The Astrophysics Spectator

Issue 2.18, May 11, 2005

Home Commentary Surveys Research Background Store Previously Site Info
Logo for The Astrophysics Spectator.

The basic layout of the site is as survey paths, which can be found under the Surveys link at the top of this and most other pages on this site. Each survey begins with a basic overview of the subject. Part of this overview include simulators of astrophysical phenomena that allow the reader to experiment with the phenomena. The later pages in a survey present the subject in greater and more mathematical depth. A path ends with research pages that describe current research projects and results in astrophysics.

The links at the top of each page are Home, which is the current home page of this site, Commentary, which is an index of short essays on topics loosely related to astrophysics, Surveys, which is the index of survey paths, Research, which is the index of research pages and the page leading to recent news items, Background, which is the index page for all background information on astrophysics, including survey pages, simulator pages, tables, bibliographic references, and lists of web resources, Previously, which is an index of previous home pages, and Site Info, which describes the site and its author, and gives contact information.

On the home page is found an addition link. This is the Store link, which leads to reviews of worthwhile books on astronomy and other relates subjects. Links on these pages enable the reader to buy these books from, which helps to financially sustain this web site.

Each Wednesday, a new issue of The Astrophysics Spectator is published that comprises a new home page, a new commentary, whatever news the author notices, and background, research, and simulator pages added to the survey paths. The home page acts as an index to the newly added pages. This site also has an RSS channel, whose link is given at the bottom of the right-hand column of this page.

May 11, 2005

With this issue of The Astrophysics Spectator, I introduce a simulator for the “Special Relativity” survey path. This simulator shows the motion of a free-falling body as seen by a traveler accelerating at a constant rate.

Over sufficiently short lengths, the world of a traveler accelerating at a constant rate is indistinguishable from the world of an observer hovering over a black hole. In this world, the traveler hangs over an event horizon that separates him from a universe that can no longer reach him. Objects burst upward away from the event horizon at a tremendous rate of speed, but they settle slowly back to it at a glacial speed. Light traveling in this accelerated world bends towards the event horizon; this effect makes objects appear higher above the event horizon than they actually are. To our traveler, the event horizon appears to wrap upward, forming a bowl that contains our traveler. Free-falling objects in this world appear to follow complex paths across the sky.

The Constant Acceleration Simulator allows the reader to see this world for himself. With two mouse clicks, the reader can define a starting point and a maximum altitude for objects in free-fall. The simulator follows the motion of the object both as measured in a Cartesian coordinate system and as seen by a traveler fixed within this accelerating world. The simulator also shows the path followed by the light propagating from a free-falling object to the traveler, and it shows the shape of the event horizon as seen by the traveler.

The basic properties demonstrated by the simulator are the properties near the event horizon of a black hole. The only effect not seen by a traveler undergoing constant acceleration that that appears at a black-hole's event horizon is the tidal force. The strength of this force is proportional to the ratio of the length of the free-fall path to the black hole radius. As the radius of a black hole goes to infinity, the tidal force goes to zero, so the world of constant acceleration is the world of an infinite-radius black hole.

Jim Brainerd


Constant Acceleration Simulator. The free-fall motion of bodies relative to a traveler accelerating at a constant rate is the same as that of bodies near a black hole. With the Constant Acceleration Simulator, the reader can experiment with the motion of objects in an accelerated reference frame. The simulator shows the motion of objects both as measured in a Cartesian coordinate system and as seen by the accelerating traveler, demonstrating the effects of time dilation and of light propagation close to the traveler's event horizon. This simulator is part of the “Special Relativity” survey path. (continue)


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