.
However, the Earth itself would still generate gravity due to it's large mass.
Meaning gravity would still work the same as we know it on Earth.
So what is the speed of the Earth's revolution?
Time for some math:r (radius) = Distance from Earth to Sun = 1 AU (astronomical unit) = 149,597,870.700 km = 92,955,807.273 mi.
c (circumference) = 2π (pi) × r
c = 2π × 1AU = 2πAU
s (speed) = d (distance) / t (time)
s = 2πAU / 1 year
1 year = 365.2425 days (average) = 8,765.82 hours = 525,949.2 minutes = 31,556,952 seconds
s = 2πAU / 31,556,952 seconds
Meters: (s) = 29.78586598501628292410932409645 km/s = 29.79 km/s = 30 km/s
Miles: (s) = 18.508079058925936311875241255636 mi/s = 18.51 mi/s = 19 mi/s
Now we could do a bunch of math to find the escape velocity (speed) of Earth.... but lets not...vₑ (escape velocity) = 6.951 mi/s = 11.190 km/s
This is the velocity you need to have to get into outer space (er... not fall back to Earth in technical terms).Note: This ignores friction (wind).
As you can see, if Earth were to stop instantly, a human would be going almost triple the escape velocity and far surpass the Earth's atmosphere (and reach space).
So what exactly
would happen? You would propel outwards towards space going 19mi/s or 30km/s while Earth's gravity slows you down, then you would exit Earth's atmosphere and keep going. (Assuming you are standing on the front side of the Earth, obviously, otherwise you would hit the surface and liquify. Also assuming you are standing in the exact center of the front side, for simplicity's sake, to avoid complicated distances.)
So how fast would you be traveling through space?
g (Earth's Gravity) = 9.80665 m/s²
This number will decrease your velocity by itself every second. So we need to find the final velocity after the distance of gravity affecting you has been surpassed.
That distance is: "The Kármán line, at 100 km (62 mi), also is often regarded as the boundary between atmosphere and outer space."
Lets first convert (g) to same units as (s): 9.80665 m/s² = .00980665 km/s².
v² = u² + 2ad
v: final velocity = ??
u: initial velocity = +(s) (from above math time) (the upforce is positive)
a: acceleration = -(g) (the downforce is negative)
d: distance = 100km
v = SquareRoot ( u² + 2ad )
v = SquareRoot ( 885.2364824773500222157287711852 )
v = 29.752923931562592260378341185323 km/s = 29.75km/s
You will notice this is almost the same as the first number.
This is because gravity is really small compared to your initial velocity, it barely affects you.
(30,000m/s vs. 10m/s/s: Based on this, it would take 3000 sec or 50min just to stop you. Compare that to the number found below.)
How much time will it take to reach space?
u + at = v
at = v - u
t = (v - u) / a
t = 3.3591545995513925480141445985122 seconds = 3.36sec
From 100km (space), what would be the time to linearly (it is directly in front of you) smack into the moon?
d = m - u
m: Average distance from Moon to Earth = 384,392 km
u: Initial Distance = 100km
d: Final Distance = ??
d = 384,292km
t = d / s (using speed after you hit 100km; 29.75km/s)
t = 12,916.108712002390028374592774361 seconds = 215.27 minutes = 3.59 hours = 3 hours 35 min 16sec
You would smack into the Moon, liquifying your body, after traveling for 3 hours 35min 16sec through space.
What if you were on the back side of the Earth?
Well you would hit the Earth with a velocity of 29.79km/s instantaneously.
Convert this to m/s for easier time below = 29,790 m/s
The mass of an average adult human being is 70kg.
So the momentum of "yourself" would be (v × m) or 2,085,300 kg·m/s
Now lets find the kinetic energy of yourself..
Eₖ = (p²) / (2m)
p: momentum = 2085300 kg·m/s
m: mass = 70kg
Eₖ = 31,060,543,500 kg·m²/s²
1 kg·m²/s² = 1 Joule
Eₖ = 31,060,543,500 Joules = 31 Gigajoules
This is around 7.4 tonnes of TNT exploding.
A complete theorized crater size would be expected at around 30 meters in diameter (15 meters deep).
This on hard rock, such as a really thick pavement.
If the Earth instantly stopped revolving around the Sun.
a) You would smack into the Earth at 29.79km/s releasing about 7.4 tonnes of TNT worth of energy upon impact.
Note: You would form a crater about 30 meters in diameter and 15 meters deep on rock / thick pavement.
b) You would be ejected from Earth's surface at nearly 3x the escape velocity needed (around 4x the speed of a space shuttle).
You would venture into space and escape Earth's atmosphere roughly 3.36 seconds after the "event".
Then continue traveling through space at roughly 29.75km/s (almost the same you started out with).
Until you eventually smacked into an object in space thereby liquifying your body.
If that object were the Moon, it would take you roughly 3 hours 35min 16sec to linearly hit it from space.
Note: This assumes...
1. No resistance / friction / air (fairly insignificant).
2. No rotation of Earth. (Otherwise angular velocity must be used. NO WAY.)
3. Gravity stops at 100km (it is so small already, it would make almost no difference, as it gets smaller anyway)
4. The velocity itself doesn't rip your body apart.Edited by kennyparker1337 - 10/9/12 at 2:56am