﻿ GravXPit
Mechanics:

GRAVITY VERSUS THE GRAVITY PIT

In this experiment, we use an analogy of coins falling into a pit to explain how planets move around the Sun.  Because the Sun’s mass, the space-time is curved around it, as a pit, making the planets orbit it.  However, in the system coin-pit, different of planetary system, there are friction and air resistance that make the coin lose energy and fall in a spiral moving.  Thus, to compare these two systems, we have to consider each period of the coin as unique and there are no friction and air resistance.

The similarity:
• The planets are kept in their orbit by the force of gravity (FG) that the sun exerts on them. Where, by Newton:

,

where, G is the gravitational constant, M is mass of Sun, m is mass of planet and r is the distance between planet and Sun.

• The force of gravity is strongest when the distance r between the Sun and the planets is smallest.

• The centripetal force (FC) is , where v is the speed of the planet.

• In this system  FG = FC.

• So, we get ,

.

• That way, v is proportional to .

As conclusion:

• The force of gravity is strongest near the sun.

• The period of the planets is shortest for the planets closest to the sun.

• The speed of the planets is greatest for the planets that revolve closest to the sun.
• The weight (P) of the coin creates a normal force (Fn) that it is perpendicular to the surface of the pit.

• This normal force has a horizontal component that is the centripetal force (FC) responsible for the orbit of coin around the center of the pit.

• This centripetal force is greater when the slope of the surface is steeper, that is, when the radius (r) is smaller.

• By the vector decomposition:

• Fn cosα = P = mg, and

• Fn sinα = where m is the coin mass, g is gravity acceleration and v is the coin speed. Then, tanα =

• The pit has a hyperbolic superficial, where the relation between depth of the pit (y) and its radius (r) is   , and k is a constant.

• By the geometric of the pit: tanα

• Then, we get

• That way, v is proportional to .

As conclusion:

• The slope of the gravity pit is greatest near the center.

• The period of revolution of the coin is shortest when the coin is closer to center of the pit.

• The speed of the coin is greatest when the coin is   near the center.