#1, lets say the earth and by earth I mean every single molecule on above or inside stopped spinning at the same instant, so there is no falling down or tidal waves or anything like that, just magically POOOF! everything stops.
how much if any more would we weigh? and how much more at the equator than say the poles? (I assume the poles wouldnt feel anything at all.
the second Q,
lets say the planet suddenly shrinks down to a golf ball in size leaving the atmosphere intact. how far above the golf ball sized earth would your average human orbit the new tiny planet? (orbit because in this case the spin remains so when the planet suddenly changes size everyone is still hurtling along at the current spin speed of whatever surface they were on)
I don’t have any of your answers, just a request for clarification, without which this question is going to get confusing…
When you say ‘shrinks down to a golf ball in size’, you are implying that the mass (and significantly, the gravity) stays the same as at present? (I ask, because without that, we’re not going to orbit it at all.
It would be a bloody mess. Instead of orbiting the shrunken Earth, everyone would fall at terminal velocity and splatter themselves against their fellow humans.
The “increase” in weight is equal to , say, w, which is m * v^2 / r, where m is the mass of the object concerned, v is the rotational velocity of the earth at the equator and r is the radius of the earth.
v = 2Pir / t, where t is the length of a day (2pir gives us the circumference of the earth). Substituting this back in, we get
w = m * (2 * Pi * r / t) ^2 / r
w = m * 4 * pi^2 * r / t^2
Equatorial radius of the earth = 6378km = 6.38 * 10 ^ 6 m
Time taken to complete one revolution = 24 hours = 86,400 s
So at the equator, for a person of mass 70kg, weight 686N, the “increase” in weight would be 2.36N or about 0.34%.
Question 2: no one would orbit for very long because of drag forces from the equator, leading to a quite incredible population density on the surface of the new earth of 270 billion people per square meter, or a lot of standing on shoulders. Assuming no drag force from the atmosphere (hey, we’re already imagining miraculous shrinking, right?) and someone at the equator, the orbital radius r is
r = GM/v^2
= 3.99 * 10^14 / 464 ^ 2
= 1.85 * 10^9 m, or about 1.85 million km.
A lot less crowded, but a lot more lonely. Note that the radius of the earth is irrelevant here, so the shrinkage was a bit unnecessary, as it happens.
ok this one is confusing? how is the radius not relevant? if it werent then wouldnt we already be flying off into space? and how do you arrive at the orbital distance of 1.85 million km? " The diameter of the earth at the equator is 7,926.41 miles (12,756.32 kilometers)."
my guess is that we would end up in an orbit that is smaller than the current diameter not larger? or am I reading that wrong?
(and I never really considered the total population of earth in this orbit, we would end up as Rings probably all pretty and red)
You are not going fast enough to orbit the Earth, and would fall into the golf ball. A person on the surface of the Earth is only moving at about 1,000 miles per hour, no where near fast enough to maintain an orbit. Velocity would increase as you fell, but without doing the math, my hunch is you would never reach orbital speed.
Regarding your first question: Note that the spinning of the earth makes its shape non-spherical, with an equatorial bulge. The effective force of gravity minus the rotation effect makes the pull perpendicular to the surface at e very point, so “down” is the direction we think it ought to be.
If you stop the earth spinning (along with everything on it), then the earth will still have that weird equatorial bulge, but not the centrifugal* force that produced it. Immediately, gravity will no longer point directly “down”, normal to the surface, which will be interesting. Equally interesting will be vthe fact that the earth will try to redress this change byre-arranging the mass so that it more nearly resembles a sphere. Exactly how traumatic this will be, I don’t know, but even a small change in the earth’s shape is going to involve the motion of a huge amount of material all at once.
*Yes, I know it’s a “fictitious” force. But if you know that much, you know what I mean and why I say it. Don’t write in.
If the Earth is rotating at a 1,000mph, how in the hell do we not notice it. Does that mean if you could jump high enough to remain aloft for a minute, the earth beneath my feet initially will have traveled 16.6 miles?
And the 1.85 million km are the radius of an orbit on which an object would travel if it had that speed.
To orbit at what pre-shrinking would have been the surface of the earth, your speed would have to be:
v = sqrt(GM/r) = sqrt(4 * 10^14/6.38 * 10^3) = 7,900 m/s = 17,700 miles/hour,
But how are we moving along with it if our feet aren’t on the ground( which is the part that is moving, I assume!). If you jumped while on the roof of a moving train you’d fly to the back, wouldn’t you?
Only because of air resistance, though – if you jumped on the roof of a train in a vacuum, you’d keep moving at the same speed as the train, because you’re already moving at the speed v (of the train), and there’s no force acting on you, and Newton’s first law (inertia) states that any object not subject to external forces moves with constant speed in a straight line.
Wouldn’t it then be so dense as to be a Black Hole and such people, things and the atmosphere into itself?
You wouldn’t have been here to ask nor I to reply!
Inertia. “An object in motion tends to stay in motion.” We are in motion, right now, at 1000 miles per hour. If we jump up, we don’t stop our lateral movement in relation to the planet because inertia keeps us moving while we’re in the air.
Can you explain this; if the space shuttle or a rocket travels at 17,000 mph, say( I think that’s about the top-end speed of man-made craft.), how come once it leaves our atmosphere, it doesn’t get left ‘behind’ by Earth, which is supposedly traveling about 36,000 mph through space? Is there a ‘behind’ on our orbital flight path?
Because, again, it’s moving with the revolution of the earth as well as with its rotation. If our frame of reference was large enough to be aware of our actual movement through space, we’d REALLY get sick, because we’re moving in a circle in a circle in a circle…we rotate around our axis, we revolve around the sun, and the entire solar system revolves around the galactic center. But because of inertia (which doesn’t suddenly end when we leave the ground), we don’t actually feel it.
Not quite – the Schwarzschild radius of the earth is about 9 mm, while the radius of a golf ball is approx. 21 mm.
You’d experience some pretty serious tidal forces over the length of your body, though…
