- Kepler's 2nd law of planetary motion:
The orbital radius of
planet or other orbiting
body
acted on by a central force
(which in general is NOT
an inverse-square law force)
sweeps out equal areas in equal times.
This means the body moves faster the
nearer it is to the center of force,
fastest when closest, and slowest when farthest.
Recall for astronomical orbits
(which is usually what one means by
orbits without qualification),
closest approach is periapsis
and farthest remove is apoapsis
in general terminology.
- In the animation, the
green arrow represents the
velocity of the
body
and the middle purple arrow represents
central force
on the body.
The other two purple arrows represent the components of the
central force
in the direction
of motion and perpendicular to the direction of motion.
- Kepler's 2nd law
is now understood to be a consequence of the
conservation of angular momentum
of an object acted on only by a
central force
(which in general is NOT
an inverse-square law force).
In a
gravitationally-bound
gavitational two-body system,
gravity is the
central force.
Planets orbiting the Sun
and moons orbiting a
planet obey
Kepler's 2nd law
to high accuracy.
Astronomical perturbations
always forbid it from holding exactly.
- Johannes Kepler (1571--1630)
and immediately succeeding astronomers
did use
Kepler's 2nd law
for calculating orbital motions by
calculations by hand.
Such calculations
were very tedious, but gave far higher
accuracy/precision
than ever achieved before,
and so they had to do them.
- Among other things
Kepler's 2nd law
broke the hold of
uniform circular motion
on the minds of astronomers.
From
Greco-Roman antiquity,
astronomers
had been fixated on
the
Platonic principle of uniform circular motion
(probably NOT actually posited by Plato (428/427--348/347 BCE))
which held that the motions of the
Heavens could only
explained in terms of
compounded
uniform circular motions
even though they had NO
theory allowing them to
predict how the compounding had to happen.
They just fitted the observations with
whatever compounded
uniform circular motions
worked well enough.
Ptolemy (c.100--c.170 CE)
actually violated the
Platonic principle of uniform circular motion
with his equant device
without, however, denying the principle and later
astronomers working
in the tradition of
ancient Greek astronomy
considered this the
crime of Ptolemy---including
Nicolaus Copernicus (1473--1543).
Platonic principle of uniform circular motion
is, in fact, a WRONG
theory of
celestial mechanics.
By dispensing with
Platonic principle of uniform circular motion,
Kepler
helped to set path to the true
dynamics
found by
Isaac Newton (1643--1727):
i.e., Newtonian physics.
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