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 October 29 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 October 29 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.

[MJ kihara]

13 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.

 

13 hours ago, swansont said:

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

Assuming mass(sun) is a point or a spot,where do you indicate it in the above diagram ?

[Genady]

6 hours ago, MJ kihara said:

 

Assuming mass(sun) is a point or a spot,where do you indicate it in the above diagram ?

[swansont]

6 hours ago, MJ kihara said:

Assuming mass(sun) is a point or a spot,where do you indicate it in the above diagram ?

It’s not something that the graph definitively shows. The graph depicts the precession of an orbit. 

[MJ kihara]

12 minutes ago, Genady said:

Parallel to the time axis? It's becoming a confused diagram...just put a zigzag😟

[Genady]

3 minutes ago, MJ kihara said:

Parallel to the time axis? It's becoming a confused diagram...just put a zigzag😟

On a scale of an asteroid orbit shown, the Sun is considered at rest relative to the orbit center.

[MJ kihara]

4 minutes ago, swansont said:

It’s not something that the graph definitively shows. The graph depicts the precession of an orbit. 

It used to be a graph depicting; an orbit....a path. ...a wavy line... a geodesic...it's becoming something else,after the above modifications... of course both sun and asteroid are free falling in space...let the background be fixed.

[swansont]

Just now, MJ kihara said:

It used to be a graph depicting; an orbit....a path. ...a wavy line... a geodesic...it's becoming something else,after the above modifications... of course both sun and asteroid are free falling in space...let the background be fixed.

Per Genady’s description, it’s a graph showing how the x-projection of the major axis varies in time. The major axis is a constant value for an ellipse, so if it varies, it’s because the ellipse is precessing.

[MJ kihara]

7 minutes ago, swansont said:

Per Genady’s description, it’s a graph showing how the x-projection of the major axis varies in time. The major axis is a constant value for an ellipse, so if it varies, it’s because the ellipse is precessing.

No that is not his description;

20 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.

There is a time when the asteroid is on major axis,and as it free fall on the minor axis.

The Opening statement is about depiction of geodesic/ orbit.

I now see we are talking past each other

My intention is that the graph should also fact in the velocity of the asteroid.

[Genady]

5 minutes ago, MJ kihara said:

There is a time when the asteroid is on major axis,and as it free fall on the minor axis.

The horizontal coordinate on the graph is projection of the asteroid position on the direction of the major axis.

A geodesic is a line in spacetime, i.e., in four dimensions. To illustrate it in two dimensions, one needs to take a projection.

[MJ kihara]

Of course velocity from viewer standing on earth surface.

18 minutes ago, Genady said:

 

A geodesic is a line in spacetime, i.e., in four dimensions. To illustrate it in two dimensions, one needs to take a projection.

The asteroid has already factored that by being in that orbit, therefore,the orbit becomes a geodesic.

An observer on earth surface will note increase in speed towards minor axis.

[swansont]

55 minutes ago, MJ kihara said:

No that is not his description;

You say that but then quote “The horizontal axis here is some x, e.g., ellipse's major axis”

My summary refined it somewhat; since the major axis of an ellipse is just some number it doesn’t vary in time, so the only way for the graph and description to make sense is that it’s a projection.

But Genady has clarified that it’s supposed to be the asteroid’s x-position. 

 

 

37 minutes ago, MJ kihara said:

Of course velocity from viewer standing on earth surface.

No, since that observer would be in motion relative to both. A velocity discerned from the graph would be of the asteroid relative to the sun.

[MJ kihara]

7 minutes ago, swansont said:

 

My summary refined it somewhat; since the major axis of an ellipse is just some number it doesn’t vary in time, so the only way for the graph and description to make sense is that it’s a projection.

It boosted the understanding.

 

9 minutes ago, swansont said:

46 minutes ago, MJ kihara said:

 

No, since that observer would be in motion relative to both. A velocity discerned from the graph would be of the asteroid relative to the sun.

Let's simplify it,the observer is having a telescope, a watch, a pen and a piece of paper,he is doing the plot...the arguments was that the sun position is fixed...it's clear at a given length/distance the asteroid will be using less time(from observer watch) to cover it as it approaches the sun( towards the minor axis).

[swansont]

19 minutes ago, MJ kihara said:

Let's simplify it,the observer is having a telescope, a watch, a pen and a piece of paper,he is doing the plot...the arguments was that the sun position is fixed...it's clear at a given length/distance the asteroid will be using less time(from observer watch) to cover it as it approaches the sun( towards the minor axis).

The simplest is an observer is fixed with respect to the sun, since the sun is stationary. 

Less time to cover what? 

[Genady]

1 hour ago, MJ kihara said:

increase in speed towards minor axis.

This will manifest in the shape of the wavy curve. It will be flatter farther from the Sun and steeper closer to it.

Edited October 30 by Genady