CONCEPTUAL PHYSICSUniversal Gravitation

The falling moonNewton said that the force that pulls between

the Earth and a falling apple is the same as the force that pulls between the Earth and the moon….gravity.

If the moon did not fall, it would move in a straight line and leave the earth.

Newton hypothesized that the moon was a projectile circling the Earth.

The moon has a component of velocity parallel to Earth’s surface, a sideways or tangential velocity, fast enough to ensure

motion around the earth rather than into it.Fig 10.2 p135

The falling EarthEarth and the planets orbit the sun the same

way the moon orbits the Earth because of gravity.

Why don’t the planets fall into (or crash) into the sun?Because of their tangential velocities.

What would happen if their tangential velocities were equal to zero?

The law of Universal GravitationNewton’s law of universal gravitation states

that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object and inversely proportional to the square of the distances between the centers of mass of the objects.

The greater the masses, the greater the force of attraction. The greater the distance between the object, the less is the force of attraction between them.

F=G m1m2

d2

F: force (N)G: universal constant of gravitation

G= 6.67x10 -11 N m2/kg2

m: mass (kg)d: distance (m)

The small value of G indicates that the force of gravity is a very weak force. It is the weakest of the four fundamental forces of nature.

Gravity and Distance : The inverse-square lawThe greater the distance the weaker the

force.But, gravitational force is never zero.

Universal GravitationWhy is Earth round? Because of gravitation.Everything pulls on everything else. Sometimes

the effect is small compared to bigger objects.Ex. Jupiter deviates from its normal orbit due

to perturbation caused by the pull of the planet Saturn.

These perturbation have made it possible to discover different planets.

Read pg141 sect. 10.6 universal gravitation

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1) Calculate the force of gravity of gravity between Earth (mass= 6.0x1024 kg) and the moon (mass= 7.4x1022 kg). The average Earth-moon distance is 3.8x108m.

2)Calculate the force of gravity between a new born baby (mass=4 kg) and the planet Mars (mass== 6.4x1023 kg), when Mars is at its closest to Earth (distance= 8x108 m).

3) Calculate the force of gravity between the new born baby above and the obstetrician (mass= 75kg), who is 0.3m from the baby. Which exerts more gravitational force on the baby, Mars or the obstetrician?

CONCEPTUAL PHYSICSUniversal Gravitation