Display of Frames of References

[GlobeMaker]

Proposed Display of Frames of References in Celestia
Rev. 1 Dec. 9, 2005

Abstract

The proposed frames of reference would be made by line segments in Celestia. The display of a single infinite line through the Galaxy would be initialized. When activated in Celestia, gravity would bend the line, relative to the viewer. The gravity of stars would bend the line using motion. The line would have gaps so its motion is visible in several directions.

A second version goes beyond the single line. A wire-frame plane would be made flat to start with. Then, after gravity is turned on, the plane would warp its shape in a way that is relative to the viewer's position in space-time. Stars and other masses would affect the frames of reference. Dark stars would be sent through the infinite plane to watch the response. The line segments would move towards stars and fall into them. This approximated display of an infinite mesh of line segments would be replenished from infinity as segments fall into stars. This illustrates the accelerating frames of reference that can be used to describe gravity.

Details

The frames of reference for gravity were described by Einstein and his collegues. There are some frames that are standing still, relative to the viewer. Some frames of reference are at a relative velocity. A frame of reference that is at rest relative to a body in free fall is accelerating, if it is near Earth. Some accelerations could be changing with higher derivatives, relative to the Celestia camera.

The design of the technique is in an early phase. One goal is to link the wire frame elements to asteroids that are in a belt that is coincident with the wire-frame plane. Extension to three dimensions is proposed as a last phase of work by the author and other possible open-source contributors.

Open Source Document
Anonymous

[selden]

The display may need to be pre-calculated before showing it with a fast speed of motion.

Precalculations would have to be limited to the locations in space of the endpoints of the line segments, assuming they're fixed in space, just as orbit paths are precalculated now.

One of its design requirements is that Celestia always calculates the locations of all of the objects being drawn on the screen every time the screen is updated.

[GlobeMaker]

Response to comment, "Precalculations would have to be limited to the locations in space of the endpoints of the line segments, assuming they're fixed in space, just as orbit paths are precalculated now.

One of its design requirements is that Celestia always calculates the locations of all of the objects being drawn on the screen every time the screen is updated."

One goal for this work to comply with the usual requirements for Celestia. As Selden has alerted me, the frames of reference must be drawn at the usual speed of motion for the Celestia display. The initial frame of reference diplays will be so simple that computational speed will not be an issue.

The first display of frames of reference will be shown next week. This will be a display of a simple ruler, constructed as a .3ds add-on. The ruler will be 1 kilometer long. It will be made from six points connected by 8 triangles. The next phase will place rulers in a line that is one megameter long, with one kilometer gaps between rulers. The rulers will be connected hierarchically to make objects next week like :

A collection of rulers for any length.

An elevator in which historical thought experiments take place.

A lever long enough to move the Earth, as Archimedes envisioned.

A frame of reference that is at rest relative to the Celestia Camera.

A frame of reference that has a constant velocity relative to the Celestia Camera.


This simple work will lay the foundation for more elaborate frame of reference displays in the future.