Are we heavier during the day? (Thought experiment/want answer)

[xwolfhunter]

Sorry for the ineloquent title, I had some space issues.

First, a little backstory, as this is my first post and I'm new to the realm of physics.

I am currently taking an AP physics class at my high school, and as I am also taking AP calc, I got interested in some of the historical figures responsible for these branches of reasonable thought. After a while, I got into Galileo, and am reading his Dialogue Concerning the Two Chief World Systems. As I was reading this earlier this evening, a sentence about the natural state of the Earth sparked my imagination into asking this question: What if people at some point in time thought that gravity was explained by a constant upward motion in the ground, before it was proven that the Earth is spherical? This got me into thinking about the effects of actual Earth movement on the forces we experince, and I came to a question: How do our relative gravities change throughout the day (excluding the presence of the moon, since I can't visualize that too and wanted this to be a simple thought experiment)?

Basically, since I'm sure this has been thought of by every physics major after learning about centripetal force and gravitational force, the two forces that I thought applied to the situation, I thought I'd come here to see if I'm right. So here I shall propound (a word I picked up from the Galileo book :) my thoughts on the subject:

First, I decided to exclude all points on the globe except for the equator, since it was the easiest to visualize and I thought the experiment would apply to all infinitely small horizontal slices of the earth, except for of course the points at the equators.

I then decided that the Earth's rotation in the experiment would be along the y-axis, since it was simpler to visualize and still, I think, hold's true even though the axis does tilt, since the x-distance from the sun still changes as time passes.

Then I decided to see if the Earth's rotational motion would affect the outcome of the experiment, to which I thought no, since it is equal along all points at which it can be measured, again, on a single infinitely small horizontal slice of the earth.

The last point which I took into account in setting up my visualization was this: That the Earth's rotation would take one year to complete, simplifying the scenario further, giving me only two points to keep track of, namely the point closest to the sun, and the point furthest; and that it would ultimately not affect the outcome of the experiment as at noon one is at the former point; and that at midnight, the latter.

So, excluding rotational forces and following all those restraints which I have applied to the experiment, I thought I should decide which forces apply to the situation. Knowing only basic classical, I would guess, physics, I came to the conclusion that, to my obviously limited knowledge, only centripetal and gravitational forces would apply.

The rest of the experiment is actually quite simple. I decided that, as both points follow the same period, the outside one obviously must have a greater centripetal force, and the inside one a smaller. I also decided that as the force of gravity is determined in part by distance, the closer point must be experiencing more force due to gravity than the outer point.

Now came the point at which I decided the outcome of the experiment. As I did not know the points which will be discussed momentarily, I could not lean more heavily on one outcome than the other, so as I stand currently the probability of either outcome, or a third to be discussed in the next sentence, is equal. But I found it to be that if the force of the sun's gravity were more powerful than the centripetal force on earth, we would be heavier during the night than the day, since the sum of the forces of gravity on the two would be greater than those of the centripetal force; but that if they were equal, the directional nature of the forces would cancel out exactly, leaving an $\chi$-$\chi$ situation; and if they were lesser, we would be heavier during the day than the night, as the sum of the centripetal forces on the two points would be greater than those of the sun.

This is how I stand currently, and I would appreciate knowing which of the forces on Earth is stronger, that of the sun or that of the centripetal force. Also, and as I am a rank beginner at this I would not doubt it in the least, if there is a flaw in my logic or a concept I have failed to grasp properly, I would appreciate it being pointed out to me as well.

Thanks!

-XWolfHunter

 

[russ_watters]

Does it matter which forces are stronger? Even in a situation where there is no circular motion, you still have what you described, but didn't name: the tidal force: http://en.wikipedia.org/wiki/Tidal_force

 

[Baluncore]

The Earth has two tidal bulges due to the moon, and two smaller tidal bulges due to the Sun. At noon and at midnight you are further from the Earth's centre due to the Solar bulges, so you weigh less than at dawn and at dusk. The tidal effect of the Moon is more significant.

Ignoring rotational effects, there are two Sun generated Earth tides each day, high at noon and at midnight, the situation is symmetrical. Your average weight is therefore not dependent on day / night.

 

[xwolfhunter]

I'm a little bit confused. russ_watters: In a situation in which there occurs no circular motion, where only the tidal forces exist, then wouldn't the point closer to the sun experience more gravity anyway? According to the equation I got in class for gravitational force, yes, it would. Therefore you would be heavier at midnight than during the day, if you walked to the other side of the earth. If there is circular motion, then I would initially think it would matter which of the forces, centripetal or gravitational, would be stronger. Perhaps a more detailed explanation of your thoughts would help me understand?

Baluncore: Your post confused me a little as well. If you weighed less at noon or midnight than dawn or dusk, which I would agree with if the effects of the tidal forces existed without the outside gravity, then even then your weight would be determined by the day/night cycle, since it changes throughout the day. I wasn't referring to any average weight either, as that obviously remains constant in any closed circular system.

Maybe I'm just not well-suited to physics, but I'm utterly confused by those posts. I could use a more detailed explanation, if you could provide one.

 

[Baluncore]

I believe you asked about weight during the day as opposed to the night, not the weight at noon, midnight, dawn and dusk.
Day begins when the top limb of the Sun rises above the horizon and ends when the upper limb sets below the horizon. Your weight changes throughout those periods so it must be averaged over the separate periods.

On average the days are longer than the nights.

 

[anorlunda]

In addition to tidal bulge, there is a simple daily variation.

At noon, with the sun overhead Earth, You, Sun are in alignment. EYS. The Earth and Sun's gravity pull you in opposite directions.

At midnight the alignment is. YES (you, earth, sun, no pun intended) The Earth and sun's gravity pull you in the same direction.

The masses or the Earth and sun, and their distances to you don't matter; this kind of daily variation occurs anyhow as long as the Earth spins and you are on the surface.

The magnitude of this daily variation is, of course, very small

 

[DrGreg]

In a situation in which there occurs no circular motion, where only the tidal forces exist, then wouldn't the point closer to the sun experience more gravity anyway? According to the equation I got in class for gravitational force, yes, it would. Therefore you would be heavier at midnight than during the day,

The point you are missing is that the Earth isn't a fixed platform. It is being pulled towards the Sun too.

At midnight, you are being pulled downward towards the Sun but the Earth beneath you is being pulled even more. So the net effect is that you are being pulled upwards relative to the Earth.

At noon, you are being pulled upward towards the Sun and the Earth beneath you is being pulled less. So the net effect is that you are being pulled upwards relative to the Earth.

At 6 am and 6 pm, both you and the Earth are being pulled towards the Sun by the same amount so there is no net pull relative to the Earth.

 

[xwolfhunter]

DrGreg, that makes a lot of sense. I didn't actually think about that before, of course. However, I would like to know why the Earth is being pulled less than you at noon. I would still think it's being pulled more than you, regardless of your position, thus your gravity is slightly different.

I would, before proceeding, like to know whether, as I now think it does, the gravitational force equals the centripetal force. Or perhaps the centripetal force is slightly less, due to imperfections and loss of energy due to friction etc. How would this be answered?

Baluncore: Sorry - yeah, I meant at noon vs. midnight, or more specifically, the points in time at which you are the closest and the longest to/from the sun, respectively.

 

[DrGreg]

DrGreg, that makes a lot of sense. I didn't actually think about that before, of course. However, I would like to know why the Earth is being pulled less than you at noon. I would still think it's being pulled more than you, regardless of your position, thus your gravity is slightly different.

When I say "pulled" I'm referring to force per unit mass (i.e. acceleration) rather than force. The reason the Earth is being pulled less than you at noon is because the centre of mass of the Earth is further away from the Sun than you are.

 

[mic*]

Re: centripetal force, same as gravity etc. question.
Paragraph two. First few lines.

http://www.physicsclassroom.com/class/circles/u6l4b.cfm

 

[xAxis]

xwolfhunter, your use of words 'centripetal' and 'gravitational' is confusing. Before you start any kind of experiment or discussion it is good to define well the terms you use.

"In addition to tidal bulge, there is a simple daily variation.
At noon, with the sun overhead Earth, You, Sun are in alignment. EYS. The Earth and Sun's gravity pull you in opposite directions.
At midnight the alignment is. YES (you, earth, sun, no pun intended) The Earth and sun's gravity pull you in the same direction.
The masses or the Earth and sun, and their distances to you don't matter; this kind of daily variation occurs anyhow as long as the Earth spins and you are on the surface.
The magnitude of this daily variation is, of course, very small"Not really, the Earth is in orbit around the sun, together with everything on it. So it is kind of opposite, as DrGreg explained.