The blue arrow points from the primary’s center to the spacecraft. Its length is a scalar distance. Boldface denotes a vector: three components with a direction. Plain denotes its magnitude. A dot means a derivative with respect to ; two dots mean a second derivative.
The collects the three coordinates of the spacecraft. The superscript writes them as a column.
is how changes with . The dot and the derivative fraction mean the same thing; is not equal to .
is how changes with , so it is also the second derivative of .
The green arrow is tangent to the path. The red points toward the primary, generally in a different direction from . A state vector combines and : six numbers, plus an and reference frame.
Combine the three components and three components to describe the instantaneous state.
state = [, , , , , ]ᵀ
Model assumptions
The arrow uses the distance scale. and arrows use separate display scales, not distance units.
Variables in this lesson
Position vector and radiuskm is a vector from the chosen origin. = || is its length; it is not altitude.
Velocity and speedkm/s includes direction. is its nonnegative magnitude.
Accelerationkm/s²Rate of change of . Do not confuse vector with .
Elapsed times from the simulation’s chosen initial .
Gravitational parameterkm³/s² times total two-body mass, approximately the primary mass for a spacecraft.
TRY THISPause and drag the slider to explore the orbit. Compare the three arrows at and a quarter of an orbit later.
How this connects
Start by connecting position, velocity, and acceleration to the view. Next: Why an orbit keeps falling.