Original Enterprise Systems Diagrams

[Mytran]

It sounds like any mass reduction generators went out with the burned out star drive, rather Spock gave an order back to the planet (probably needed an impulse burn to set up the course), then we see the Enterprise drifting (?) in front of the asteroid for the next two months. It appears that the ship is on energy conservation mode, i.e. don't burn up your fuel manoeuvring. The ship had enough left in her to achieve orbit and escape orbit before the impact.

Hey, did you realise it's only been a little over a year since we last had a serious discussion about this?
https://www.trekbbs.com/threads/moving-slow-at-warp-speed.297708/#post-12755895
The perfect time to dive back in, I say!
At which point I'm going to withdraw my assertion that the mass-reduction power of the nacelles was still in operation - your subsequent posts show that this is simply not necessary

...my concern is that no thrust or power is necessary to travel with the asteroid. Just provide an initial thrust and you're done. If impulse engines were working, of even thrusters they could manage to pull out ahead of the asteroid and get to the planet faster.

Infact the idea of "impulse speed" speed doesn't make sense, because you don't need power to maintain speed in space.

What we are talking about now is Newtonian physics which I usually avoid in Trek talk because let's be honest; starships do not operate according to those principles! The amount of fuel required for a thruster style engine to push a vessel to even 10% of lightspeed alone is MASSIVE - probably far more than the mass of the ship itself!
Owing to that I think the presence of sub-spacey mass-reduction units (likely housed in the nacelles) is a foregone conclusion - at least under normal circumstances.

In this episode, the Enterprise could easily have spent a certain portion of her impulse fuel in matching the asteroid - a tiny percentage of lightspeed true, but without the mass reduction field of the nacelles it would nonetheless be a major drain on the fuel supply. However, since we are dealing with Newtonian physics for a change, this would be the most economical solution available. I assume enough fuel was kept in reserve to slow the ship down again once it reached the planet.

Speed calculations (Oh Yes!):
At the speed of light, 59.223 days yields a distance of up to 10,261 AU (or only 0.16 Light Years). Even at 1/10 light speed (c), they could travel 1000 AUs. The fastest known comet/meteor is at 150,000 MPH or a slow 0.0002 c which would travel only 2.3 AUs in our example.

For an asteroid to become a meteor requires it to hit a planet though, which is why the speed can vary so much (depending on the angle of attack). https://www.amsmeteors.org/meteor-showers/meteor-faq/#3

In open space, the fastest asteroid on record is the recently discovered "2019 AQ3", zipping round the sun at a whopping 13,975 mph!
https://www.space.com/43263-fastest-orbiting-asteroid-found-2019-aq3.html
https://www.spacereference.org/asteroid/2019-aq3
This is a speed of approx 38.8KM/S or 0.00013% of lightspeed
A typical asteroid moves at 25KM/S or 0.00008% of lightspeed

• The Oort cloud is an area of space comprising a spherical cloud of comets which lies between 50,000 and 200,000 AU from the Sun.
• The distance of Neptune to the Sun is about 30 AUs.
• The distance of Mars to the Sun is about 1.5 AUs.
• The distance of our Asteroid Belt to the Sun is about 2.8 AUs.

Theories: Oort Cloud range is too far, so, is not an option since light speed is needed at that range. Neptune range is a possibility, but the asteroid would need to be moving at least 10 times faster than any known asteroid in our solar system, so, this is not an option. I assume that the Enterprise under Impulse Drive can attain speeds of at least 1/4 c, so, she could be capable of zipping thought any solar system in about 17 hours, and she can easily travel 2.3 AUs in about one hour! One hour on full impulse should be easy based on the other examples of 7 and 14 hours. The Enterprise must be extremely crippled and near empty on impulse fuel. Depending on what side of the Sun you are on compared to the planet, both the Mars and Asteroid Belt ranges are both likely if they are drifting at an asteroid-type speed. YMMV .

The issue of speed is a crucial one and was discussed at some length in this old thread
https://www.trekbbs.com/threads/killer-asteroid.292243/page-4
Spock states that they have been en route to the asteroid for "several" hours, at least part of which was done at Warp 9.
Assuming that local gravitational anomalies limited the Enterprise's total average speed to that of a mere 300,000KM/S then we can calculate that 3 hours at lightspeed would take the Enterprise 3,240,000,000 KM (slightly further out than Uranus).
If the asteroid then takes 59.223 days to travel that same distance, it is going at 633 KM/S which is only 0.002% of lightspeed but still 16 times faster than the fastest known asteroid in our real world.
I really can't see how we make the objects any slower

After that? She drifts awaiting a tow to a repair base (I assume Spock phoned home and requested a tow when first crippled, so, maybe they won't have to wait too long. Strange that Starfleet couldn't send any relief ship inside of two months...strange. I guess there aren't many starships, after all. )

I don't mind this - it reinforces the fact that space is really, really BIG.
A portable repair shop probably arrived 5 minutes after the credits rolled, anyway.
Certainly there is none of the usual doom and gloom associated with the Enterprise being severely broken which was seen in other episodes.