Silly Question

Board@Work

This is probably a silly question but it has been bugging me for years...

What force is it exactly that is causing this...

The world is revolving at a huge speed. so What is stopping me from going up in a helicopter a few hundred feet, let the earth revolve beneath me and then landing in say moscow a few mins later. Essentially i don't move but the earth does..


???

Capt'n Midnight

If you are in a train and jump up in the air you will land back on the same spot. This is because you and the train are moving at the same speed. - Jumping out of a train is a different matter.

To get into orbit around the earth you have to orbit in ~90 minutes - that's 24,000 miles so it's about 18,000 miles per hour. By building your launch pad near the equator you can gain 1,000 mph from the earths rotation.

If you were to go up high enough then the 1,000mph you get would be enough to stay in orbit above the same point - geo synchronous.

The nearest thing to do up and down somewhere else trick might be a ballistic missile but then most of it's journey is on it's own steam.

Bass.exe

Yep, it's the force of inertia. Your helicopter is moving in the same direction as the Earth, at the same speed as the Earth rotates. Even after lift-off, you still have this lateral(or is it circular?) motion, as "A body in motion remains in motion until an unbalanced external force acts upon it" (e.g. Wind).
And because an object which is attached to a central point(the Earth) must rotate around it, the helicopter will rotate with the Earth.

carl_

markororke wrote:

This is probably a silly question but it has been bugging me for years...

It's not really a silly question. It's the sort of thing people often wonder but don't ask.

Victor

Air resistance is another answer.

Sev

Now this is all considered in the absence of air resistance.

Well I dont believe this has been answered fully yet. You might be wondering why since you have an initial velocity from rotating on the earth that you dont just drift in to space when you take off in the helicopter while the earth continues rotating.. well.. gravity is always acting, and its attracting you towards the earth, and the helicopter is always fighting against gravity to stay where you are in one (macroscopically rotating) place. And while there may not appear to be any resultant force in the frame of reference of the rotating earth.. in the inertial frame (ie. from space), there is a resultant centripetal force thats keeping you rotating in a circle.

The reason being is that because youre on a rotating earth in a rotating reference frame, there is a ficticious centrifugal force that is counteracting the force of gravity. The force of gravity is effectively reduced because youre on a rotating eart. If the earth rotated faster.. we would weigh less and the helicopter would use less fuel to stay aloft. This missing gravitational force.. the difference between the real gravitational force of the earth and the effective one in our rotating reference frame is the magnitude of that centripetal force that the observer in space (in the inertial frame) see's keeping your helicopter moving in a circle.

Then theres also the coriolis force. However this only acts when an object moves in a rotating reference frame. Consider a man jumping on the earth.

Your on the earth, and its rotating very fast, so when you jump up into the air, from a frame of reference in which the earth is rotating (ie. in the eyes of somebody floating in space, watching a rotating earth) you would appear to be jumping laterally with the earth. Because you were already moving at the speed that the earth's surface rotates at when you initially jumped.

Now in the eyes of the man jumping on the rotating earth, you still dont appear to jump directly vertical. If you change your coordinates to a rotating reference frame... in otherwords, if you consider the earth as stationary and not rotating, and you jumping off a stationary earth then there is this introduced ficticious coriolis force that curves the path of your flight. Think about it, it makes sense, your jumping off a rotating earth. Correct me if im wrong, but im pretty sure that you'll land back in the same place regardless, because the coriolis forces will be equal and opposite on your descent.

But if the journey is just one way, like dropping something from a height, what many people dont realise is that the path of the falling object is not really vertical, because of the coriolis force. If you dropped a penny from a height of 100 metres.. like off the spire for example, it'd drift by about 2cm from the vertical by the time it hit the ground. So if youre ever trying to skull somebody with a penny from atop the eiffel tower, be sure to take that into account.

This coriolis force is the same reason why rotating weather systems form, and why storms rotate in the opposite direction in the southern hemisphere.

Sev

By Inertial Frame, I mean a frame of reference which is not rotating, like from the point of view of the static solar system or galaxy, which sees the earth rotating. Although what people really mean by "Inertial Frame" could maybe be somewhat open to philosophical debate. That's an issue for another day.

Sev

For an object at the equator, this ficticious centripetal acceleration that acts in the rotating frame is only like, 0.03m/s^2. Nothing to get worked up about, its very small but corresponds to the central force required to keep an object rotating in a circle of the earth's radius.

It makes me wonder tho, what the value of 9.81 given to g corresponds to. Because at the north pole, this ficticious force wouldnt exist. But then the earth isnt a perfect sphere but is flattened at the poles. And maybe the reason it's flattened is because the earth is rotating, and its shape moulded to accomodate an equal pull of gravity all over its surface? Anybody want to answer that one? It seems to make sense anyway.. maybe im right.

Capt'n Midnight

Normally I find Asimov condesending but I have to agree with him on " centripetal force" and "coriolis force" sometimes it's better to use the word inertia.
Newton (not a nice guy) said something about a body in motion continues in a straight line at constant speed unless a force is exerted on it. In this case the forces are air resistance and gravity.

BTW: all the schemes where you catch a lift on a passing asteroid have a slight flaw in that you need to travel at the same speed as it , in which case you already have the necessary kenetic energy to go where it could go..
BUT - if you had some super strong bungie cords then you could use them to catch up with a faster body and then catapult ahead of it ...

ALSO - if you could get some super strong tethers - will, you could have interesting options. you could use the kenetic enrgy of a mass falling into the gravitional well of a planet to raise another object out of the well - so you could raise the helicopter into orbit, wait until it got to where you wanted to go and drop down again - this time transferring the energy back to another helicpoter so it could go to orbit.. more useful on the moon since no air resistance and lower mechanical strength needed.
( or just use a space elevator )

http://www.tethers.com/MXTethers.html
http://guthvenus.tripod.com/gv-se-flywheels.htm

another alternatice is to drill a hole between two points, and setup a vacuum tube with magnetive levitation, you put on your metal space suit and jump into the hole, you fall down and then back up the other side, no helicopter required..