### Gravity
Let's start with Newton's Law that force is proportional to acceleration:
force = mass * accel in N
When I'm standing on earth, it is constantly accelerating me so that I stay glued to the ground. That acceleration is called **standard gravity**.
std g = 9.80665 m/s^2
Now some personal info:
weight = 62 kg
With that out of the way, we can measure the force that the earth exerts on me:
earth force = force(weight, std g)
=> 608.0123 N
That was fun! We now know that the earth exerts `734 N` of force on me. All the time. But we love her anyway.
Change the values in blue above to find out how much she exerts on you!
#### Newton's Universal Gravitation
Previously, we used the fact that the earth constantly accelerates us at the rate `std g` to keep us on the ground.
But where did this number come from? We can use Newton's Law of Universal Gravitation to calculate it. Here's that law:
force of gravity = G*(mass * other mass)/dist^2 in N
It states that the force due to gravity is proportional to the masses of two objects and *inversely* proportional to the squared distance between them.
The constant of proportionality is `G` - a very different number from the `g` we knew before. It is:
G = 6.67384e-11 m^3/kg/s^2 #gravitational constant
Let's now use the law to calculate that value of `g = 9.8m/s^2` from above. We'll do it by using the mass of the earth and the ma
mass of earth = 5.972e24 kg #googled
radius of earth = 6,378,100 m #googled
earth gravity = force of gravity(
mass = mass,
other mass = mass of earth,
dist = radius of earth)
=> 9.7974 m*mass/s^2 in N
And there it is! Well it's not quite `9.81m/s` but that's just because our input numbers for earth's mass and radius weren't exactly what is used to calculate standard gravity, but it's darn close!
How close is it? Well let's give it our mass and see how close to `734 N` it gets:
earth gravity(mass = weight in kg)
=> 607.4417 N
So close! It calculated `733 N`.
Why not try changing the numbers to see how much gravity would affect you if you lived on mars?
Or we can just plot the various weights:
plot(earth gravity(mass=mass), 0..200kg)
We can see that the slope of that plot is our standard gravity of `9.8m/s^2`.