Universal Gravitation Ch3 Universal Gravitation

Gravity If the force of gravity is being exerted on objects on Earth, what is the origin of that force? Newton’s realization is that it must have come from the Earth He realized that gravity must be what keeps the Moon in orbit

Applying the Law of Universal Gravitation There are 2 equal, but opposite forces present. For the force of attraction to be noticeable, at least one of the objects must be very large The inverse square relationship between FG and r means the force of attraction diminishes rapidly as the two objects move apart Also, there is no value of r, that would make this force 0 This equation only applies to spherical objects, to two objects whose sizes are much smaller than their separation distance

Example 2 - Spacecraft

3.4 Satellites & space stations

Satellite Motion A satellite is an object or a body that revolves around another body. Satellites can be categorized as natural satellites or man-made satellites.

Satellites in Circular Orbit Newton related the cause for heavenly motion (the orbit of the moon about the earth) to the cause for Earthly motion (the falling of an apple to the Earth) and this led him to his notion of universal gravitation. He surmised that the same force that pulled an apple downward as it fall from a tree was responsible for keeping the Moon in orbit

Satellites in Circular Orbit Why doesn’t the moon hit the ground? The Moon travels at the speed that keeps it at approximately the same distance, called the orbital radius, from Earth’s centre. As the moon circles Earth, it is undergoes constant free fall toward Earth (same is true for all natural and artificial satellites). A satellite pulled by the force of gravity toward Earth follows a curved path. Since Earth’s surface is curved, the satellite falls downward at the same rate as Earth’s curvature If the orbiting free-falling satellite, has the proper speed for its orbital radius as it falls toward Earth, it will never land.

Motion of a Satellite in Uniform Circular Motion Combining Newton’s law of Universal Gravitation, and equation for Centripetal Acceleration involves the satellite’s speed. Used to analyze the motion of a satellite in uniform circular motion

Apparent Weight Apparent Weight: the net force exerted on an accelerating object in an non-inertial frame of reference

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