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Kepler's First Law of Planetary Motion

Kepler's First Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. He formulated his first two laws based on the observations of his forebears, Nikolaus Copernicus and Tycho Brahe.
Polish astronomer Nikolaus Copernicus put forth a theory that stated a heliocentric model for the solar system. According to this heliocentric theory, all the planets, including Earth, orbit the Sun in circular orbits.
On the other hand,...

Kepler's Second Law of Planetary Motion

Kepler's Second Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. His first law states that all planets orbit the Sun in an elliptical orbit, with the Sun at one of the ellipse's foci. Therefore, the distance of a planet from the Sun varies throughout its revolution around the Sun.
While in an elliptical orbit, the total energy of the planet is conserved. Therefore, the planet slows down when it is at apogee and...

Kepler's Third Law of Planetary Motion

Kepler's Third Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. In 1909, he formulated his first two laws based on the observations of his forebears, Nikolaus Copernicus and Tycho Brahe. However, in 1918, he published his third law of planetary motion, which gives a precise mathematical relationship between a planet's average distance from the Sun and the amount of time it takes to revolve around the Sun. It...

Reduced Mass Coordinates: Isolated Two-body Problem

Reduced Mass Coordinates: Isolated Two-body Problem

In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...

Pole and System Stability

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.

Second Order systems II

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If ζ...

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Updated: May 8, 2026

Bringing the Visible Universe into Focus with Robo-AO

Bringing the Visible Universe into Focus with Robo-AO

Published on: February 12, 2013

Planetary system disruption by Galactic perturbations to wide binary stars.

Nathan A Kaib¹, Sean N Raymond, Martin Duncan

¹Department of Physics, Queen's University, Kingston, Ontario K7L 3N6, Canada. nkaib@astro.queensu.ca

|January 8, 2013

Summary

Wide binary stars, distant companions to planets, can significantly alter planetary systems over billions of years. These systems often eject planets and increase the eccentricity of others.

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Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Area of Science:

Exoplanetary Science
Astrophysics
Computational Astrophysics

Background:

Many exoplanets are found in wide binary star systems with separations over 1,000 AU.
The impact of these distant companions on planetary evolution is understudied.
Wide binary orbits are dynamic, influenced by galactic tides and stellar encounters.

Purpose of the Study:

To investigate the influence of wide binary companions on planetary system evolution.
To understand how dynamic wide binary orbits reshape exoplanetary systems.
To compare the orbital characteristics of planets in wide binaries versus isolated stars.

Main Methods:

Numerical simulations of planetary systems in wide binary configurations.
Modeling the long-term evolution of planetary orbits under varying binary dynamics.
Statistical analysis of simulated and observed exoplanet eccentricities.

Main Results:

Wide binary companions can dramatically reshape planetary systems, often billions of years post-formation.
Planetary ejections and increased orbital eccentricities are common outcomes.
Giant exoplanets in wide binaries exhibit statistically higher eccentricities than those around isolated stars.

Conclusions:

Contrary to prior assumptions, wide binary companions actively perturb planetary systems.
The observed eccentricity distributions suggest initial planetary system similarities, with wide binaries later scattering outer planets.
Most isolated giant exoplanet systems likely harbor undetected distant planets.