Geodesics.

[MJ kihara]

44 minutes ago, swansont said:

Less time to cover what? 

Same distance/length as units chosen by the observer in his co_ordinate system.

 

23 minutes ago, Genady said:

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

Am glad at least I can agree with you on something.

Now consider this the asteroid have been interrupted by unexpected object in its orbit that causes it in its next lap to plunge on surface of the sun....how will the wavy curve appear or end?

44 minutes ago, swansont said:

Less time to cover what? 

Same distance/length as units chosen by the observer in his co_ordinate system.

 

23 minutes ago, Genady said:

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

Am glad at least I can agree with you on something.

Now consider this the asteroid have been interrupted by unexpected object in its orbit that causes it in its next lap to plunge on surface of the sun....how will the wavy curve appear or end?

[swansont]

4 hours ago, MJ kihara said:

Same distance/length as units chosen by the observer in his co_ordinate system.

Why would they differ? You said you wanted to keep this simple.

[Genady]

6 hours ago, MJ kihara said:

Now consider this the asteroid have been interrupted by unexpected object in its orbit that causes it in its next lap to plunge on surface of the sun....how will the wavy curve appear or end?

What is there to consider? What does make this scenario interesting or non-trivial? It is just a graph of \(x=x(t)\) function with \(x\) and \(t\) axes flipped.

[MJ kihara]

7 hours ago, swansont said:

Why would they differ? You said you wanted to keep this simple.

What I mean is as the observer on earth is making his plot he will realize as per scale he has chosen the asteroid will be covering same distance as before at a lesser and lesser time as it approaches the sun i.e as it's moving from major axis region towards the region of minor axis....i.e the velocity of the asteroid will be increasing towards the sun.

6 hours ago, Genady said:

What is there to consider? What does make this scenario interesting or non-trivial? It is just a graph of x=x(t) function with x and t axes flipped.

Our wavy line that represent the orbit or the geodesic will increase in frequency and just terminate to a bigger mass;sun(a spot) and if you draw that diagram without the axes it will just be a wavy line increasing in frequency then terminating into a bigger spot(or a point whatever is used to represent the sun)

[Genady]

6 hours ago, MJ kihara said:

geodesic will ... just terminate

Beyond the crash event, the geodesic will coincide with the worldline of the Sun (the red line).