[Just thinking (OP)]

How would 5he earth stop orbiting? Would it grind to a halt or suddenly start travelling toward the sun? Did the sun dissappear or was the earth ejected such as in an orphan planet?

Good question but I only put this problem out there as a hypothetical situation. No mechanism for the earth stopping in its tracks.

[Janus]

    Anyway, other articles consider the journey toward the sun to be over in about 65 days but that seems to be because they reckon the tidal forces from suns gravity would rip the planet apart before we even reach the outer edges of the sun.

Tidal forces wouldn't effect the answer significantly.  The Roche limit( as measured in multiples of the primary's radius) is dependent on the relative densities of the bodies.
The Earth is some 4 times denser than than the Sun.  If we treat the Earth as a fluid body, this puts the Roche limit at 1.55 Sun radii from the center of the Sun our  just over 1/2 Sun radius above its surface.
Treated as a rigid body, the Roche limit ends up at ~0.8 the Sun's radius, or under the Sun's surface.  The actual Roche limit for the Earth will likely fall somewhere between.
But even if we put it at 1/2 the Sun's radius away, the Earth is just ~350,000 km from the surface, and will be moving close to its final speed of over 616 km/sec.  In other words, it is only around 10 min from surface impact.

[Just thinking (OP)]

So it's easier if you just consider a simple 2-body case.

That was my intention just the earth and the sun with the earth starting from a standstill.

[Eternal Student]

Hi again.

The quick and dirty method of computing the fall time is to assume the Earth's orbit is an extremely eccentric ellipse with the Earth's present distance being at perihelion.  This puts the Semi major axis at half the perihelion distance, and you can just calculate half the period of such an orbit.  This works out to be about 64 days.

   Please check your use of the term perihelion.  I think you want the earth at aphelion to start with.  I'm also not sure that "perihelion distance" is a well defined term.  See if the diagram in post #10 is what you were saying.
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   The main thing is that Just thinking is getting some slightly different answers from different people, ranging from two months through to six months.  Perhaps we should try and get some concensus on this.
   I reckon that 91 days is the right answer assuming loads of things  (the sun is a point mass etc.)
It's less than this is you consider other stuff - for example the possibility that the earth will be torn apart by tidal forces and volcanic activity before it actually hits the sun.
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How would 5he earth stop orbiting? Would it grind to a halt or suddenly start travelling toward the sun? Did the sun dissappear or was the earth ejected such as in an orphan planet?

i.d.k.    Our calculations were based on the velocity of earth being suddenly brought to 0 relative to the sun.  How you do this is a problem for the engineers.  Let's say a tractor beam was used by an alien spacecraft which brought the earth to a standstill (relative to the earth) and then we did the calculation to see what happens when they turn that beam off and allow the earth to fall into the sun.

Best Wishes.

[Janus]

This works out to be about 64 days.

Thanks Janus. Have you taken into account that the earth is starting from a stand still it will take some time to get going?

Yes.  It, like anything else, will start "falling" immediately, and at the same acceleration.  However, that is not to say that the mass of the Earth is completely irrelevant.  It can have an effect on impact time, just in the opposite manner that you seemed to imply.  Increasing the mass of the Earth would decrease the time to impact.  The reason for this is that not only is the Earth falling towards the Sun, but the Sun would fall towards the Earth due to Earth's gravity.  Since the Sun is some 333,000 times more massive than the Earth, the amount it would "fall" towards the Earth is pretty insignificant, and we can safely ignore it.
However, if the Earth had a mass that was a much larger fraction of the Sun's, you would have to account for it. 

[Eternal Student]

Hi again.

Tidal forces wouldn't effect the answer significantly.

   You may very well be right but earth isn't a rigid body.  It's a dangerously loose collection of techtonic plates.   The possibility of earth breaking apart was an idea presented here:
https://www.wired.com/2014/12/empzeal-earthfall/
   I certainly haven't done anything with the tidal forces,  it was only mentoned because their answer was less than 91 days but they make it clear that earth never reaches the sun. 

Best Wishes.

[Janus]

Hi again.

The quick and dirty method of computing the fall time is to assume the Earth's orbit is an extremely eccentric ellipse with the Earth's present distance being at perihelion.  This puts the Semi major axis at half the perihelion distance, and you can just calculate half the period of such an orbit.  This works out to be about 64 days.

   Please check your use of the term perihelion.  I think you want the earth at aphelion to start with.  I'm also not sure that "perihelion distance" is a well defined term.  See if the diagram in post #10 is what you were saying.

Oops, I did mean aphelion.  Just one of those mental lapses.  It might have something to do with the fact that in orbital mechanics so many of the parameters and equations use perihelion as the reference, that I got used to using it.

[Janus]

Hi again.

Tidal forces wouldn't effect the answer significantly.

   You may very well be right but earth isn't a rigid body.  It's a dangerously loose collection of techtonic plates.   The possibility of earth breaking apart was an idea presented here:
https://www.wired.com/2014/12/empzeal-earthfall/
   I certainly haven't done anything with the tidal forces,  it was only mentoned because their answer was less than 91 days but they make it clear that earth never reaches the sun. 

Best Wishes.

That's why I used the purely "fluid body" Roche limit to get the 10 min from impact answer.  That is the furthest point at which the Sun could begin to pull the Earth apart.

[Eternal Student]

Hi.
   I've had a bit more time to consider the situation described in the OP.
The diagram in post #10 is incorrect.  An elliptic orbit like that one is not a solution in the usual two body problem (where the sun can move about the barycentre).
   Simplifying the problem to a one-body central force problem  (where the sun is assumed to remain stationary) we should have the sun at a focus of the ellipse not at the centre of the ellipse.
    Anyway.... re-working the time to impact, we need  T/2 as our estimate   and the semi-major axis a ≈ 0.5 A.U.   
This gives Time to impact ≈ 64.7 days.
  Which means that at least two contributors are agreeing on the impact time   (Janus and Eternal Student), if that helps you (Just Thinking).

- - - - - - - -
  For a brief aside:    Consider a one body problem.  A body is attracted to a fixed point in space with a force following an inverse square law on distance  (e.g.   Newtonian gravity).  Assume the body is at rest initially but a distance  r ≠ 0  from the point of attraction.   The point of attraction is just a point in space, there's nothing solid here so the other body could pass through.

Diagram:

    *                                      *
  body                          Point of attraction
     <-------------  r ------------->

     At first glance it would seem that the body would be accelerated toward the point of attraction and pass through it,   following a similar but mirror image motion on the other side until it eventually stops and starts to move back the other way.... etc. etc.  an endless oscillation.   (Take a moment to consider the problem yourself).
   However, there is no way to determine such motion.  Why?  Because the force on the body would be undefined when it reaches the point of attraction and so Newton's F=ma can't be used.  If we are going to use Newtonian Mechanics then we must avoid the position of the body ever being exactly at the point of attraction. 
    If you considered the motion as a limiting process of a proper elliptical orbit around the point of attraction it would seem that the body approaches infinite velocity as it closes on the point of attraction but cannot pass through it.  Instead there is something more like an elastic collision, the body receives an infinite impulse and reverses direction of travel instantly.  Fairly weird in my opinion.
   
Best Wishes.

[Just thinking (OP)]

This gives Time to impact ≈ 64.7 days.
  Which means that at least two contributors are agreeing on the impact time   (Janus and Eternal Student), if that helps you (Just Thinking).

Thanks Eternal Student I'm in agreeance with this calculation and thank all that has taken the time with this as well as all the explanations given.

[Halc]

Instead there is something more like an elastic collision, the body receives an infinite impulse and reverses direction of travel instantly.  Fairly weird in my opinion.

Intuitive actually. Motion straight through would totally discard Keplerian mechanics. Regardless of the eccentricity of the orbit, the 'point of attraction' must remain at one focus of the elliptical orbit, and not in the center as you've depicted in post 10.

Of course, Newtonian mechanics breaks down if you get too close to the point of attraction since the mass ends up with speed faster than light. In reality, if the orbit gets too eccentric, it starts to precess. If it gets really close (as the photo-sphere), it never comes back.

[Eternal Student]

Hi again.

Intuitive actually.

   Well thanks for that.  It didn't seem intuitive to me late one night.   

Best Wishes.