What Does the Astro Physics Equation from Lewis Season 8 Episode 2 Mean?

[DaveC426913]

TL;DR Summary

Is this as much nonsense as I think it is?

I know, I know, I'm committing the cardinal sin of putting any stock in the technobabble of a TV show, but this one seems egregious.

Lewis (English WhoDunnit-in-Oxford on Britbox) Season 8 Episode 2 "The Lions of Nemea" had an astro physics professor who said this:

"... and so we see that one AU cubed is equal to G times the mass of the Sun times one year squared times four pi squared...."

Not only can I not imagine what this could possibly be referring to but the units don't even match.

m³ = N · kg · s²

m³ = kg² · m

(Did I get that right? Also: Sorry, I just cannot manage LaTeX)

 

[phinds]

Even if it were right, and clearly if the units don't match it isn't, it would just be numerology, or in this case more likely just entertainment technobabble.

 

[collinsmark]

TL;DR Summary: Is this as much nonsense as I think it is?

I know, I know, I'm committing the cardinal sin of putting any stock in the technobabble of a TV show, but this one seems egregious.

Lewis (English WhoDunnit-in-Oxford on Britbox) Season 8 Episode 2 "The Lions of Nemea" had an astro physics professor who said this:

"... and so we see that one AU cubed is equal to G times the mass of the Sun times one year squared times four pi squared...."

Not only can I not imagine what this could possibly be referring to but the units don't even match.

m³ = N · kg · s²

m³ = kg² · m

(Did I get that right? Also: Sorry, I just cannot manage LaTeX)

I'm not (presently) a subscriber of BritBox, so I can't watch the episode myself, but going by your quote, it almost makes sense if

• He's talking about the orbit of the Earth around the Sun,
• with the assumption that the orbit is circular,
• The mass of Earth is relatively small compared to the Sun, such that we can assume their common barycenter is pretty much the same location as the Sun.
• ignoring any gravitational effects of other bodies,
• and also assuming that both the Earth and the Sun are spherical (i.e., tidal effects can be ignored).

The centripetal force on the Earth in such a model is:

$F = m_🜨 \frac{v^2}{R}$,

where,

• $m_🜨$ is the mass of the Earth,
• $v$ is Earth's orbital speed (again, with the simplistic model discussed above)
• $R$ the distance between the Earth and the Sun.

We can re-write this equation, knowing that the orbital period $T$ is one year, and Earth traverses $2 \pi R$ per year,

$F = m_🜨 \frac{ \left( \frac{2 \pi R}{T} \right)^2}{R} =m_🜨 \frac{\frac{4 \pi^2 R^2}{T^2}}{R} = m_🜨 \frac{4 \pi^2 R}{T^2}$,

Along with all that, we also have Newton's law of universal gravitation,

$F = G \frac{m_🜨 m_☉}{R^2},$

where.

• $G$ is Newton's gravitational constant. This is usually verbalized/pronounced "big gee." Note that this is different than "little" $g$, the typical acceleration due to Earths gravity at its surface. They're different. Little $g$ plays no role here.
• $m_☉$ is the mass of the sun.

Equating the forces gives:

$m_🜨 \frac{4 \pi^2 R}{T^2} = G \frac{m_🜨 m_☉}{R^2}$

We can see that the mass of the Earth, $m_🜨$ , cancells out from both sides, leaving

$\frac{4 \pi^2 R}{T^2} = G \frac{m_☉}{R^2}$.

Rearanging variables gives us,

$R^3 = \frac{ G m_☉ T^2}{4 \pi^2}$

So it's pretty close to what was quoted. The only mistake I see is instead of saying "... times 4 pi squared ..." should have been "... divided by 4 pi squared."

 

[Ibix]

m3 = N · kg · s2

$G$ has units of $\mathrm{N\ kg^{-2}\ m^2}=\mathrm{kg^{-1}\ m^3\ s^{-2}}$ so that $F=GMm/r^2$ is dimensionally consistent, which is where your dimensional analysis went wrong. As derived in the previous post, the original quote is a lightly mangled version of Kepler's third law applied to an idealised circular orbit for Earth.

 

[pinball1970]

TL;DR Summary: Is this as much nonsense as I think it is?

Lewis (English WhoDunnit-in-Oxford on Britbox) Season 8 Episode 2 "The Lions of Nemea" had an astro physics professor who said this:

The British are pretty stuffy so they check that kind of thing.

 

[collinsmark]

The British are pretty stuffy so they check that kind of thing.

I wish they did that more with American shows*. I actually find it quite refreshing that they put at least some effort in.

*(There are exceptions of course. The writers of The Simpsons and Futurama, for example, are surprisingly good at doing their due diligence. So much so that they have on occasion actually embedded humor and hidden jokes into the math that nobody would recognize unless one understands the math.)

 

[Vanadium 50]

As they say in Minnesota (or South Canada as we sometimes call it)

If you're wondering how he eats and breathes
And other science facts,
Just repeat to yourself "It's just a show,
I should really just relax"

 

[collinsmark]

As they say in Minnesota (or South Canada as we sometimes call it)

If you're wondering how he eats and breathes
And other science facts,
Just repeat to yourself "It's just a show,
I should really just relax"

I met Mike Nelson once through a friend of a friend at a small dinner party. We all ate homemade pizza and played charades. It was pretty fun. We didn't talk much science though.

 

[collinsmark]

In case anybody's completely lost regarding the previous two posts, here's a reference. (Btw, Mike Nelson was the lead writer for MST3k, even back in the beginning when the show's creator, Joel Hodgson, was the host. @Vanadium 50's quote is from the lyrics to the intro.)

 

[PeroK]

TL;DR Summary: Is this as much nonsense as I think it is?

I know, I know, I'm committing the cardinal sin of putting any stock in the technobabble of a TV show, but this one seems egregious.

Lewis (English WhoDunnit-in-Oxford on Britbox) Season 8 Episode 2 "The Lions of Nemea" had an astro physics professor who said this:

"... and so we see that one AU cubed is equal to G times the mass of the Sun times one year squared times four pi squared...."

Not only can I not imagine what this could possibly be referring to but the units don't even match.

m³ = N · kg · s²

m³ = kg² · m

(Did I get that right? Also: Sorry, I just cannot manage LaTeX)

Did Lewis recover the missing Earth? Once the astrophysicist told him cryptically where to find it.

 

[Nugatory]

The only mistake I see is instead of saying "... times 4 pi squared ..." should have been "... divided by 4 pi squared."

So.... Who is going to get picky over just a bit more than three decimal order of magnitude?

 

[DaveC426913]

Did Lewis recover the missing Earth? Once the astrophysicist told him cryptically where to find it.

No. The astro physicist immediately died.

 

[DaveC426913]

The centripetal force on the Earth in such a model is:

$F = m_🜨 \frac{v^2}{R}$,

where,

• $m_🜨$ is the mass of the Earth,

Am I overthinking your work? He said mass of the Sun.

So it's pretty close to what was quoted. The only mistake I see is instead of saying "... times 4 pi squared ..." should have been "... divided by 4 pi squared."

I confirmed he said times.

 

[strangerep]

"... and so we see that one AU cubed is equal to G times the mass of the Sun times one year squared times four pi squared...."

He's trying to talk about (or derive) Kepler's 3rd Law, (see also this video), applied to the earth. The correct formula is $$R^3 ~=~ \frac{GM_\odot T^2}{4 \pi^2} ~,~~~~~~ \mbox{where} ~M_\odot~ \mbox{is the mass of the sun}~.$$

 

[collinsmark]

Am I overthinking your work? He said mass of the Sun.

Regarding the centripetal force, it is the mass of the Earth. This mass cancels the other mass of the Earth, which is part of Newton's universal law of gravitation. The only mass that doesn't cancel in the end is the mass of the Sun.

I confirmed he said times.

'Kinda sounds like somebody did some research but then the actor flubbed his line, and the director didn't catch the mistake or was too lazy to shoot another take.

 

[Vanadium 50]

I wonder if when lawyers watch Law & Order are bothered by "Sentenced to 6 to 8 years?!? For this crime they get 7 to 10! This show stinks!"

 

[Ibix]

I wonder if when lawyers watch Law & Order are bothered by "Sentenced to 6 to 8 years?!? For this crime they get 7 to 10! This show stinks!"

TV Tropes has quite a lengthy section on "Artistic License - Law" for Law & Order and each of its spin-offs, so I suspect so, yes.

 

[DaveC426913]

I wonder if when lawyers watch Law & Order are bothered by "Sentenced to 6 to 8 years?!? For this crime they get 7 to 10! This show stinks!"

Yeah, I getcha. But there's a difference between 'in my opinion that's not plausible' and '2+2=5'.

The most egregious one I saw was on CSI: Vegas where Gil Grissom - Mister OCD - describing a victim falling off a building, saying "Well, terminal velocity [sic] is 9.8 metres per second [sic], so he should have landed ... here."

 

[Vanadium 50]

terminal velocity [sic] is 9.8 metres per second

Are you sure this wasn't just a bad translation into Canadian? In 'Merica we use feet and yards.

 

[DaveC426913]

Are you sure this wasn't just a bad translation into Canadian? In 'Merica we use feet and yards.

That wouldn't change anything about the mistakes:

1. terminal velocity (relevance?? It was only a six story fall. The relevant value would be acceleration due to gravity)
2. acceleration due to gravity is 9.8ms squared

Grissom is essentially saying the guy achieved terminal velocity after one second, and then fell at a constant velocity of 9.8m/s thereafter. What is he - a kite??

 

[PeroK]

That wouldn't change anything about the mistakes:

1. terminal velocity (relevance?? It was only a six story fall. The relevant value would be acceleration due to gravity)
2. acceleration due to gravity is 9.8ms squared

Grissom is essentially saying the guy achieved terminal velocity after one second, and then fell at a constant velocity of 9.8m/s thereafter. What is he - a kite??

You expect too much from a humble script writer.

 

[DaveC426913]

You expect too much from a humble script writer.

Not from the script writer, no. But the science consultant shoud be stwuck about the head and shouldews and thwown woughwy to the gwound.

 

[Vanadium 50]

You expect too much from a humble script writer.

https://www.imdb.com/name/nm0936976/?ref_=fn_al_nm_1

Ed Witten's brother.

 

[PeroK]

Not from the script writer, no. But the science consultant shoud be stwuck woughwy about the head and shoulders and thwown to the gwound.

There's an atrocious film about climbing K2 called Vertical Limit. The climbing scenes are absurd; yet, Ed Viesturs, one of the world's leading Himalayan climbers, was credited as climbing consultant - and appeared in the movie as himself. If I ever meet Viesturs, I intend to ask him when was the last time he climbed with nitroglycerine dangling from his climbing harness!

 

[DaveC426913]

There's an atrocious film about climbing K2 called Vertical Limit. The climbing scenes are absurd; yet, Ed Viesturs, one of the world's leading Himalayan climbers, was credited as climbing consultant - and appeared in the movie as himself. If I ever meet Viesturs, I intend to ask him when was the last time he climbed with nitroglycerine dangling from his climbing harness!

Yeah. Consultants are certainly overridden for the sake of the plot. I can understand that. You can imagine Viesturs just throwing his hands up and stomping back to his chair in despair.

In Cliffhanger, with Stallone, they made it like peaks were just an hour apart. "You meet me by 4PM at the summit of that peak in the next valley. And you better have the money, or the girl gets it!"

 

[Janus]

$G$ has units of $\mathrm{N\ kg^{-2}\ m^2}=\mathrm{kg^{-1}\ m^3\ s^{-2}}$ so that $F=GMm/r^2$ is dimensionally consistent, which is where your dimensional analysis went wrong. As derived in the previous post, the original quote is a lightly mangled version of Kepler's third law applied to an idealised circular orbit for Earth.

To be exact, G does not need to have a value given in m³ kg^-1 s^-2 That's for when you are working in MKS units. You can express it in AU, solar masses and years, giving it a value of
39.478 AU³yr^-2M_s^-1

 

[DaveC426913]

To be exact, G does not need to have a value given in m³ kg^-1 s^-2 That's for when you are working in MKS units. You can express it in AU, solar masses and years, giving it a value of
39.478 AU³yr^-2M_s^-1

Right. It doesn't matter what units you use. That's why I converted everything to M/K/S.