Can we stop the Earth from spinning?

Question

When we walk on the ground, we push the ground backward and hence the ground pushes us forward and we change our position. The effect of our force on the Earth is very minute (literally negligible) because it's massive !!

Also we know that each point of an spinning ball has tangential velocities as shown below.

Now imagine that people all around the world decide and get aligned together with their motor cars and try to move with some considerable velocity $v$ by pushing the earth back as shown in this figure at the same time.

This time also the force is negligible (since the earth is extremely massive ) , but I think taking the whole population on their motor cars and being driven to the same velocity at the same time can cause some effects . So by how much amount (numbers) will it influence the rotation speed of the earth if they all moved at the same time ?

Or conversely, can we increase the rotational speed of the earth by moving in the opposite direction and alter the day - night duration?

Note: the total population of the earth as in September $2020$ is about $7.8 billions$ and take the average mass of them between $50 kg$. Consider they start from rest and accelerate uniformly and travel $100m$ in $2s$ i.e. their acceleration is $50m/s^2$. Take the mass of their cars to be $1000kg$. Assume that all the cars are similar.

I apologise for the edit but otherwise I would have to ask the same question again. Kindly respond to it.

The force is definitely still negligible, you are underestimating the mass of the earth or overestimating the total mass of humanity — Triatticus, Sep 30 '20 at 11:32
This sounds like something xkcd would have already spoken about... EDIT: Whaddaya know? https://xkcd.com/162/: not the same thing, but similar... — Philip, Sep 30 '20 at 11:37
Possible duplicates: Do mankind and manmade activities/constructions have any effect on the rotation of the Earth? , Is Earth's orbit altered by recoil from take-off/launch/recovery of aero/space vehicles? and links therein. — Qmechanic, Sep 30 '20 at 17:43

Arnav Mahajan · Answer 1 · 2020-10-01T06:43:54.523

3

Okay, if we have to calculate the speed with which each person needs to walk/run to stop the earth we may try to conserve the angular momentum.

Lets say that the world population is $P$ and average mass of each person is $m$. Then the total mass of humanity would be $Pm$. Say everyone walks with a speed $v$. Then on conserving the angular momentum we get:

$$(Pm)Rv = I_{earth} \omega_{earth}$$

Where $I_{earth} =$ Earth's moment of inertia $= \dfrac25 m_{e}R^2$. Where $m_e$ is mass of earth $R$ its radius. And $\omega =$ angular velocity $= \dfrac{2 \pi}{t}$ ($t = $ duration of day).

On substituting the expressions we get: $$v = \dfrac{4 \pi m_e R}{5Pmt} \approx 2.92 \times 10^{15} ms^{-1}!$$ That's a whole lot of speed! A lot greater than light.

I took the values as:

$m_e = 5.972 \times 10^{24} \mathbb{kg}$

$R = 6.371 \times 10^{6} \mathbb{m}$

$P = 7.59 \times 10^{9}$

$m = 50 \mathbb{kg}$

$t = 8.62 \times 10^{4} \mathbb{s}$

edited Oct 01 '20 at 06:43

answered Sep 30 '20 at 12:53

Arnav Mahajan

808

2

Everyone would reach escape velocity long before relativistic mass, which you would need to take into account, became an issue – Adrian Howard Sep 30 '20 at 13:03
@Arnav Mahajan why did you conserve angular momentum ? Did you conserved it by taking the Earth and total population as a system ? – Ankit Sep 30 '20 at 14:02
Although it's pretty insignificant, it's worth noting that the moment of inertia of Earth is probably lower because the Earth isn't uniform density, and is more dense near the core where you get less inertia. – JMac Sep 30 '20 at 18:19
Your result comes out in $\mathrm{m}^2,\mathrm{s}^{-1}$, not in $\mathrm{m},\mathrm{s}^{-1}$, because you have your angular velocity wrong by a factor $R$. Also the factor in $I$ is $2/5$, not $3/5$, but that's a minor detail. Your result, which doesn't make physical sense because it's calculated non-relativistically, is hence off by 7 orders of magnitude. – pela Sep 30 '20 at 20:04
Apologies for posting an answer with such severe calculation errors. I have corrected them. @pela Thanks for pointing them out! – Arnav Mahajan Oct 01 '20 at 06:47
@JMac I have taken some basic approximations to simplify the things a bit – Arnav Mahajan Oct 01 '20 at 06:59
@Ankit Yes I took them as a single system – Arnav Mahajan Oct 01 '20 at 07:03

score 2 · Answer 2 · answered Sep 30 '20 at 13:04

Back of the envelope calculation:

The earth is a solid sphere with an average density several times that of the human body. Even billions of people will only be a thin layer if spread around the whole surface of the earth. So the mass of billions of people is minute compared to the mass of the earth.

The earth rotates once in $24$ hours. The equator is about $40$ thousand km long, so at the equator the earth is rotating at almost $500$ m/s - about $50$ times as fast as a running person.

Put these two facts together and you can see that the angular momentum of billions of people running in the same direction is really negligible compared to the angular momentum of the earth. There would be no measurable effect on the earth’s rotation.

score 2 · Answer 3 · answered Sep 30 '20 at 15:40

The system planet+people is isolated and no external torques act on it, so its angular momentum $L_{tot}$ is conserved. Let's write $$L_{tot} = L_{pl} + L_{earth} \, ,$$ where $L_{pl}$ is a complex function of all the positions and velocities of the world population and cars, while $L_{eath}$ is the angular momentum of a solid sphere (but you can also consider corrections due to oceans, magma and other liquid things).

As the people start walking in the same direction (say against the Earth rotation), then $L_{ppl}$ decreases and the planet spins up a bit.

If we start walking in the same direction of the Earth rotation, then $L_{pl}$ increases, while $L_{earth}$ decreases (the planet spins down and the day is a bit longer).

However, as soon as we stop walking we modify again $L_{pl}$: it is easy to see that, because of the conservation of $L_{tot}$, the day will come back to its original length. So, to modify the day permanently we have to walk forever.

Or... we have to walk to the equator and stay there (so we modify the moment of inertia and the whole planet slows down).. or to the poles if we want shorter days.

Of course the effects are small, as other answers point out.

score 1 · Answer 4 · answered Sep 30 '20 at 12:17

1

The entirety of all humans is still negligible to the mass of Earth. However if everyone were to run in the same direction at once, the minute change would be canceled when they stopped, as stopping would transfer their momentum back to the Earth. Every action and reaction on the surface of Earth equal out.

answered Sep 30 '20 at 12:17

Adrian Howard

8,513

1

I know that everything will be normal when they stop but I want to know the things that will happen when they are running. Wait I am gonna add some details. – Ankit Sep 30 '20 at 12:19
Even if everyone could run for 24 hours at the linear velocity of the Earth's latitude they were at, it would make less than a femtosecond difference to the length of the day., – Adrian Howard Sep 30 '20 at 12:37
What if everyone ran in single file around the equator? – Natsfan Sep 30 '20 at 15:02

Can we stop the Earth from spinning?

4 Answers4