100-Diameter Limit (Freelance Trav article)

[Lurking Grue]

In the Sept/Oct 2019 issue of Freelance Traveller, there was an article about the 100-diameter limit and an alternative way of calculating it by using mass instead of diameter as a basis. Link to the article: https://www.freelancetraveller.com/features/rules/navigation/hundreddiam.html

I liked the article a lot and considered using that in my own campaign. However, when I tried using the formulas given in the article to calculate safe jump distance from a star or planet, I get very different results than given in the article. Granted I am lousy at math, so most likely I have made a mistake somewhere, but I cannot seem to find out where. I plugged the formula into Excel and let it chew the numbers for me, but no joy. I'm still getting different results. Could someone, please, check my math.

The formula in the article --> Safe Jump Distance (km where g=10^-10 m/s^2) (M=world mass in kg; uses modified relationship): D=(3.369×10^-11)×M^1/2.7

When I run that through Excel, using the mass of Earth (5.97x10^24 kg), I get D = 7.44923x10^13 km, which is a whole lot more than 1,292,143 km given in the article table.

Here's how I entered the formula into Excel --> =(3.369*10^-11)*(5.97E+24^1/2.7)

What am I doing wrong or is the formula in the article wrong, perhaps?

Motto of the day: Putting the *science* into science fiction.

 

[AnotherDilbert]

Here's how I entered the formula into Excel --> =(3.369*10^-11)*(5.97E+24^1/2.7)

^ takes precedence over / so you calculated (3.369*10^-11) * (5.97E+24^1) / 2.7.

You want = 3.369e-11 * ( 5.97e24 ^ (1/2.7) ) but the result is nonsensical: ~0.05.

 

[AnotherDilbert]

Solving the data given a few paragraphs above it should be:

f = GM/r^(2.7) ⇒ r = ( G/f × M )^(1/2.7), where G/f = 6.67408e-11 / 1e-10 = 0.667408, so

r = ( 0.667408 × M )^(1/2.7) = 1 291 952 569.69 m = 1 291 952.569 km, which is approximately what is given in the table.

Excel formula = ( 0.667408 * E11 )^(1/2.7), where cell E11 contains the mass.

 

[AnotherDilbert]

Using modern values for G and Earth mass M⊕:

G = 6.67430e−11 [m³/(kg×s²)]
M⊕ = 5.9722e24 [kg]

We get G/f = 6.67430e−11 / 1e-10 = 0.66743 and

r = ( 0.66743 × 5.9722e24 )^(1/2.7) ≈ 1 292 144 658 m ≈ 1 292 145 km which is very close to the tabulated value in the article.

 

[Lurking Grue]

Thank you, good sir or madam! Much appreciated! *two thumbs up*

P.S. This brings my Ultimate Mad Ref World Domination Plan, part 23B, to completion. Most excellent! Part 23A was basing ship acceleration on thrust vs mass (and not volume). You could say, mass was kind of critical to my plans. Right? And that I was after a Mass Effect... geddit, eh, eh? Okay, sorry. I'll show myself out.