Universal Gravitation

Universal Gravitation

Author: Jesse Voltin

Students will be able to explain how gravitational forces are calculated. Students will also be able to explain how inverse square functions work.

Continuation of Newton's gravitational laws.

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Newton's Law of Gravitation

Newton's law of universal gravitation depends on three things:

m subscript 1 which is the mass of the first object

m subscript 2 which is the mass of the second object

Both objects are being compared to one another and the resulting gravitational force between them is opposite in direction but equal in magnitude. Meaning that F subscript 1 and F subscript 2 are the same force but the are pointed directly at the other so the direction is the exact opposite.

The last portion of the equation is dependent on the distance between the two objects.

r is the distance between the objects. The G is the universal gravitational constant. 

G equals 6.67 cross times 10 to the power of negative 11 end exponent space space fraction numerator N cross times m squared over denominator k g squared end fraction

The gravitational constant is determined as the force between two 1 kg masses which are displace 1 meter from one another. This constant is multiplied by any two massive objects at any distance to give us a force that we can use to explain their attraction.



Inverse Square Law

Any two objects that have mass will have some sort of gravitational force between them. If the distance between the objects were to be increased then the force between them would dissipate as the square of the distance of separation. For example:

F equals G fraction numerator m subscript 1 times m subscript 2 over denominator r squared end fraction  (1)

The mass of the objects would not change if we were to increase or decrease the distance between objects nor would the gravitational constant. In this case we can rewrite the equation (1) as only being proportional to the distance between the objects:

F equals 1 over r squared (2)

If we already know the force of attraction between two objects we can look at the affect that the distance had on the objects by using equation (2). For example, if we know the force between two objects and we want to know how the force is affected by increasing the distance by twice as much, the solution would look as follows:

F equals 1 over r squared space space rightwards arrow from d i s tan c e to s u b s t i t u t e of space space F equals 1 over open parentheses 2 close parentheses squared space space rightwards arrow with s o l v e on top space space F equals 1 fourth  (ex 1)

Without entering in the masses a second time and having to reenter the gravitational constant we are able to determine how the force is affected by the distance.