## BIG IDEA
Most people consider gravity in terms of something falling. This is a good starting point but the interaction between two objects is an attractive force, both objects pulling. A “falling” apple is pulled by Earth but the apple is also pulling on Earth.
A great example of gravity is the cold and warm air on our planet leading to weather. Cold air is “heavier” and falls toward the ground while warm air rises. This leads to wind.
Another example of gravity is found in satellites orbiting the Earth. The objects are in free fall and travel fast enough to overcome gravity. If the satellite slows down then gravity overtakes it and the object returns to Earth.
In all of our examples, the interaction is between two masses. It turns out that that gravitational force is proportional to the mass of the objects; the greater the mass then the greater the force of gravity. We can show this mathematically:
F∝ M Where _M_ is the mass of one object
The size of the mass is not the only variable that influences the force of gravity; the distance between the two masses is also very important. The further away the two masses are then the magnitude of the force is less. We can show this mathematically, too:
F∝ $\frac{1}{r^2}$ where r is the distance between the center of the two objects.
We can combine both proportional statements into one statement and start to get a good picture of the gravitational force.
F ∝ $\frac{Mm}{r^2}$, where M and m are the masses of the object and the r is the distance between them.
The only item missing is a universal gravitation force constant to complete the equation. We will use capital G to represent the gravitational field strength. The constant has a value of 6.67 x 10-11 N·m2kg2.
$\vec{F}$= G$\frac{Mm}{r^2}$
Because the relationship between the force and distance is an inverse square relationship, we call the law **an inverse square law**. It’s just like Coulomb’s law, right? Sort of. Gravity is attractive only.
Applying the Universal Law of Gravitation
This equation is known as Newton’s Law of Universal Gravitation and it can be used to explain the gravitational force. In fact, we can calculate the acceleration due to gravity on Earth based on Newton’s Universal Law.
Start with two equations: Newton’s second law of motion and Newton’s law of universal gravitation.
F∝ G$\frac{Mm}{r^2}$ and _$\vec{F}$_ = mg
Set the two equations equal to each other.
mg = G$\frac{Mm}{r^2}$
Cancel the mass of the smaller object from both sides of the equation.
g = G$\frac{M}{r^2}$
Substitute in the values for G, M, and r.
[](https://lh4.googleusercontent.com/U1DYJKE3x4hfyqbPZZdR7JNPwOtMpCR2lDjqnyqpX8K5nkc_bQXbckJFq7gdEF-n0RFloOLqKWZ93C7wUwazAVS8qYSMpcLqpLxa88nv9tiNvVzi2JvlXiRIFZhc1Sg0vxv6K7zE)
Solve.
_g_ = 9.8 $\frac{m}{s^2}$
Technically, this value is the field strength of gravity on Earth. It is also the acceleration of an object due to gravity on Earth. The “on Earth” is extremely important. Change the location, this changes the value of the mass and r, which changes the field strength. It’s why the weight of an object (a force equal to mass time the value of g) changes with location.
---
Return [[Home|Home]]