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Comment by claar | Hacker News Reader

Absolutely, but we'll need to develop some future technology that allows multiple days of constant acceleration.

At 2G constant accel/decel, it'll take ~8.5 days to get to Uranus, reaching a top speed of 2.3% of light speed (14.2 million m/s), and experiencing 17 seconds of time dilation (https://chat.openai.com/share/b93297e1-b089-46d1-8314-a2235b...). :)

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This is incorrect, and I think this kind of low effort copy-paste of whatever ChatGPT came up with is actively harmful to the discussion. Honestly, I think this practice should be explicitly banned here.

> Distance: The average distance from Earth to Uranus is about 2.6 billion kilometers, but this can vary greatly depending on the planets' positions in their orbits.

Space.com (a relatively relatable source) thinks otherwise [1]:

> Because the solar system is in constant motion, the distance between Earth and Uranus changes daily. The closest the two get is 1.6 billion miles (2.6 billion kilometers). At their farthest, they are separated by 1.98 billion miles (3.2 billion km).

…which works out to ~2.9b km.

We can also calculate it ourselves. Earth is ~0.15b km from the Sun [2], Uranus is 2.7–3b km from the Sun on average [3]. Thus the distance varies between 2.65b km and 3.15b km, which means the average is (again) ~2.9b km.

Not 2.6b km as ChatGPT claimed.

Which changes the result to 8.9 days.

Which is not a huge difference, but would you know any better if ChatGPT said the distance is 5b km?

[1]: https://www.space.com/18709-uranus-distance.html

[2]: https://en.wikipedia.org/wiki/Earth

[3]: https://en.wikipedia.org/wiki/Uranus

I disagree. ChatGPT, at least v4 that I use, is simply fantastic for this type of back-of-the-napkin calculation. People lose out on its value with this type of pedanticism.

Let's take your question, "Would you know better if it said 5b km?". Nope, I wouldn't have a clue - or care!

ChatGPT informed me in SECONDS and 3-4 prompts that "At 2G constant accel/decel, it'll take ~8.5 days to get to Uranus, reaching a top speed of 2.3% of light speed (14.2 million m/s), and experiencing 17 seconds of time dilation."

Even if each of those numbers were off by a factor of two, it still gave me a greater intuition for the problem space than I had before.

I couldn't guess whether the flight time would be measured in days or years. With 4 prompts and 4 minutes invested, I had an answer within 11% (according to your sources, which I also didn't fact-check because it doesn't matter for this type of back-of-the-napkin work).

I didn't hide the fact of where this information came from - I cited my source. My hope was to share this new intuition of the problem space I'd received, so that HN viewers wouldn't have to invest even the small effort I did to enjoy these fun back-of-the-napkin numbers. The answer of <9 days was shocking to me!

Rather than banning intellectual curiosity and shunning use of our new amazing tools like ChatGPT/Claude/Bard/Mistral, I suggest we openly discuss and share our processes with each other. Who knows, maybe we'll learn something cool!

And for fun, and for future readers if the above ChatGPT link breaks, ChatGPT did "show its work" for the various calculations, which I think is super cool.

Here's its Python code it used to calculate travel days:

  # Constants
  acceleration = 2 * 9.81  # 2G in m/s^2
  distance_to_uranus_km = 2.6e9  # Average distance to Uranus in kilometers
  distance_to_uranus_m = distance_to_uranus_km * 1000  # Convert to meters

  # Distance for half the journey
  half_distance = distance_to_uranus_m / 2

  # Time to reach halfway point (t = sqrt(2d/a))
  # Using formula d = 1/2 * a * t^2, rearranged for t
  time_to_halfway = (2 * half_distance / acceleration)**0.5

  # Total time for the journey (double the halfway time)
  total_travel_time = 2 * time_to_halfway

  # Convert total time from seconds to days for easier interpretation
  total_travel_time_days = total_travel_time / (24 * 3600)
  total_travel_time_days

Here's its code for calculating the top speed:

  # Calculate top speed at halfway point (v = at)
  top_speed = acceleration * time_to_halfway

  # Convert top speed from m/s to km/h for easier interpretation
  top_speed_kmh = top_speed * 3.6
  top_speed_kmh

It's wondrous to me that LLMs can now execute code for such answers rather than just hallucinating their answers. I can't wait to see where this goes as AI gains access to additional tools.

I appreciate you removing your previous "So you posted a long whine" reply.

> Nope, I wouldn't have a clue - or care!

I find this just baffling right next to you talking about "greater intuition" or "intellectual curiosity". You don't care if your "intellectual curiosity" is feeding on complete misinformation?

You didn't do any "back-of-the-napkin math" (I did, but you, by your admission, don't care), you just took a plausible-looking factoid and run with it. It's equivalent to believing the first SEO spam listicle Google returned and calling it "intellectual curiosity" — worse, in fact, because at least there is a slight chance of an actual human checking those listicle "facts".

I believe the "process" you refer to is roughly:

- pay for GPT-4

- type a question in

- take the answer on faith

- post it elsewhere without doing any work to verify it

Is this correct? If so, I just don't think it's a good process. It also has no "back-of-the-napkin calculations" that you weirdly insist on, you didn't do a single addition in the entire "process".

We can reach those speeds using the technology of today; Project Orion remains entirely possible and could be built in this decade, if we so chose.

We are gods of our solar system, bound only by ourselves.

Assuming perfect efficiency in terms of adding energy to the velocity of an 80kg human payload, with zero other power usages, losses, etc, simply accellerating a human up to and back down from that speed takes about 1.6*10^16 joules, or about half of the daily output of the worlds nuclear reactors, or the ENTIRE volume of the Hindenburg as a bladder full of gasoline and a magic machine to extract 100% of the energy.

Unless we develop force fields[1] I don’t understand how traveling at such relativistic speeds would work, at .023C a 1 gram micrometeor would have the same potential energy as 25 tons of dynamite (100B Joules)

Ice shielding sounds good, but then we are back to the tyranny of the rocket equation.

[1] which we don’t even have a path to, afaik. Straight scifi right now.

> Ice shielding sounds good, but then we are back to the tyranny of the rocket equation.

Not really, we don't have to lift up ice from Earth. We can just cook water out of clays in near earth asteroids.

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