Magic Of Physics

Attraction between two bodies

Every two bodies attract each other according to Newton’s law of Universal Gravitation. Then why the chairs are not moving towards the table?

Why my chair is not moving towards the table?

This is because the force of attraction between two bodies is given by the formula GMm/R² where G=6.674×10-¹¹, M is the first mass, m is the second mass and R is the distance between them. If M=1kg, m=1kg and R=1m, force of attraction, F = .00000000006674N which is opposed easily by air and surface friction. So since G is very very very…. small, the chair is not moving towards the table. Then why are the leaves falling from trees? Why is a ball when tossed up falling back to the ground?

Why is the ball moving towards the ground?

Suppose the ball is 1kg. The mass of earth, M is 5.97237×1024 kg.Distance between the earth and the ball is R=6,378.1 km=6,378,100m.So the force of attraction between the ball and the ground is given by F=GMm/R² = 9.8 N which is the force we experience on our hands when we hold a 1 kg weight. This force or weight is considerably large enough to experience movement because M is large.

Force of repulsion on a body moving on a Circle

There is also a force of repulsion on a body moving on a circle. This force is given by   mv²/R. This is the very force we experience in a car taking a circular left turn or U-turn. Here m is the mass of the body, v is the velocity of the body and R is the radius of the circle.

Forces on a celestial body

The attractive force on a body moving in an orbit and the repulsive force are well-balanced to keep it in the orbit. The gravitational force pushes it towards the center and the force due to circular motion pushes it outwards.

What if velocity increases?

When velocity v increases, force, mv² /R increases. Thus the repulsive force overcomes the attractive force and hence the body moves away from the center. This causes the distance of the body from the center, R to increase. When R increases, though mv² /R decreases, GMm/R2decreases even to a greater extend because R² is larger than R. Thus attractive force decreases and the body moves further away from the center which means R again increases. This increase in R again causes body to move further away and thus R increases further. Thus the body keeps moving away from the center and moves out of the orbit.

What if velocity decreases?

When velocity decreases, the reverse of the above happens. R decreases and further decreases and further decreases. This causes the body to fall towards the center. Thus the body falls from the orbit.

Exercise-1

Now that you have read up to this, try this: Hire a programmer and ask him to create a program which simulates a body revolving around another body in an orbit. The inputs to the program must be M, m, R and v. Try different values for M, m, R and v and see if the body stays in the orbit, falls or moves away. You will certainly see how difficult it is to keep the body in orbit though it is the Universe your subordinate created. All of the above may not be 100% accurate. But this much information is enough to make you think how well-designed and in harmony, the Universe is.

Design without a designer

If a monkey uses a typewriter for billions of years, does it create a poem? When you see a footprint on the sea-shore do you think the waves created it? When you see an art on a paper and a pencil beside it, do you think the pencil stood up and danced on the paper and created the design?