3-Dimensional Cartesian Coordinate System
This section provides an introduction of 3-dimensional Cartesian coordinate systems, which uses perpendicular projections on 3 perpendicular axes to describe any locations in the frame of reference.
If we want to describe locations of a space shuttle flying towards a space station,
we need a 3-dimensional frame of reference and an associated coordinate system.
First, let's define a 3-dimensional frame of reference with the following reference points:
- First reference point - The center of Earth.
- Second reference point - The intersection point of the Equator Plane and the Prime Meridian plane.
- Third reference point - The North Pole.
Next, let's define a 3-dimensional Cartesian coordinate system and associate it to the above frame of reference:
- Set the origin of the Cartesian coordinate system at the center of Earth.
- Set the x-axis along the straight line from the center of Earth to
the intersection point of the Equator Plane and the Prime Meridian Plane.
Scale the x-axis with 1 km per unit.
- Set the z-axis along the straight line from the center of Earth to
the North Pole.
Scale the z-axis with 1 km per unit.
- Set the y-axis along the straight line passing through the center of Earth
and perpendicular to the Prime Meridian Plane.
Scale the y-axis with 1 km per unit.
Now we are can describe any location of the space shuttle while it's flying as a set of 3 coordinate numbers.
For example, the location of the space shuttle shown in the picture below
can be described as (19113, 20706, 11857), because:
- Its perpendicular projection on the x-axis is 19,113 km.
- Its perpendicular projection on the y-axis is 20,706 km.
- Its perpendicular projection on the z-axis is 11,857 km.
Last update: 2014.
Table of Contents
About This Book
Introduction of Space
►Introducion of Frame of Reference
What Is Frame of Reference
Frame of Reference with 2 Objects
What Is Coordinate System
2-Dimensional Cartesian Coordinate System
►3-Dimensional Cartesian Coordinate System
1 Frame of Reference with 2 Coordinate Systems
Introducion of Time
Introduction of Speed
Newton's Laws of Motion
Introduction of Special Relativity
Time Dilation in Special Relativity
Length Contraction in Special Relativity
The Relativity of Simultaneity
Introduction of Spacetime
Minkowski Spacetime and Diagrams
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