Every once in a while an old hoax resurfaces on social networks. It claims that

Question

Every once in a while an old hoax resurfaces on social networks. It claims that the alignment of two planet will produce a combined gravitational effect such that if you were to jump at the right moment you would be able to float weightlessly in the air. The most popular version of the hoax combines the gravitational force of Jupiter and Pluto - to see how it all started check out http://cn.wikipedia.org/wiki/Jovian Plutonian-gravitational .effect. In this problem you'll see exactly how absurd the whole story is. You remember from your mechanics class that you can calculate the net force on any object as a vector sum of all forces acting in it. Thus, combined force of Jupiter + Pluto just the sum of the two. Let's see what is the effect of Pluto. Mass of Pluto is 1.3*10^22 kg. Let's say that the alignment occurs when Pluto is at 35 AU from the Earth. Calculate gravitational force F_pluto of Pluto acting on you. Say your upstairs neighbor has a cat - it's a standard 5kg tubby cat, and say the distance between you and the neighbor's floor is 3m. What is the gravitational force of the cat F_Cat acting on you as it walks through the neighbor's apartment? What is the ratio of F_Cat/F_pluto ? Any comments? Without even calculating the effect of Jupiter (or Earth for that matter), hopefully it's clear that if it were true that Jupiter + Pluto would make you float, then Jupiter + cat would definitely you stick you right to the ceiling every time the cat walks above you |1]! If you wish you can also calculate the gravitational effect of Jupiter only. While it is significantly greater than that of a cat, it's still much smaller than the effect of large objects around us, such as buildings, ships, hills etc.

Explanation / Answer

Answer:

We should follow the basic formula to calculate the acting force between two objects that are as follows;

F= G*Mm/r2   --------- equation 1

Where, F= force between two objects (here force is replaced by gravity), G= gravitational constant(6.67408 × 10-11 m3 kg-1 s-2), M= mass of first object, m= mass of second object, r= distance between two objects.

*Mass of earth= 5.972 * 1024 kg

Now put the values in equation 1 to get the net forces.

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