Universal gravitation

Gravitational Force• Newton realized that the centripetal force that holds the planets in orbit is the very

same force that pulls an apple to the ground – Gravitational Force.

• Orbiting objects are in free fall.

Gravitational Force

• Yes the moon is falling and so are the rest of the planets.

• If the moon did not fall it would follow a straight line path.

• The tangential velocity of the moon is great enough to cause it to move in a circle and not into earth

Gravitational Force

• Gravitational force is the mutual force ofattraction between particles of matter.

• Gravitational force depends on themasses and on the distance betweenthem.

Gravitational Force

Gravitational Force

• Law of universal gravitation states that objects attract other objects with a force that is:

• directly proportional to the product of their masses

• inversely proportional to the square of the distance between them.

Law of universal gravitation components

• Here is what the different components stand for:

• G = universal gravitational constant,• m1 = mass of object 1,• m2 = mass of object 2,• r = distance between the centers of the

objects

Gravitational Force

• The gravitational forces that two masses exert on each other are always equal in magnitude and opposite in direction.

• This is an example of Newton’s third law of motion.

• One example is the Earth-moon system, shown on the next slide.

Gravitational Force

Gravitational Force

• As a result of these forces, the moon and Earth each orbit the center of mass of the Earth-moon system.

• Because Earth has a much greater mass than the moon, this center of mass lies within Earth.

Gravitational Force

• Gravitational forces exist between any two masses, regardless of size.

• But Remember this:• 1. the greater the masses the greater is

the force• 2. the greater the distance the smaller is

the force

Gravitational Force

• Newton’s law of gravitation accounts for ocean tides.

• High and low tides are partly due to the gravitational force exerted on Earth by its moon.

Inverse-square law

• According to Newton’s equation, F is inversely related to the square of the distance.

• F = 1 r2

Gravitation decreases according to this law. The force of gravity weakens as the distance is squared.

5-7 Gravity Near the Earth’s Surface; Geophysical Applications

The acceleration due to gravity varies over the Earth’s surface due to altitude, local geology, and the shape of the Earth, which is not quite spherical.

5-8 Satellites and “Weightlessness”

Satellites are routinely put into orbit around the Earth. The tangential speed must be high enough so that the satellite does not return to Earth, but not so high that it escapes Earth’s gravity altogether.

5-8 Satellites and “Weightlessness”

The satellite is kept in orbit by its speed – it is continually falling, but the Earth curves from underneath it.

5-8 Satellites and “Weightlessness”Objects in orbit are said to experience weightlessness. They do have a gravitational force acting on them, though!The satellite and all its contents are in free fall, so there is no normal force. This is what leads to the experience of weightlessness.

5-8 Satellites and “Weightlessness”More properly, this effect is called apparent weightlessness, because the gravitational force still exists. It can be experienced on Earth as well, but only briefly: