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        riddles >> easy >> heavier in night
        
(Message started by: Rejeev on Oct 5^th, 2004, 5:05am)

Title: heavier in night
Post by Rejeev on Oct 5^th, 2004, 5:05am

consider an object at surface of earth. the object is attracted by earth as well as sun. during night both earth and sun are pulling it from the same direction. during day time earth and sun pulls from the opposite direction. That is, the object should weigh (if we use a spring balance) more in night than the weight in day time? is it so?

Title: Re: heavier in night
Post by towr on Oct 5^th, 2004, 6:09am

::[hide]Don't forget the moon, it may be out at night and is much closer.
Also, the effect from the sun is nearly immeasurable (even the moon isn't that noticable, except for what it does to large bodies of water); you need to have very sensitive equipment.[/hide]::

Title: Re: heavier in night
Post by John_Gaughan on Oct 5^th, 2004, 8:34am

To measure the difference exactly, first measure the gravitational force between the object, Earth, and the sun. Given a 75kg human, the force of gravity between the person and Earth is 7350359 N. The force of gravity between the person and the sun on either side of the Earth is almost the same: 0.44255934260577883452610649527888 N on the close side, 0.44248407686144237506883355325081 N on the far side.

Next find the force during the day and night. During the day, take the force against the Earth and subtract the sun's daytime pull: 7350358.5574406573942211654738935 N. During the night, take the force against the Earth and add the sun's nighttime pull: 7350359.4424840768614423750688336 N.

To find the ratio of how much more the person weighs during the night as opposed to during the day, simply divide to get 1.0000001204081967635857804543601. If a person weighs 165.346697 pounds (75 kg) during the day, he will weigh 165.346717 pounds at night. You probably gain more weight by filling your lungs with air. Edit: maybe you gain more weight from drinking water? ;)

If we factor the Moon into the equation I think you will see that its impact will be negligible given the masses involved. Remember, gravity is inversly proportional to the distance squared, and the gravitational constant itself is a very small number multiplied in on the top, so it takes immense mass to overcome the distance factor. Even the sun, more massive than the Earth by several orders of magnitude, cannot make up that 150,000,000 km difference as compared to the object resting on earth. While the Moon is closer, it is not close enough to impact small objects or people, and it is not massive enough either.

I am not going to do the math, if you are interested enough I can point you in the right direction to figure it out yourself. I found the sun question interesting. I knew the sun's gravity on a person was not much, but I never realized just how trivial it is compared to Earth's gravity until today. I guess that is what I get for being bored at work :-)

Edit: changed units to Newtons. I screwed up and my units did not cancel each other out, but the number parts are correct.

Title: Re: heavier in night
Post by THUDandBLUNDER on Oct 5^th, 2004, 9:15am

Astrologers often go on about the (gravitational) effect of various planets upon us at the time that we are born.

However, it is easily demonstrated that the gravitational effect of a delivering midwife is much more than that of even Mars.

Title: Re: heavier in night
Post by towr on Oct 5^th, 2004, 1:13pm

on 10/05/04 at 08:34:04, John_Gaughan wrote:

I'm not sure what you're calculating, but it's not force, that's measured in newtons (N) or (equivalent) kg m s^-2, but not kg³/s²m (where does that extra kg² come from??)

Title: Re: heavier in night
Post by Grimbal on Oct 5^th, 2004, 3:56pm

There is another problem.

During the day, you are inside of the earth orbit, so the centrifugal force should push you towards Earth. But at night, you are outside, so the centrifugal force pushes you away from Earth.

If you were at the center of the Earth, the Sun attraction and the centrifugal force should compensate each other. That is why Earth follows its orbit. But on the surface, away from Sun, the centrifugal force is higher and the Sun attraction is lower, while when nearer to the Sun, the centrifugal force is lower and the Sun attraction is higher. In both cases, you are ligher as compared to the situation where you are at sunrise or sunset.

Title: Re: heavier in night
Post by Rejeev on Oct 5^th, 2004, 9:11pm

on 10/05/04 at 09:15:45, THUDandBLUNDER wrote:

You probably gain more weight by filling your lungs with air.

You can not gain weight by filling your lungs with air. but you can gain weight by drinking water. why?

Title: Re: heavier in night
Post by John_Gaughan on Oct 5^th, 2004, 9:22pm

on 10/05/04 at 21:11:18, Rejeev wrote:

You can not gain weight by filling your lungs with air. but you can gain weight by drinking water. why?

Buoyancy. But I do not buy that argument. I can agree that the difference will be extremely small, but not nonexistant.

Title: Re: heavier in night
Post by John_Gaughan on Oct 5^th, 2004, 9:26pm

on 10/05/04 at 15:56:41, Grimbal wrote:

If you were at the center of the Earth, the Sun attraction and the centrifugal force should compensate each other. That is why Earth follows its orbit. But on the surface, away from Sun, the centrifugal force is higher and the Sun attraction is lower, while when nearer to the Sun, the centrifugal force is lower and the Sun attraction is higher. In both cases, you are ligher as compared to the situation where you are at sunrise or sunset.

Either way, the difference is so minute that unless you weigh yourself with extremely sensitive astronomical equipment, you will never know the difference.

Title: Re: heavier in night
Post by Rejeev on Oct 5^th, 2004, 9:31pm

I am not sure giving solution myself is appropriate? (solution???? it is rather my opinion). Moreover Grimbal's response is more correct than mine. Still i feel there is some eligancy in solution.
::[hide]With respect to Sun, Earth is a freely falling body towards Sun. Hence the gravitational force of sun will be zero. (the same way in a freely falling lift objects will weigh zero). Hence object will weigh same in day and night. But as obvious from Grimbal's answer, there is difference between freely falling lift (lenier motion) and freely falling orbit (circular motion), hence weight will be slightly different at different point of earth. (this i didn't thought while framing the question)[/hide]::

Title: Re: heavier in night
Post by John_Gaughan on Oct 5^th, 2004, 9:40pm

on 10/05/04 at 13:13:47, towr wrote:

I'm not sure what you're calculating, but it's not force, that's measured in newtons (N) or (equivalent) kg m s^-2, but not kg³/s²m (where does that extra kg² come from??)

Sorry, I did get my units mixed up. You are correct, I did mean Newtons. I think I reversed some units and they wound up not canceling out, leaving that odd mess. Anyway, the number are correct. I will go back and edit that post.

Title: Re: heavier in night
Post by Rejeev on Oct 5^th, 2004, 11:20pm

on 10/05/04 at 21:22:18, John_Gaughan wrote:

Buoyancy. But I do not buy that argument. I can agree that the difference will be extremely small, but not nonexistant.

it is deviation from the main topic still:- if you fill up your lungs with air the difference in weight will be zero, if you fill up lungs with a gas which is lighter than air, weight will less and if you fill up lungs with a gas which is heavier than air then weight will be more.

Title: Re: heavier in night
Post by towr on Oct 6^th, 2004, 12:38am

And if you exhale, the air in your lungs will be under pressure, and thus denser than air outside, and you'll be heavier.. (well ok, I failed to account for temperature, but it's not that trivial)

Also it's easy to say earth is freely falling towards the sun, but the same can be said for the moon and the earth (and which falls to which is moot of course) Yet still tides are greatly affected by the moon.
The forces of the different celestial (and other) bodies still act upon you, regardless of whether you're freefalling toward any of them.

And John, 7350359 N seems rather much for a 75 kg person, as one kg weighs (here) 9.81 N, making 75 kg just short of 750 N.

Title: Re: heavier in night
Post by John_Gaughan on Oct 6^th, 2004, 7:49am

on 10/06/04 at 00:38:13, towr wrote:

And John, 7350359 N seems rather much for a 75 kg person, as one kg weighs (here) 9.81 N, making 75 kg just short of 750 N.

Yes, it does seem like a lot.

F = Gm₁m₂/r²

F = (6.674200e-11 Nm²kg^-2)(75 kg)(5.973600e24 kg)/(6.371300e6 m)²

F = (6.674200e-11)(75)(5.973600e24)/(6.371300e6)² N

F = (2.990175e16)/(4.059346e13)² N

F = 736.6149 N

This is measuring the force between Earth and a 75kg man standing on the surface (using the mean radius) considering Earth "spherical enough" to be calculated as a single point in its core. I have no idea how I got that first answer. It is correct, but the radix point is in the wrong place ::) Problem is, it is not off by any number that makes sense. Anyway, I crunched the numbers again and got it right.

I then find the average gravitational force between the sun and the man:

F_sun = 0.4425217 N

Obviously this is trivial force. I then recalculated the force on both sides of Earth, coming up with similar answers to F_sun because of the huge distance and small variation. Dividing through to get a ratio of how much more the man weighs, I get a ratio similar to the one in my previous post. It is so inconsequential that the man would never know the difference.

Title: Re: heavier in night
Post by rmsgrey on Oct 6^th, 2004, 1:34pm

on 10/05/04 at 23:20:12, Rejeev wrote:

Depends how you define weight - if you define it as the force of gravity on an object, then inhaling anything will increase your weight; if as the measurement on a weighing scale, then bouyancy and acceleration will come into it.