To displace the Earth from its orbit

[rudransh verma]

We know that the centripetal force and the tangential velocity is responsible for the motion of Earth around sun. Newton’s second law says F=ma. If we all get together(whole population) in one place like parallel to the tangent to orbit and jump can we displace Earth from its orbit?

 

[phinds]

What calculations have you done to figure out an answer?

 

[DaveC426913]

Just for making a wild approximation, here is the entire population of the world piled up in the Grand Canyon:

 

[Drakkith]

If we all get together(whole population) in one place like parallel to the tangent to orbit and jump can we displace Earth from its orbit?

Nope. You'll push the Earth a little bit in one direction when everyone jumps, and then it will come back to its original position a second later as both the Earth and the people fall back towards each other. The net result is zero net displacement.

 

[phinds]

We know that the centripetal force and the tangential velocity is responsible for the motion of Earth around sun. Newton’s second law says F=ma. If we all get together(whole population) in one place like parallel to the tangent to orbit and jump can we displace Earth from its orbit?

The Earth, including its people, is a closed system for the purposes of this problem. Do you understand what happens to the center of gravity of a closed system under zero external forces?

 

[phinds]

Just for making a wild approximation, here is the entire population of the world piled up in the Grand Canyon:

Jeez, Dave, I see you even got both Putin and Zelenskyy in the pile. How did you manage that?

 

[Lnewqban]

We know that the centripetal force and the tangential velocity is responsible for the motion of Earth around sun. Newton’s second law says F=ma. If we all get together(whole population) in one place like parallel to the tangent to orbit and jump can we displace Earth from its orbit?

A lever would be more effective.

“Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” - Archimedes

 

[rudransh verma]

What calculations have you done to figure out an answer?

Mass of Earth is $5.97219 × 10^{24}$ kilograms, acceleration is $0.006 \frac m{s^2}$. So centripetal force is 358.3314 * 10^20 N or $36.5644 * 10^{20} Kg-Force$
Suppose we take average weight as 100 Kg-force of person. When he jumps he pushes the ground with this force. Population of world is 7.9 Billion. So total force applied is $7.999 * 10^{11} Kg-force$.
Its approx half the force of centripetal force. Isn’t this force enough to displace the Earth from its orbit?
Maybe we need just the force not the people to displace it so that the Earth doesn’t gain any potential energy to move back. Maybe something applying a force from afar like a asteroid crash.

 

[Bandersnatch]

Its approx half the force of centripetal force.

It isn't. 10 is not half of 100. 10E20 is not twice 10E10.

Isn’t this force enough to displace the Earth from its orbit?
Maybe we need just the force not the people to displace it so that the Earth doesn’t gain any potential energy to move back. Maybe something applying a force from afar like a asteroid crash.

Any force whatsoever - as long as it's not generated within a closed system of an orbiting body, like this jumping, or trying to pull yourself by your own bootstraps - is enough to displace anything from its orbit. Meaning, the orbit will always change into a new one. But it might be an imperceptible change.

 

[rudransh verma]

Meaning, the orbit will always change into a new one. But it might be an imperceptible change.

I don’t think the orbit will change. If that were so it would disturb the weather system of earth. There have been many wars in history but we have not moved anywhere away from our orbit. Any changes will be reversed back immediately due to stored potential energy in the people Earth system. I was talking about tomato going up whether it would be possible that the Earth is going down instead. That is not be possible. Because we have launched rockets several times and it’s the rocket that goes up not the Earth going down. So how can in the case of tomato ?

 

[phinds]

It isn't. 10 is not half of 100. 10E20 is not twice 10E10.

Well, he was only off by ten orders of magnitude

 

[Bandersnatch]

Any changes will be reversed back immediately due to stored potential energy in the people Earth system.

That is true in the case of changes within the closed system of the Earth. Like jumping. But whenever you send a rocket away from Earth, or drop an asteroid, the change stays.

I was talking about tomato going up whether it would be possible that the Earth is going down instead. That is not be possible. Because we have launched rockets several times and it’s the rocket that goes up not the Earth going down. So how can in the case of tomato ?

This is not a question of which one goes up down, as both have to move in opposite directions by the conservation of momentum. Whether you throw a tomato or launch a rocket, the Earth has to move in the opposite direction. But since the mass of the Earth is so vastly larger, the change is imperceptible.

 

[rudransh verma]

the change is imperceptible.

Has the change ever been measured?

 

[DaveC426913]

Has the change ever been measured?

Can you propose a method about how we might do that?

 

[hmmm27]

An actually interesting datum would be if LIGO would detect it.

 

[rudransh verma]

Can you propose a method about how we might do that?

I found this https://www.jpl.nasa.gov/news/nasa-details-earthquake-effects-on-the-earth
Says "Any worldly event that involves the movement of mass affects the Earth's rotation, from seasonal weather down to driving a car," Chao said.

 

[DaveC426913]

Indeed. The Earths rotation is measurably affected by seismic events such as giant deep sea mud slides.

 

[bob012345]

Indeed. The Earths rotation is measurably affected by seismic events such as giant deep sea mud slides.

Every time a space probe is launched beyond LEO it must change the Earth's orbit a tiny amount since the mass changed assuming at some point the probe would no longer be associated with the Earth and its motion.

 

[DaveC426913]

Every time a space probe is launched beyond LEO it must change the Earth's orbit a tiny amount since the mass changed.

Technically, it does.

But we should keep in mind the scale of such events.

Rockets are less than a drop in the ocean when compared to the amount of mass falling to Earth in the form of dust and meteors daily, as well as the amount of gases being blasted off the Earth by solar wind etc.

In fact, at this scale, the Earth can hardly even be considered a compact, discrete body, what with the sphere of gas and dust in its environs, and even distributed throughout its orbital path.

And yet, despite all these components, near and far, dense and tenuous, the Earth is stable in its orbit over aeons.

 

[bob012345]

Technically, it does.

But we should keep in mind the scale of such events.

Rockets are less than a drop in the ocean when compared to the amount of mass falling to Earth in the form of dust and meteors daily, as well as the amount of gases being blasted off the Earth by solar wind etc.

In fact, at this scale, the Earth can hardly be considered a discrete body, what with the sphere of gas and dust in its environs, and even distributed throughout its orbital path.

We do have to keep facts in proper perspective otherwise someone might want to build a wall or ban space probes or start a war or something...

 

[Drakkith]

Has the change ever been measured?

An actually interesting datum would be if LIGO would detect it.

Not a chance. The effect is far too small and there are sources of noise both local and non-local that swamp the signal by many orders of magnitude. A 100-ton spacecraft launched away at 11 km/s (roughly escape velocity) has a momentum of 1,100,000,000 kgm/s, or 1.1x10⁹kgm/s. To conserve momentum the Earth must move the opposite way with the same momentum. This leads to an initial velocity in the opposite direction of only 1.8x10^-16 m/s. At that velocity it would take the Earth nearly a week to move the diameter of a hydrogen atom.

Not only is this tiny velocity impossible to measure, gravitational effects from other planets and bodies alter Earth's velocity by a far larger amount.