Hey it's a me again @drifter1!
In this article we will continue with Physics, and more specifically the branch of "Classical Mechanics".
Today's article will be about Gravitational Fields.
So, without further ado, let's "get pulled" straight into it!
Gravitational Field
Small Recap
In the previous articles about the topic of Gravity we stated that:
All particles in the Universe attract each other with a force (Fgravity) that can be described by Newton's Law of Gravitation:
This force is also called weight (w) and equal to:
The acceleration of gravity (g) that an object has while being attracted by another through Gravity can be calculated by substituting the 2nd into the 1st equation giving:
Definition
The region in which other objects are attracted to another object (with more mass) is called a Gravitational Field.
The field has infinite range, but infinitesimal forces can safely be ignored in calculations.
This means that we don't have to include the graviational attraction of other planets of the Solar System when solving problems with Gravity on Earth.
In the same way, we don't have to include the gravitational attraction of objects with small mass (like pizza) when their is the larger gravitational attraction caused by the mass of the whole Earth.
Mathematical Equation
A gravitational field is described by the following equation:
g: graviational acceleration
G: graviational constant
M: mass of the attractor object
|r|: distance away of the center of the object
: unit direction vector pointing towards the object (that's also why the value is negative)
Modified Gravity Force Equation
Using this representation, the force of gravity (or weight) is now written as:
Gravitational Field Visualization
Gravitational Field of Single Point Mass
A gravitational field of a single mass can be drawn using vectors or "field lines" that point towards the center of mass.
Using Vectors, by decreasing the length as we move further and further away from the mass, we can visualize the decrease of strength:
[Custom Visualization based on Ref3]
Using Lines, we just show the direction:
[Custom Visualization based on Ref3]
The Principle of Superposition
Before we get into the field caused by two or more masses, we have to talk about how we add-up the attractions.
Because of the Principle of Superposition the total gravitational field is given by adding the two or more vectors together.
This might sound obvious, but isn't true for every force in nature.
Elementary particles and gravitational fields near black holes don't obey this principle.
Gravitational Field of Two or More Masses
To keep things simple let's suppose a point mass m is at some point P in space and attracted by three masses with the same mass M that form a triangle.
Using two two-vector sums to add the forces we can easily visualize towards which position that point mass will be attracted to.
Let's first just visualize the four masses:
Let's now add field lines starting from mass m and heading towards each mass M:
Let's (visually) calculate the sum of the gravity force vectors of the two upper masses:
Lastly, let's calculate the total attraction vector by adding the previous result to the lower gravity vector:
The vector lengths were not accurately taken and so the result might be incorrect here.
I guess that the concept has been made clear though.
