Johannes Kepler (1571-1630), a German mathematician and astronomer and
a key figure in the 17th century astronomical revolution.
He discovered that the Earth and planets travel about the Sun in elliptical orbits;
gave three fundamental laws of planetary motion, and also did important
work in optics and geometry.

Kepler problem

پراسهی ِ کپلر

parâse-ye Kepler

Fr.: problème de Kepler

1) Given the trajectory of a particle moving in a → central force
field, determine the
law governing the central force.
2) Inversely, considering a central force -k/r^{2}, determine the
trajectory a particle moving in the field will take.

A → NASA space telescope launched in March 2009 to discover
Earth-size planets using the → transit method.
The telescope has a diameter of 0.95 m and its
only instrument is a → photometer
that continuously monitors the brightness of over 145,000
→ main sequence stars in a fixed field of view of
115 deg^{2} (about 12° diameter). The expected
mission lifetime is 3.5 years extendible to at least 6 years.

An equation that enables the position of a body in an elliptical orbit to be
calculated at any given time from its orbital elements. It relates the
→ mean anomaly of the body to its
→ eccentric anomaly.

1) The planets move about the Sun in ellipses, at one focus of which the Sun is situated.
2) The → radius vector joining each planet with
the Sun describes equal areas in equal times.
3) The ratio of the square of the planet's period of revolution to the cube of the
planet's mean distance from the Sun is the same for all planets.

A → supernova in → Ophiuchus,
first observed on 1604 October 9, and described by Johannes Kepler in
his book De stella nova (1606). It reached
a maximum → apparent magnitude of -3 in late October.
The star remained visible for almost a year. The → light curve
is that of a → Type Ia supernova.
The → supernova remnant consists of a few filaments
and brighter knots at a distance of about 30,000 → light-years.
It is the radio source 3C 358. Also known as SN 1604 and Kepler's supernova.

The ratio between the square of a planet's → orbital period
(P) to the cube of the mean distance from the Sun (a)
is the same for all planets: P^{2}∝ a^{3}.
More accurately,
P^{2} = (4π^{2}a^{3}) /
[G(M_{1} + M_{2})], where
M_{1} and M_{2} are the masses of the two orbiting
objects in → solar masses and
G is the → gravitational constant.
In our solar system M_{1} = 1. The
→ semi-major axis size (a is expressed in
→ astronomical units
and the period (P) is measured in years.

The angular velocity of a point in a circular orbit around a central mass. It
is given by:
Ω_{K} = (GM/r^{3})^{1/2},
where G is the → gravitational constant, M is
the mass of the gravitating object, and
r is the radius of the orbit of the point around the object.

A circumstellar disk (such as an → accretion disk
or a → protoplanetary disk) in which the
→ angular velocity at each radius is equal to the angular velocity
of a circular → Keplerian orbit at the same radius. The
main characteristic of the Keplerian disk is that
→ orbital velocity
varies as r^{-1/2}. This means that an object on an orbit closer to the central
mass turns more rapidly than that on a farther orbit.
This velocity difference is at the origin of internal friction or kinematic viscous forces
between disk particles, which heats up the material.

The orbit of a spherical object of a finite mass around another
spherical object, also of finite mass, governed by their mutual
→ gravitational forces only.

A → rotation curve in which the speed of the orbiting body is
inversely proportional to the → square root of its distance
from the mass concentrated at the center of the system.

Shearing motion of an ensemble of particles, each on a nearly
circular, → Keplerian orbit.
→ Orbital velocity decreases as orbital radius increases,
yielding shear. Viscous drag on such shear, due to ring-particle collisions, plays a
key role in ring processes (Ellis et al., 2007, Planetary Ring Systems, Springer).