When moon is directly overhead you will weigh slightly less!

Well, it’s all related to gravity.

Newton’s law of gravitation (also called as law of attraction) is used to explain the gravity or gravitational force. It states that: Every massive particle in the universe attracts every other massive particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

Earth applies much huge gravitational force on a standing person, this is because of very large mass of earth (approximately 5.97*10*24 Kg). Considering moon, it has relatively smaller mass (7.34*10^22 Kg). So, moon exerts tiny gravitational force as compared to earth.

As forces are vectors as they have both direction and magnitude, direction of gravitational force applied by earth is towards the center. At the other end gravitational force applied by the moon acts in opposite direction to that of the moon i.e., “upwards”. Therefore, gravitational force of moon acting directly above the object reduces gravitational force of earth acting on that object to some extent. Means when moon is exactly above us, it pulls us towards itself with some amount of force, resulting in decrease in weight of a person.

Mathematically it can be showed as:  F_earth – F_moon = Actual F which is being applied to person in this situation. (Where F_earth    is gravitational force due to earth and F_moon  is gravitational force due to moon).

Though gravitational force of moon acting on a person is small compared to earth (approximately a millionth of earth’s gravity!) still it is of considerable amount.

Weight is nothing but net force of gravity acting on object. Hence,

W = F = Mass*(g_{earth –} g_moon )

where g_moon is acceleration due to gravity considered for moon on earth itself, which comes out to be approximately 3.6*10^-5 m/s^2. So, its difference with acceleration due to gravity of earth generally comes out to be around 1*10^-6 m/s^2, which is the difference you see in your weight when multiplied by mass.

General calculations showed that only slight decrease in weight is there around 0.5 - 0.6 gms when moon is overhead.

Credits and References :

written By : Chetaneshwari Nivargi & Vaishnavi Patil

https://www.quora.com/Why-do-we-weigh-less-when-the-moon-is-directly-overhead#:~:text=So%2C%20when%20the%20Moon%20is,other%20positions%20of%20the%20Moon

https://www.thenakedscientists.com/articles/questions/how-much-less-do-i-weigh-when-moon-directly-overhead

https://www.reddit.com/r/askscience/comments/1a51vm/is_a_person_noticeably_lighter_when_the_moon_is/

 

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