Question

In the movie Avatar (blue people not the other one) the humans on pandora do not present any indication that gravity has changed. The gravity on pandora is 20% less then on earth. using calculations, and any scene from the movie, show that the humans on pandora are not being affected by gravity as they should be.

Answer 1

THIS IS A CLASSICAL EXAMPLE REQUIRING THE USE OF THE FAMOUS NEWTONS LAWS OF GRAVITY AND OTHER LAWS OF CLASSICAL MECHANICS.

By the newton's law of gravity, the force of attraction of the two masses M₁ and M₂ have to be separated by some distance d and possess such tendencies that natural order of inertial frames of references prevail. In this circumstances, we are to confirm that some of the parts of the two masses experiences equal and opposite forces, whose magnitude is

Newtons (N)

We know that G = 6.673×10^-11 N m² kg^-2

Now assume that we are on earth , so that our relationships between the acceleration due to gravity and the universal gravitational constants are established beforehand:

Now let the mass M₁ be allowed to be the reference and let this be allowed to undergo linear acceleration ( in order to avoid the complex intergro-differential relationships prevailing had the case under study been chosen as to be rotationally accelerating)

Thus this relation yields...............................................................................................................(1)

Thus equation (1) is the required relationship for establishing proportionality between the acceleration due to gravity and the Gravitational constant.

Let us remind ourselves that this Gravitational constant G is indeed very emphatically referred generally as THE UNIVERSAL GRAVITATIONAL CONSTANT. Thus this happens to be of such nature as to prevail its existence even at the remotest infinity of universe no matter which law of astrophysics shall apply.

With this we shall use the given fact: the gravity in pandora planet is 20% less than that of earth. This leaves us to conclude that had the case been that Pandora is assumed to be of a shape exactly as spherical and oval shaped as earth but only of lesser dimensions, we are given that the case should, in all probabilty, apply onto the equator portion to simplify the method of deduction. This means g being 9.81 ms^-2 on earth at equator, the same value on pandora is

.......................................................................(2)

...................................................................................................................(3)

Scene in Avatar:

Here, the main character, the male alien who, after sometimes having rode the flying creature comes to a near cliff of a mountain. There, the scene reminds of handgliding on earth like situation. But however, the alien descends in smooth transition with bare minimum effort, by just slipping from the side of the flying creature onto the land area of the mountain. This is because the pull of the planet pandora is less compared to earth. The scenaio looks more like a 7 to 8 feet descent. However, this being the case on pandora would seem of a less impactfull landing than on earth, which actually could translate into same impact for no more than 2-3 feet height of descent. For the case of investigation let us take this descent to be 7 feet. The next thing here is the mass of the alien. Let the weight of the alien be 80 Kg: We assume that the entire mass of the body is centered around the point of the leg from where point the descent happens from the saddle to the land area on the hill in (a) vertical motion (b) slant motion. This solution will visit only vertical descent. For slant motion, projectile cases should be referred in classical mechanics textbooks (available in leading university curriculum)

Using Equ (1)

Thus we see that

Thus from Avatar scene of descent of alien from flying creature onto the top of hill from 7 feet height (=2.1336 m) is equivalent to a distance

on earth

This is 6.26099 feet height on earth. Thus an advantage of 1 feet is gained due to reduction in grativy on the planet pandora.