# Earth, Gravity, Helicopter, rocket, and rotation question

Well, I have a couple questions. StraightDope has never let me down, so hopefully a few people can help me out. I’m having poker night tonight at my house, and these questions were brought up previously and no one really knew the answer.

Ok, First question. One of newton’s laws says something like every action has a reaction (I know it’s not exactly that). So, with that said, when we launch something into space, the rocket puts a push on the earth. So if all our space shuttles are launched at the Cape, do they have to worry about launching at different times so the force on the earth doesn’t accumulate and push us out of our normal orbit, even by a few millimeters? I know it’s not that big of a force, but let’s say that ALL the world’s rockets were launched from that same spot. Would that do anything?

Ok, second question. You’re in a helicopter, and you have 4 hours of fuel. I take off from my yard and hover, never moving. Let’s say that the wind isn’t there, and heck, we can even say we’re inside a dome football stadium at the 50 yard line. So I’m hovering, never moving the controls, and the helicoper never moves right or left. With the earth rotating, when I land, shouldn’t I be somewhere other than where I started? The earth rotates, I stay where I am, and I would think that I would come down somewhere else, but common sense tells me that’s not the case.

Well, anyways, can anyone shed some light?

Thanks!

Not sure about the rockets…can’t imagine rockets would be able to alter the earth’s orbit…

As for the helicopter…I believe this will help you…If the helicopter in quetion was in a flying airplane would it land in a different part of the plane? No.

Your experiement must be held outdoors, not inside a dome.

If outside the helicopter would drift but, due to the atmosphere, not by any huge amount. It is using air to exert a force on the ground directly below, that and the surrounding air tend to keep it in place. However, the higher it hovers the more it can drift.

Very long pendulums are also affected by the earth’s rotation.

For the rocket question, the change on the orbit of the Earth is negligible. Don?t worry about it changing the orbit; it is probably helping by offsetting all those jumping Chinese.

With the helicopter question, you state that you do not move. When you took off from the ground you were moving at the same speed as that of the surface. Assuming that you do not decelerate then you will still be moving at that speed, but farther away from the center of the Earth. You would indeed land in a slightly different spot depending on how high you went, but again it would be a very slight difference for any reasonable altitude.

For the rocket question, the change on the orbit of the Earth is negligible. Don’t worry about it changing the orbit; it is probably helping by offsetting all those jumping Chinese.

With the helicopter question, you state that you do not move. When you took off from the ground you were moving at the same speed as that of the surface. Assuming that you do not decelerate then you will still be moving at that speed, but farther away from the center of the Earth. You would indeed land in a slightly different spot depending on how high you went, but again it would be a very slight difference for any reasonable altitude.

For every action there is an equal and opposite reaction. It’s Newton’s third law of motion.

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So, with that said, when we launch something into space, the rocket puts a push on the earth. So if all our space shuttles are launched at the Cape, do they have to worry about launching at different times so the force on the earth doesn’t accumulate and push us out of our normal orbit, even by a few millimeters? I know it’s not that big of a force, but let’s say that ALL the world’s rockets were launched from that same spot. Would that do anything?

Ok, second question. You’re in a helicopter, and you have 4 hours of fuel. I take off from my yard and hover, never moving. Let’s say that the wind isn’t there, and heck, we can even say we’re inside a dome football stadium at the 50 yard line. So I’m hovering, never moving the controls, and the helicoper never moves right or left. With the earth rotating, when I land, shouldn’t I be somewhere other than where I started? The earth rotates, I stay where I am, and I would think that I would come down somewhere else, but common sense tells me that’s not the case.

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You have to remeber that you already have a velocity with respect to someone obsevring you from say, outerspace. You started off from the ground at one point, and so you already have a velocity in the direction of the earth.

Think of a moving train. You’re inside the train throwing a ball in the air. The train is moving along the tracks, and yet, when you throw the ball in the air it doesn’t fly out behind you. Imagine yourself standing by tracks looking at the guy throwing the ball as the train passes. What do you see? The ball is moving with the velocity of the train.

I’m not a Physicist so I’ll leave the more involved answers to them

For every action there is an equal and opposite reaction. It’s Newton’s third law of motion.

I don’t believe so, no. The energy required to move something is encumbent on it’s mass. The more mass, the more energy is required. I don’t think even launching all the worlds rockets from the same spot on earth would even come close to the energy required.

You have to remeber that you already have a velocity with respect to someone obsevring you from say, outerspace. You started off from the ground at one point, and so you already have a velocity in the direction of the earth.

Think of a moving train. You’re inside the train throwing a ball in the air. The train is moving along the tracks, and yet, when you throw the ball in the air it doesn’t fly out behind you. Imagine yourself standing by tracks looking at the guy throwing the ball as the train passes. What do you see? The ball is moving with the velocity of the train.

I’m not a Physicist so I’ll leave the more involved answers to them

Yes, you would move relative to the ground.

Assuming there’s no wind, and the helicopter is able to move straight up, this is how it breaks down:

When the helicopter is at rest on the ground, it’s spinning around the center of the Earth. Everything is moving around the Earth at an angular rate of 15 degrees per hour (360 degrees in a day/24 hours). Hence, in 4 hours, you’d rotate 60 degrees. Now, when the helicopter takes off from its mark, it has a velocity which is dependent on the distance from the rotational axis of the Earth. The top of a tower is spinning around faster than the base of a tower more quickly, or it would fall behind–just like on a race track, the cars on the outside of a turn have to go faster to keep up with the cars in the center (which is why the cars almost always take turns as close to the inside of the curve as possible).

So while the helicopter is hovering, it is falling behind the surface of the Earth, and when it lands, it will be slightly to the west of its initial point.
An aside about the shuttle launches… One reason the tip of Florida is such a good launch point is that it’s closer to the equator than any other feasible launch point in the US, and so it’s spinning faster than (say) Maine. The shuttle gets a bit of an extra boost as a result.

Rockets don’t push against the earth, they push against their exhaust gases. There may be a little push against the pad in the first couple of seconds of a rocket’s launch, but for most of a booster’s burn, the force exerted against the rocket is dispersed in the exhaust as pure heat. This doesn’t create a net force against the planet.

Think of it as analogous to a rifle’s recoil. You feel the kick in reaction to the bullet accelerating down the barrel, not as some sort of feedback from the impact with the target. In a rocket’s case, the molecules in the exhaust act as little bullets, and the ship lifts due to the recoil. Since the bullets are so little, they bounce off each other and the air (while the rocket is still in the atmosphere), so they never even hit ‘the target’ (the ground). So they don’t transfer their momentum to the planet, at least not in an organized, all-in-one-direction sort of way.

Forgot one thing–if you’re at the North Pole (geographic), you won’t drift relative to the Earth. In fact, the further from the equator, the less you will.

As far as the helicopter goes, if it is hovering without any motion, it is doing so in a thick layer of atmosphere which is rotating at the same speed as the rest of the Earth, so that the helicopter will not move appreciably from its starting point. See the train analogy above - the ball is moving in relation to the train and the air inside the train, which is moving at the same speed. Since this is a closed system for practical consideration, the motion of the train relative to the Earth has no significant effect.

Note that this is to some extent due to the small size of the helicopter/ball in comparision with the Earth - the same will not be true if the parameters are changed. For example, IIRC, in a rotating space station a thrown ball would display noticable differences in flight path depending on the direction of throw (with, against, or across the rotation).

You’d be in a geosynchronous orbit around the Earth. As we all are.

There is an equal and opposite force on the Earth from the rocket. The same force which accelerates the rocket accelerates the Earth in the opposite direction. However, since the mass of the Earth is so many billion times that of the rocket, this acceleration is tiny. This is Newton’s Second Law, F=ma. (Nitpick: actually, for a rocket burning fuel and thus losing mass, F does not equal ma, but the rate of change of mv).

And even that would only be true of a perfectly rigid Earth. In reality, the force accelerates only a local part of Earth around the launch pad. This motion then propagates away from the launch pad, gradually decreasing due to damping, so that no net acceleration is imparted to the Earth.

The rotors of the helicopter act solely on the surrounding air. The surrounding air is stationary relative to the Earth’s surface. And even were one to escape the atmosphere, you were travelling in the direction of Earth’s spin and there is nothing to stop you continuing to do so: This is Newton’s first law, that an object will continue at rest or in a straight line at uniform velocity until acted on by a resultant force.

Since momentum is a vector, it has to be in an all-in-one-direction sort of way, as long as the exhaust gases are in the atmosphere and the rocket is point toward the earth. Eventually that momentum gets transferred to the earth. But the mass of the earth is 6e24 kg, and the mass of rockets is many orders of magnitudes less, so you’ll never notice it.

Also, a force can’t be dispersed as heat. Forces are not the same thing as heat.

A recoil from a rifle will be transferred to the shooter and through him/her to the earth, assuming the shooter stays fixed and isn’t flung off into extremely low-earth orbit. Again, it’s a vector. The only way to change the momentum is to exert a net force for a period of time.

Nope. First of all, the point about the Earth being so much more massive than the rocket(s) has been mentioned, but also the Earth is bombarded by tons upon tons of rocks and space dust every year so the “impact” of a launching rocket would tend to get lost in this “background noise” of impacts hitting randomly all over the planet for the last, what, 4.something billion years?

First of all, you’re making an eroneous assumption about helicoptors. Actually more than one. First of all, if you don’t move the controls at all you’re going to crash - chopper pilots are constantly in motion in order to balance the aircraft. Second, it’s all about how you define “not moving”. When you however over a spot on the ground (whether you’re inside or outside a structure) you are motionless relative to the ground You are NOT motionless in regards to the rest of the universe. Likewise, if you fly in formation with another aircraft you are motionless relative to the other aircraft, not in relation to the ground or anything else (unless you’re talking about helicoptors hovering in formation). When you’re hovering what you’re really doing is flying in formation with the ground.

I wasn’t going to post in this thread, because I fel the questions were answered. But there is one thing that I would have liked to comment upon, and which Broomstick mentioned:

This is true. Unlike most fixed-wing aircraft, helicopters are inherently unstable. The pilot must make constant, minute control inputs in order to keep the machine stabilized.

Hovering is flying over a spot. If you are hovering over your lift-off point, then by definition you do not move from it.

The “ball on the train” example is a classic depiction of how things appear from different perspectives (Relativity). Try this one as well: You’re floating in deep space, as far from anything as you can be. You see a light approaching, and soon you see that the light is on another space traveller. The space traveller waves as he floats by at 10 meters per second, and you wave back. Who is moving? Is the other space-suited figure moving toward you at 10 meters per second? Or is he motionless, and you are approaching him at 10 meters per second? Without a point of reference, motion is meaningless.

So a ball on a train, as seen from the passenger’s viewpoint, will go straight up and come straight down. From an observer standing by the tracks as the train goes by, the ball will arc up and travel laterally many meters before arcing back down. So the ball either moves laterally, or it doesn’t. Which observer is correct?

Now let’s say an observer is floating above the Earth. He is orbiting the sun such that his position over the Earth is constant; but he is not orbiting the Earth, so the ground is moving below him. As he watches the helicopter hover, he sees it moving from west to east; much as the observer standing by the train tracks observes the ball travelling a distance along the tracks. The helicopter pilot observes himself going straight up and coming straight down, much as the oberver on the train sees the ball move straight up and straight down.

Anyway, the thing to remember about hovering is that the helicopter is hovering within an air mass, which is moving with the Earth. Assuming still air, or compensating for a headwind, the helicopter will remain over its point of lift-off.

What if you’re an avid caver?

I’m pretty sure that that is not right. There has to be some.

About the rocket question, conservation of momentum would apply. Yes, the rocket pushes on the air, and the air pushes on the ground. If you can’t visualize it, search for Cecil’s column on whether a truck is lighter if the birds enclosed in the freight area lift off and fly around.

So to put some numbers to it, a rocket with mass of 5e5 kg, leaves the Earth at 8e3 m/s. The mass of the Earth is 6e24 kg, so it will recoil the other way at a speed of 7e-18 m/s. Accumulate this speed for three months (1/4 orbit), and the orbit will be off by a whopping 5 nanometers. Launch a million rockets, all timed so that their effects add up, and the orbit might be off by 5 mm from where it would otherwise be. I think it’s safe to say that they don’t worry about it.

About the helicopter, as Broomstick correctly pointed out, the answer depends on how you define “not moving.” If you choose it so that the microwave background radiation is isotropic, which is the universe’s preferred “at rest” frame, then the helicopter would sit still while Earth, the solar system, and our entire galaxy rushes away from it at about a million miles per hour.

Yes but when the Shuttle is launched into orbit, it stays in orbit around the Earth, and eventually lands again. If you draw a control volume around the Earth, no mass is ejected from the control volume at all, and thus the entire Earth-Shuttle system must maintain the same momentum (since there’s no other mass to transfer it to) and the same velocity. So no change whatsoever. Er, right?

Even if you don’t move the controls in any directions, you are still being pulled by the earth with its gravitational force. The earthe pulls you along with as it rotates on its axis once every 24hrs. It is for this reason that you jump the same distance (all things remaining same) whether from east to west or west to east.

About the rocket q, a simple explanation. the numerous nuclear tests that have been done produce more power than a rocket leaving for space, but that still hasn’t altered earth’s orbit. So it would take a s*itload of rockets (covering entire USA, IMHO) leaving for space to produce that kind of energy. Remember Einstein’s equation, E=mc squared? well in the case of rocket, the m (mass) is pretty small, so less E (energy) is req, but Earth’s m is massive, so it would require a lot of E.

Hope this helps