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If you weighed an object at mid day and then again at midnight, would the objects weight change ( ever so slightly ) due to the centrifugal effect of the earth travelling around the sun ?

What I am trying to understand is if the object is weighed at mid-day the centrifugal effect however slight would press the object against the scales - where as 12 hours later when the same object is on the far side of the earth the centrifugal effect would do the opposite and marginally push the object away from the scales causing it to weigh a little less ?

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  • $\begingroup$ Do not forget that the sun's gravity, opposite to the centripetal force, is also acting. $\endgroup$
    – user126422
    Jun 25, 2017 at 23:04
  • $\begingroup$ @WillyBillyWilliams: I think you mean that the sun's gravity is opposite to the centrifugal force. The sun's gravity is the centripetal force. $\endgroup$
    – user4552
    Jun 25, 2017 at 23:48

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No, there is no effect of the type you're imagining. The earth is free-falling through the gravitational fields of the sun and the moon, and therefore we experience apparent weightlessness with respect to our weight in those fields. This is similar to the apparent weightlessness of astronauts aboard the ISS. Just as those astronauts can't tell by any experiment, without looking outside, the difference between up and down in the earth's gravitational field, neither can people on earth tell by gravitational experiments the difference between the sunward and anti-sunward directions. Apparent weightlessness occurs because you and the object you're using for reference (earth or ISS) are free-falling together, with the same acceleration.

Cf. Weightlessness for astronauts

We can detect the (fictitious) centrifugal force of the earth's rotation, but this is constant in time, so it just causes a variation of the earth's gravitational field (measured relative to the earth's surface) with latitude.

The only time variation is due to tidal effects. These have a period of 12 hours (not the 24 hours you were imagining), and are quite small. Tidal effects slightly decrease your weight when the moon or sun is overhead and underfoot. They arise because you and the earth are at different distances from the moon or sun, so you accelerate slightly differently. The lunar effect is about $10^{-3}$ m/s2, which is about the same as the effect due to changing your elevation by 30 cm.

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  • $\begingroup$ Hi Ben and thank you for your comprehensive answer. I think your observations and examples illustrate your point well. However if indeed orbiting bodies do not experience a centrifugal force this in my mind leads to a paradox. My understanding is observation of rotating galaxies led to the introduction of dark matter to stop the galaxies from flying apart. If the force that should cause the galaxy to unravel is not centrifugal, my question now is what is that force ? $\endgroup$
    – Harvey
    Jun 26, 2017 at 16:59
  • $\begingroup$ @Harvey: Centrifugal forces only exist if you choose to adopt a rotating frame of reference. My analysis above is in an inertial frame. If a rotating body breaks up and flies apart, then in an inertial frame, we don't describe that as happening because there's an outward force. The simplest case to analyze is when there is no inward attraction at all. Then the pieces just go in a straight line because they're obeying Newton's first law. $\endgroup$
    – user4552
    Jun 27, 2017 at 1:26

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