Little Story of Infinity: Snowy flies!
After flying to the Moon, Snowy recently flew back into the air during the Zero Gravity mission! Same astonishment for Tintin's best friend, but is it really the same phenomenon?
All bodies are subject to the law of universal gravitation formulated by Sir Isaac Newton. We have all heard of the legend describing Newton leaning against a tree, discovering this law of gravity after an apple fell on his head!
The true story is not very different, as described by William Stukeley, biographer and friend of Isaac Newton, in his Memoirs of Sir Isaac Newton's life published in 1752:
[...] after dinner, the weather being warm, we went into the garden, & drank thea under the shade of some appletrees, only he, & myself. amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind"why should that apple always descend perpendicularly to the ground," thought he to him self: occasion'd by the fall of an apple, as he sat in a comtemplative mood: "why should it not go sideways, or upwards? but constantly to the earths centre? assuredly, the reason is, that the earth draws it. there must be a drawing power in matter. & the sum of the drawing power in the matter of the earth must be in the earths center, not in any side of the earth. therefore dos this apple fall perpendicularly, or toward the center. if matter thus draws matter; it must be in proportion of its quantity. therefore the apple draws the earth, as well as the earth draws the apple."
From this thought came the famous mathematical formula describing the force of attraction between two bodies:
The object of mass m is therefore attracted by the body of mass M located at a distance r from it. And conversely, the body of mass M is attracted by that of mass m, just like the apple attracting the earth! The symbol G here represents the gravitational constant.
When Snowy walks on the Earth, he is attracted by it in proportion to its mass. The moon being less massive than the Earth, the force felt by Snowy is smaller and he therefore "flies away" more easily.
We all know this force very well, since it is the weight! If Snowy's weight therefore changes when he lands on the Moon, his mass does not change (So Snowy hadn't dieted during the rocket trip!). Rearranging Newton's formula, we get
where g gathers G as well as the mass M and the square of the distance r between the two objects.
This g is therefore dependent on the body on which Snowy is standing, but also Tintin, Captain Haddock and the Dupondts.
During the parabolic flight, Milou and Tintin aboard the ESA plane experienced a situation of microgravity. They were still well attracted by the Earth but the acceleration of the plane almost compensated for this attraction. The sum of the forces felt by the occupants was therefore almost zero for a few seconds. Once again, Snowy was not put on a diet during the flight!
It's your turn to play!
And you, what weight would you have on the Moon or Neptune? Use the table below to find the g of each celestial body and multiply it by your mass (in kg)! Where to go on a trip to feel lighter?
As Tintin had made clear to the Captain, who was also surprised to fly away, his weight on the Moon was 6 times less than that on Earth! On the other hand, the Captain would have felt almost three times heavier if he had gone to Jupiter!
About the author :
Gwenhaël W. De Wasseige is assistant professor at UCLouvain in astroparticle physics. Each month, Gwenhaël will tell us through her Little Story of Infinity the latest news about the universe and the domain of the infinitely s