On the night side of Earth, the sun’s gravitational pull on me will be additive to that of Earth, whereas on the light side it will be subtractive. So, do I weigh more at night?
Mike Follows
Sutton Coldfield, West Midlands, UK
Advertisement
The answer depends on your location, your distance from the centre of Earth and any local variation in gravitational field strength due to the density of underlying rock.
Crunching the numbers, the weight of someone living on the equator would increase by about 0.1 per cent when on the dark side of Earth compared with the lit side. For a person with a mass of 62 kilograms this equates to a gain of around 70 grams – roughly the mass of a hen’s egg and certainly less than the fluctuations in your mass due to what you ingest or eliminate throughout the day.
This calculation takes into account the fact that Earth’s axis is tilted by about 23 degrees. If Earth were tilted at 90 degrees, there would be no diurnal variation. If you are at the same latitude as the UK, the diurnal variation in mass would be down to about 20 grams.
Celestial mechanics are complex and my calculations have omitted the effect of motion, but it is worth noting that Earth’s spin will make you about 4 per cent lighter at the equator than at the poles.
@dudnees
via Twitter
Weight depends on the distance from Earth’s centre of mass. This increases on both the light side and the night side because the tidal effect of the sun stretches Earth in the sun’s direction. So, you weigh less on both the light and night sides compared with your weight at sunrise or sunset.
Michael Paine
Sydney, Australia
The question is similar to “why are there two tides per day?” The answer is that centrifugal acceleration needs to be taken into account. In the case of tides, Earth and the moon revolve around a common centre of gravity – their barycentre. This creates a small centrifugal acceleration that is strongest on the opposite side of Earth from the moon and causes the tides to rise there. Conversely, the pull of the moon’s gravity is strongest where the moon is overhead, so the tides rise at that point also.
The same effects – gravity and centrifugal acceleration– apply to Earth and the sun. So, on the night side of Earth, the sun’s gravity will be weaker, but this is balanced by the greater centrifugal acceleration. The opposite occurs on the day side. If these effects didn’t balance, Earth would dive into the sun or fly off into space.
Eric Kvaalen
Les Essarts-le-Roi, France
No, because when you are on the side of Earth away from the sun, the centrifugal force away from the sun is greater. This effect is equal to the extra gravitational pull from the sun on the sunny side of Earth. At sundown or sunrise, you weigh more.
The same thing happens with the moon. When the moon is high or beneath your feet, you are lighter, and when the moon is on the horizon, you are heavier. The moon’s influence on your weight is about two times greater than that of the sun.
In any case, the effect is small. If you weigh yourself on scales with springs, the differences in the readings would be just a few milligrams. But, of course, if you weigh yourself on scales that use sliding weights, as in a doctor’s office, you would be measuring mass, not weight. There would be no difference at all due to the sun and the moon, but only due to changes in your mass between different times of the day.
@PrideOfHumility
via Twitter
That is a lot of variables! Solar, lunar, oceanic and terrestrial tides, even magma displacement. Maybe the question should be: “If Earth were a giant, smooth, barren, glass marble of uniform density with no moon, would I weigh more on the night side than the day side?”
To answer this question – or ask a new one – email lastword@newscientist.com.
Questions should be scientific enquiries about everyday phenomena, and both questions and answers should be concise. We reserve the right to edit items for clarity and style. Please include a postal address, daytime telephone number and email address.
żěè¶ĚĘÓƵ retains total editorial control over the published content and reserves all rights to reuse question and answer material that has been submitted by readers in any medium or in any format.
Ěý
