Speed of Earth and how we remain on Earth.

[Turtle]

___It may also have to do with the centers of gravity for both the ball & the Earth. The gravitational attraction of 2 bodies is relative to the center of gravity as I recall, & since the Earth's is changing (moving) in your example the ball must follow.

___The shuttle does not exactly go straight up, they go up heading East to take advantage of the Earth's rotational inertia to save fuel. If they went straight up the trail would curve to the West as Earth is turning East, ie counter-clockwise. ;)

[maytheforcebewithyou]

This sounds like the classic dynamics problem used to weed out perspective engineering students. I assume you refer to the earth's velocity around the sun as 15 mi/sec. The simplest explanation is the earth is not accelerating in its repsective plane of motion at the time the ball is thrown. The earth is also rotating about its axis at 1024 mi/hr and is essentially non-accelerating. I assume when you say the ball does not land 75 mi at a point on the surface of the earth from the original point at which the ball was thrust upward. Now the ball would land 75 mi further from a point measured along the earth's track around the sun. So the key points here are: (1) none of the bodies involved are accelerating, or their accelerations are essentially negligible in the horizontal direction and (2) from which point in space do we choose to serve as our frame of reference (i.e. point of origin from which to measure displacements of the various bodies in motion relative to one another, notwithstanding relativistic effects).

 

So an interesting question to pose is: What instantanious acceleration is required in the rotation of the earth in order to cause the ball to land 75 mi further back on the earth's surface from when the ball was first thrown upward in the span of 5 seconds? Express your answer in multiples of g. Assume no air resistance. Assume you throw the ball hard enough for it to stay aloft for at least 5 sec. Good luck.

[Qfwfq]

Earth's acceleration is indeed small and is undetected in most circumstances, but it does have effects. See Coriolis, Foucault, cyclones and anticyclones...

 

Try this consideration: you are inside a car going fast but at a constant speed and you are holding a ball of lead. Do you have to push the ball forward to keep it at the same speed as the car? Of course not!!!

 

If you hold it out the window, that's a different thing. Unlike the air inside the car, that outside isn't at the same speed as the car.

[amt7565]

The easiest explanation I have from learning everyone's post here is that, as the Earth moves around the Sun at 15miles/sec, the gravity also moves, that is; the Earth warps space along it's route. This explains that anything up in the air also must follow the same 'slide' motion along the Earth's path.

 

But there should be some minor differences in distances still. For example; sattelites in the sky should have some of their parameters set often to take care of this, so that they can remain at a position that is desired.

[Guest kyle8921]

So wait... if there were no air resistance, the ball would continue to move about me (were I in a moving convertible) and NOT fall straight back down? What force is making it continue with me? And, could this be tested in a vaccuum, or in space?

[Qfwfq]

What force is making it continue with me? And, could this be tested in a vaccuum, or in space?

Inertia. Although still often called "force of inertia" it is not a force according to modern terminology. It simply means that it takes a force to slow the ball from the speed of the car to a halt on the ground.

 

This has been tested plenty. Even without a vacuum, try dropping an orange from a car window while speeding along the highway. It takes a while for air resistance and friction on the ground to stop it, it will roll after you for some way.

[Guest kyle8921]

It's just really hard. I picture sitting in a car, throwing a ball up, and it floats over my head and continues to move with. I guess I thought that the car would continue to move forward, but the ball would just stay vertical from where you threw it, say point X.

 

So, let's say that we're driving, and somehow there is no air resistance. Once the car gets to point X, I throw the ball 10 feet above me. If I continue the drive, the ball won't stay over point X, but continue to follow the car?

[nkt]

It's just really hard. I picture sitting in a car, throwing a ball up, and it floats over my head and continues to move with. I guess I thought that the car would continue to move forward, but the ball would just stay vertical from where you threw it, say point X.

 

So, let's say that we're driving, and somehow there is no air resistance. Once the car gets to point X, I throw the ball 10 feet above me. If I continue the drive, the ball won't stay over point X, but continue to follow the car?

Kyle, you can test this easily for yourself next time you are being driven in a car, or on a bus or train. You can also learn some neat stuff about acceleration.

 

Just wait till you are moving, and try dropping the ball. It will, to you (what is called "in your inertial reference frame") drop vertically, as long as the car is not accelerating. The air inside the car is all moving with you, so it doesn't push the ball any more than it pushes on you. If you open the window, the air pushing on you will push on the ball in the same way, and this is identical to a cross wind if you were standing still.

 

You will also notice that, as the car accelerates, the ball appears to fall "behind" you, and when it brakes, it falls in front. (The air inside the car does exactly the same, but you don't notice it as it moves so much faster, and with smaller particles!)