Law of universal gravitation

Newton correctly deduced that an attractive gravitational force exists between all objects that have mass. The gravitational force is a universal force that exists between any two objects that contain mass. The strength of the gravitational force depends on the mass of the objects and the square of the distance between them. The equation Newton derived for gravity is called the law of universal gravitation. Read the text aloud
(7.5) F=G m 1 m 2 r 2
F  = force (N)
G  = gravitational constant
   = 6.67×10−11 N m2/kg2
m1  = mass of object #1 (kg)
m2  = mass of object #2 (kg)
r  = distance between centers (m)
Law of universal gravitation
Law of universal gravitationEquation (7.5) says that the attractive force between two masses (m1 and m2) is proportional to the mass of both objects multiplied together. If one object doubles in mass, then the force between the objects doubles. If both objects double in mass, then the force of gravity between them is multiplied by four. The force is inversely proportional to the square of the radial distance r between the masses. This means that increasing the distance by a factor of 2 decreases the force by (1/2)2 = 1/4. Read the text aloud
The gravitational constant G in equation (7.5) has the value 6.67×10−11 N m2/kg2. The value of G is the same everywhere in the universe. Read the text aloud Show Einstein’s theory of general relativity
Gravitational forces always come in pairs, just like all other forces. If the action force is the force acting on m1 from m2, then the reaction force is the force acting on m2 from m1. Similarly, consider the weight of an apple in your hand. If the apple’s weight is the action force, the reaction partner is the force of the apple pulling back on the Earth itself—not the normal (support) force from your hand holding up the apple! Read the text aloud
The force of gravity between two objects is always directed along the line connecting their centers of mass. As objects move, the force of gravity changes its direction to stay pointed along the line of those centers. Read the text aloud Gravitational force between a person and an apple is much less than the gravitational force between the Earth and an apple Show Centripetal force
The attractive gravitational force between ordinary objects is tiny because gravity is a relatively weak force. It takes a planet-sized mass to create gravity strong enough to feel. The attraction between you and a 0.1 kg apple is 0.0000000004 N whereas the attraction between Earth and the apple is 0.98 N. Earth’s force is larger because it has a mass of 5.98×1024 kg, compared to a person with a mass of 60 kg. Read the text aloud Show Why do we say gravity is a <i>weak</i> force?
Calculate the force of attraction between the Earth (m = 5.98×1024 kg) and a giant alien mothership (m = 500,000 kg) whose centers are 20,000 km away from each other.
  1. 4.99×105 N
  2. 9.97×1012 N
  3. 1.28×1027 N
  4. 6.67×10−11 N
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