Question of the Week

Do we weigh less at night?

Sun, 3rd May 2009

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Question

Christoph, Utrecht asked:

My question is do we and objects weigh less at night time? I could imagine that an additional gravitational upward pull of the sun during day time will work to a certain degree against the downward pull of the earth.

Answer

We put this to Mark McCaughrean, Professor of Astrophysics at the University of Exeter.

Your question is the question specifically whether the Moon and the Sun, the positions of them in the sky make us weigh more or less and they do a little bit. Typically the overall variation due to the positions of the Sun and the Moon might be as small as about 10 or 15 mg which is less than an aspirin so it really isnít going to make much difference. You certainly wonít feel that difference in weight.

Itís somewhat complicated. People have written in suggesting well, the Moon can pull to one side depending where it is and of course the Moon isnít always out at night, itís out in the daytime just as much as it is out at night but people donít tend to look. So thereís a little effect there but there are much bigger effects at work.

The one that people havenít written about which is actually quite important for most people and as to do with atmospheric pressure, the atmospheric pressure will change from day-to-day, people know about highs and lows and that the typical change during a night to the high pressure zone move into a low pressure zone might actually change the weight of a person by as much as 6 grams so not 10 or 15 milligrams but 6 grams. Which is the weight of a pencil, for example.  And thatís all to do with the buoyancy of the air when the pressure goes up.

But the biggest way of losing weight, if you really want to lose weight quickly is to move location, move to somewhere nearer the equator where the centrifugal force or more correctly the centripetal acceleration of the earth reduces your weight because the earth is spinning and at the equator itís spinning the fastest and also going to higher altitude.  You can lose as much as 300 or 400 grams that way, about half a per cent of your body weight.  So if you really want to lose weight astronomically then move to Mexico City, near the equator and at high altitude.  On the other hand itís probably not the best place to go at the moment...

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Surely you would weigh least at midday when the gravitational pulls of Earth and Sun were closest to direct opposition.

The position of the moon also would be significant:
if you want to cheat at ďWeight Watchers ģĒ arrange to be weighed when there is a solar eclipse at midday.  RD, Tue, 28th Apr 2009

No, that wouldn't work because of the (more significant) gravitational attraction from the other fatties in the room with you... chris, Tue, 28th Apr 2009

I would think you would weigh more at night because of the position of the Sun and Earth. Ignoring the moon at the moment, the mass of the Earth and Sun are grater than you and would have the largest of the gravitational affects in this theory. The Sun and Earth pulling on you at the same time would make you heaver at night when both are lined up in the same direction from you.

Distance on the other hand also has a large affect on how much gravity you experience. This part of the theory would mean that Earth and Moon have the largest affects on gravity. We know that were the Moon is in itís orbit the Earth is misshapen. I would think if the sun was just on the other side of the planet you might weigh less at night.

I donít think the Moon (being so small) would counter 100% of the pull from the sun. Therefore, you should weigh more.

It is just a theory and I have done no calculations to even attempt to prove or disprove. I do still believe could prove rather accurate. techmatt, Wed, 29th Apr 2009

At first glance this seems to make sense.  Weight is a measurement of how much force you're applying to the earth's surface by standing on it, and this force is the effect of how much gravity is pulling you "down" towards the earth.  When the sun is directly overhead, you'd expect it would lift you slightly, and when it's on the other side of the earth, you'd expect it to pull you down slightly. 

There's a catch, however.  It is true that the sun pulls you towards it, but it also pulls the earth towards it.  The net effect is that both you and the earth are pulled towards the sun at the same rate, which will virtually negate any effect on your weight. 

There's another catch if you want to dig really deeply into this.  The earth's center is slightly closer to the sun than you are, so it will be pulled slightly more than you are.  This would tend to make you a tiny tiny bit lighter at night than during the day, but the effects due to the moon and variations in the earth's density are going to be much much larger. jpetruccelli, Wed, 29th Apr 2009



I new there was something I was forgetting. techmatt, Wed, 29th Apr 2009

The answer is no (Ö on average Ö depending on your definition of night.)

Simply put, our orbit around the sun is very stable. So if we experience a light moment at midnight, we must have a similar moment around noon. Itís a balance between gravity and centrifugal force. At night when the sun is below our feet, the spin of the earth makes us go around the sun just a little faster. The centrifugal force of that makes us just a little lighter. Plus, weíre farther from the sun also making us lighter. During the day when the sun is above us, we get lighter 2 ways too. We go around the sun slower and we get a little closer.

The best evidence of this is in the tides. When the earth, sun and moon are lined up, the tides are stronger. And the tides are weaker during a half moon.

The moon is more fun. Itís closer. And each day the gravity difference is greater. Thatís why the moon has a greater effect on the tides. Once again, the moonís orbit is very stable. Thatís why there are 2 high tides a day. Gravity makes us lighter under the moon. But it isnít enough to explain how we get lighter again 1/2 a day later. The answer is a strange form of centrifugal force. The earth and moon have a common gravitational center (barycenter) that is closer to the earthís surface than the pole. The earth spins around that center once a month. That spin causes a centrifugal force away from the center. When the moon is high, weíre closer to that center and the force is less. But 12 hours later, weíre farthest from that center and the force is greater. And that explains the other high tide.
thenewmans2009, Thu, 30th Apr 2009

At 100Kg, what difference in weight to expect ? Is it measurable for the ordanary person ? Dr Guz, Fri, 1st May 2009

Counting only the change over a day, 8.5 grams (3oz). So you're lighter at noon and midnight and heavier at sun rise and set. How much heavier. Just using gravitational force, compare sun set to noon. The difference is the radius of the earth. The other parts of the formula cancel out. (Gm/r^2) / (Gm/(r-r)^2) becomes r^2 / (r-r)^2. The formula relies on SI units so use meters. Sun is 149600000000 meters away. Earth is 6378000 meters to the center.

100mg+8.5g = 100kg*149600000000m^2/(149600000000m-6378000m)^2
(that's 220lbs +3oz) thenewmans2009, Sat, 2nd May 2009

Oops , of course, 100kg is my mass. But to the sun, that only weighs 60 grams. So ...

60g * 1.496e11m^2 / (1.496e11m - 6.378e6m)^2 = 60.0051162

So 100kg weighs 5mg more at dawn than at noon. Does that match what he said? thenewmans2009, Fri, 8th May 2009



Focusing solely on the Sun's influence on a Being (located on the surface of the Earth - ignoring the Moon and Atmosphere):

The Mass ratio of Sun to Earth is 333,000 (2.0 * 10^30 / 6.0 * 10^24)
The Distance ratio of Sun/Earth from a spot on the Earth's surface is  23,000 (93m / 4k - in miles, but who cares what units, use Angstroms if you wish)
Distance ratio squared is 530,000,000
Mass / Distance Ratio Squared is .0006 (333,000 / 530,000,000)
Additive Sun pull at night = .06%
Subtractive Sun pull at day = -.06%
Difference in Weight night - day = .12%
Difference in 100kg man = .12kg = 120g

Are any of these calculations wrong?

This is consistant with thenewmans2009's post "100kg is my mass. But to the sun, that only weighs 60 grams. So ..." (Although I don't follow his "So ...). The Sun's attractive power on Newmy is 60 g (and negative 60g at Noon). PERIOD.
Mdeva, Sun, 31st May 2009


Yes, that's right. I like how you did that. But that's not the answer to Dr Guz's question.

And that's because you didn't take centrifugal force into account. In other words, your path around the sun changes through the day. So the correct answer is about 10,000 times smaller. thenewmans2009, Fri, 26th Jun 2009

earth being a satellite of the sun isnt d gravitational force of d sun which is providing d necessary centripetal force zero? sbXI, Sat, 5th Feb 2011

Make sure to drink the water while in Mexico City, to weigh even less! Bob, Mon, 2nd Nov 2015

Another term is due to Earth's orbit around the Sun: At midnight the orbit tends to throw us off Earth away from the Sun, whereas at noon the orbit tends to compress us toward the center of Earth away from the Sun. Ron, Mon, 8th Feb 2016

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