the lord of the rings - Were there any other ways into Mordor?

The two ways that Frodo considers in order to make his way into Mordor are The Black Gate and The Pass of Cirith Ungol.

These seem to be the only ways that anyone considers taking at any point, yet they both seem nigh impassable due to the dangers i.e. the amount of Sauron's forces watching The Black Gate, and the proximity to Minas Morgul & Dol Guldur as well as Shelob's lair at the pass.

So were these the only two ways that people approaching from the West could get into Mordor?

I can believe that geographically these were the only two ways to cross the mountains from the West, but could one simply walk into Mordor anywhere else, such as coming from the East?

If there were more ways into Mordor, what was stopping Frodo from entering through that way? Was it better guarded, were they unknown to the Fellowship, or would the journey to get to these alternative entrances have been too difficult?

Answer

Possibly.

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  An early (1944) draft of The Two Towers indicates a pass in the southern Ephel Dúath, called the Nargil Pass:

  
  

  
  

  Now Orcs have passed south through Nargil pass into the Southland beyond [? River] Harnen.

  
  

  ^{History of Middle-earth VIII The War of the Ring Part 3: "Minas Tirith" Chapter 1: "Addendum to 'The Treason of Isengard'" (ii) The Muster of Rohan}

  
  
  

  
  

  Nargil Pass appeared on a map drawn by Tolkien in 1943. However it doesn't appear on any subsequent maps, so its canonicity is unclear

  
  

  It seems plausible that there are other ways over (or through) the mountains; mountains are unpredictable, and it's not at all unprecedented for them to form in a such a way that would allow you to slip through.

  
  

However, the major barriers preventing Frodo from taking an alternate route are

• Time. Between Sauron's ongoing war against the rest of the world, the hobbits' dwindling supplies, and the mounting effort Frodo has to make to resist the Ring's influence, there's an enormous incentive to get the Quest over with quickly. They could perhaps have found another way, but would they have done so in time (and, more importantly, would they have believed they could have found one in time)


• Lack of guidance. Mordor is not extensively charted, and the Ephel Dúath even less so. This is related to the above, but they had no guide able to lead them any other way. Gollum, on the other hand, does know a way out, and they know he's not lying (because they know he escaped before, and they know that escape via the Black Gate is implausible at best). Cirith Ungol may be a crappy bet, but it's a known quantity