Geodesics.

[MJ kihara]

How many different ways can someone illustrate geodesics.

Can a wavy line be used to illustrate a geodesic?

[MigL]

59 minutes ago, MJ kihara said:

Can a wavy line be used to illustrate a geodesic?

You can use dashed, or dotted, lines also ...
There are many ways to illustrate the path taken by test particles in free-fall, through space-time, such that the path length is minimized.
( in the context of GR )

Edited 20 hours ago by MigL

[MJ kihara]

10 hours ago, MigL said:

to illustrate the path taken by test particles in free-fall, through space-time, such that the path length is minimized.

Assuming we have an asteroid having an elliptical orbit around the sun..can this orbit/ geodesic be illustrated as a wavy line  extending from the larger mass(sun)?

[swansont]

26 minutes ago, MJ kihara said:

Assuming we have an asteroid having an elliptical orbit around the sun..can this orbit/ geodesic be illustrated as a wavy line  extending from the larger mass(sun)?

A wavy line extending from the mass would not illustrate the path of the orbit. It might illustrate something else.

[Genady]

The horizontal axis here is some x, e.g., ellipse's major axis. The vertical axis is time. The wavy line is the orbit.

[MJ kihara]

2 hours ago, Genady said:

The horizontal axis here is some x, e.g., ellipse's major axis. The vertical axis is time. The wavy line is the orbit.

...and since the wavy line is the orbit and the orbit is the path tracing the asteroid as it free fall,then  wavy line is the geodesic...

You wavy line is not for an elliptical orbit?

[Genady]

15 minutes ago, MJ kihara said:

...and since the wavy line is the orbit and the orbit is the path tracing the asteroid as it free fall,then  wavy line is the geodesic...

You wavy line is not for an elliptical orbit?

I think it is for an elliptical orbit.

[Mordred]

One other possibility as a reference for the image isnt provided it could also indicate the action due to path of least resistance via Euler-Langrangian with the straightline arrow indicating the mean average.

I sometimes encounter similar diagrams in least action articles involving gravity.

Typically used when describing infinitisimal variations as opposed to more classical treatments.

However that's just a possibility without a reference to go by.

Edited 6 hours ago by Mordred

[MJ kihara]

12 minutes ago, Genady said:

I think it is for an elliptical orbit.

I don't think so...the asteroid is  orbiting sun elliptically...that's for a circular orbit.

[Genady]

4 minutes ago, MJ kihara said:

I don't think so...the asteroid is  orbiting sun elliptically...that's for a circular orbit.

I think it is for a general ellipse, including circle. I don't see what makes it limited to circle.

[MJ kihara]

20 minutes ago, Genady said:

I think it is for a general ellipse, including circle. I don't see what makes it limited to circle.

I think specifically it for a circle... avoiding definition complications.