The Earth - Does it spin? (probably not)

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Well, no, I argue that it doesn't move at all under you, for the same reason that a ball thrown upward isn't deflected above you:  The Earth is moving you with it, and when you jump, you're only changing the outward radial component of your velocity.  Because the acceleration due to gravity is radially inward, it only affects the radial component of your velocity, and thus the horizontal component is unaffected.

Did you forget that rotating bodies exhibit centripetal acceleration?

Did you forget about gravity?

But all credible sub-fields of modern physics (String Theory and other unifying theories aside) are based on empirical evidence.  A science based on speculation alone is not a science at all.

Not at all - all theoretic science (the science of Copernicus, Newton, Hawking etc., etc.) is integrally based on speculation. The theorist, unlike the zeteticist, seeks to find evidence which appears to support his speculation. The good zeteticist deals only in facts.

Quote from: cwolfe on December 23, 2007, 06:15:42 PM

But all credible sub-fields of modern physics (String Theory and other unifying theories aside) are based on empirical evidence.  A science based on speculation alone is not a science at all.

Not at all - all theoretic science (the science of Copernicus, Newton, Hawking etc., etc.) is integrally based on speculation. The theorist, unlike the zeteticist, seeks to find evidence which appears to support his speculation. The good zeteticist deals only in facts.

I disagree entirely.  What supposed "facts" do you have to work with, other than "the Earth appears flat up close"?  Cite specific examples.

And like I've said over and over and over again ad nauseum, which doesn't seem to be sinking in.  I will bold it this time.  Newton based his laws on empirical observation.

Quote from: Tom Bishop on December 23, 2007, 11:01:44 PM

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Well, no, I argue that it doesn't move at all under you, for the same reason that a ball thrown upward isn't deflected above you:  The Earth is moving you with it, and when you jump, you're only changing the outward radial component of your velocity.  Because the acceleration due to gravity is radially inward, it only affects the radial component of your velocity, and thus the horizontal component is unaffected.

Did you forget that rotating bodies exhibit centripetal acceleration?

Did you forget about gravity?

I'm wondering, how is gravity going to increase your speed to you can maintain your location above the spot you jumped from?

I was also wondering this...

Not quite sure if I understand the question.  Could you elaborate?

Well, if you're traveling the same speed as the surface of the Earth, but you're taking a longer route, something is going to have to speed you up so you can maintain your location above a certain part of the Earth.  I thought you said gravity did that, so I'm wondering 'how?'.

Well, if you're traveling the same speed as the surface of the Earth, but you're taking a longer route, something is going to have to speed you up so you can maintain your location above a certain part of the Earth.  I thought you said gravity did that, so I'm wondering 'how?'.

Well, no, I think my final conclusion was that when you're jumping, you're only changing the radial component of your velocity.  Gravity only changes the radial component of your velocity.  Because you're not jumping very far, your moment of inertia does not change much at all, so you remain over the same spot you were at, because of conservation of angular kinetic energy.  Remember, rotational kinetic energy depends on the moment of inertia, as well as the angular velocity.

How long you're jumping for doesn't really matter.  There's going to be a difference if your jump is 3 seconds long just as well as 36 hours long.  What makes up for the difference in speed needed to maintain your location above a point on Earth?

How long you're jumping for doesn't really matter.  There's going to be a difference if your jump is 3 seconds long just as well as 36 hours long.  What makes up for the difference in speed needed to maintain your location above a point on Earth?

Actually, there really shouldn't be a difference in the amount of time you're elevated, by my reasoning.  My argument has to do with your moment of inertia from the Earth's axis of rotation.  If your moment of inertia doesn't change much, neither will your angular velocity.

You say the angular velocity isn't changing much, but 'much' means it's still changing.  Since it's changing, you're going to end up in a different place than you started but by a minute amount.

You say the angular velocity isn't changing much, but 'much' means it's still changing.  Since it's changing, you're going to end up in a different place than you started but by a minute amount.

Sure, why not?  What does it matter anyway?  We've pretty much answered the original poster's question.

It matters because you're not landing where you jumped from (in a perfect jump).

OK

This problem can be simplified, if we consider the situation where we are jumping on the north pole.  Also, we can consider the jumper and the earth as a whole system.

In this instance, we have 2 vector quantities:  The system's rotational velocity (1 revolution per day) and the jumper's linear velocity (m/s upwards, as they jump).

The jumper remains part of the whole rotating system, even if he is in the air, because the jumper's rotational velocity has not been affected.

The above explanation assumes the jumper does not exert any torque (rotational force) during the jump.