WS MoreOrLess: How do we calculate the distance to the sun?

Summary

More or Less (BBC Radio 4)

Episode: How do we calculate the distance to the sun?

Date: September 29, 2014
Host: Tim Harford
Guests: Andrew Ponson (Astrophysicist, UCL), Annabelle & Serena (Listeners, ages 12 and 10), Francis Ratniex (Professor of Apiculture), Hannah Moore (BBC), Edward O. Wilson (quoted)

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Overview of the Episode

This episode of More or Less investigates the surprisingly challenging question: How do we know the distance to the sun? Host Tim Harford, with help from young listeners and experts, explores the scientific methods used to make this calculation, touching on historical and modern techniques. The episode also debunks the oft-repeated claim that all the ants in the world weigh as much as all the humans, showing how misleading numbers can travel even in reputable circles.

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Key Discussion Points & Insights

1. How Do We Calculate the Distance to the Sun?

Segment starts: [00:13]

• Listener Question:
  Annabelle and Serena ask how we can know both how far away the sun is and how big it is, given these seem like two unknowns with no “knowns.”

  • Annabelle: “You need both to calculate, I think.” [00:53]
  • Serena: “It doesn't really make sense because in algebra the unknowns can only be one less than the knowns… so surely we can't know.” [01:07]

• Explained by Andrew Ponson (Astrophysicist):

  • The key is using what we know about how planets move around the sun—a relationship first described by Johannes Kepler and linked to gravity by Isaac Newton.
  • By timing how long it takes for Mars and Earth to orbit the sun (Mars: ~2 years, Earth: 1 year), astronomers can compare the “relative” sizes of their orbits.
  • To get an actual distance, we need to know how far away Mars is at a certain point.

    “Then you add in what you know about how far it is from Earth to Mars. And this gives you all the information you need to solve this problem and work out the distance to the sun.” —Andrew Ponson [02:29]

• How do we know the Earth–Mars distance?

  “...the best estimate that we have is from something called radar ranging. ... We send a big radio pulse towards Mars that bounces off Mars and comes back to us ... because we know how fast radio waves travel, ... we can work out from that exactly how far away Mars has to be.” —Andrew Ponson [02:45–03:15]

• Accuracy and Confidence:
  Despite not having sent anything physically to the Sun with a tape measure, the estimates are put to the test by spacecraft navigation and accurate planetary data.

  “So it is a guess, but we have a lot of confidence in it.” —Andrew Ponson [03:58]

• Official Distance:

  “It is 150 million kilometres away.” —Andrew Ponson [04:15]
  “Well, that's the number that I remember. I think it's 149,500,000 or something like that.” —Andrew Ponson [04:20]

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2. Do All the Ants in the World Really Weigh as Much as All the People?

Segment starts: [04:43]

• The Claim:
  There are more than 100 trillion ants worldwide, and they collectively weigh as much as all humans.

• Origin of the Claim:
  Dr. Edward O. Wilson, Harvard biologist, based the claim on broad estimates. He extrapolated from the idea that there are about 10^18 insects, 1/100 of which are ants, and each human weighs about 1 million times more than an ant, with 7.2 billion humans yielding a comparable mass to the global ant population.

  “...maybe all the people and all the ants will weigh the same.” —Edward O. Wilson (quoted) [05:55]

• Fact Checking:

  • There is huge variation in ant species and numbers—no one really knows how many ants exist.
  • The claim relies heavily on “rounded” and guestimated numbers at each stage.
  • The BBC documentary cited 100 trillion ants vs. Wilson’s estimate of 10,000 trillion.

• How Much Does an Ant Weigh?

  “Ants vary greatly in weight…experts agree the average ant weighs about 6 milligrams, making roughly 150 ants to the gram.” —Hannah Moore [07:43]
  This is about 1/10th the weight used in E.O. Wilson’s calculation.

• Is the Claim Plausible?
  Professor Francis Ratniex:

  “I don't think it's true now, but if we go back in time, I'm sure it was true at one point... maybe two or 300 years ago, that was the point at which humans outweighed the ants.” [08:28]

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Notable Quotes & Memorable Moments

• On the algebra of unknowns:

  “In algebra, the unknowns can only be one less than the knowns. And so in this case there are 2 unknowns and 0 knowns. So surely we can't know.” —Annabelle [01:07]

• On the reliability of distance measurements:

  “We haven't flown anything into the sun with a tape measure, we've done lots of stuff that would come out quite wrong if we were wrong about the distance.” —Andrew Ponson [03:50]

• On weighing ants:

  “It's very easy to weigh an ant...you cool the ant and that way it stops moving and you can put it on the balance and it doesn't run away.” —Francis Ratniex [08:06]

• Tim’s reaction to the sun’s distance:

  “Wow, that's a very round number.” —Tim Harford [04:18]

• On “dinosaur ants”:

  “Thirty millimetres. That's as long as a decent sized thumb. Monster ant.” —Tim Harford [07:33]
  “They're actually called dinosaur ants, Tim.” —Hannah Moore [07:37]

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Timestamps for Important Segments

• [00:13] — Introduction of guests and framing of the sun distance question.
• [01:33] — Andrew Ponson explains how astronomers deduce the sun’s distance.
• [02:45] — Techniques for measuring the Earth–Mars distance.
• [03:34] — Confidence in our knowledge of the sun’s distance.
• [04:15] — The (approximate) answer: 150 million km to the sun.
• [04:43] — Introduction of the “ants weigh as much as humans” claim.
• [05:35] — Details and origins of the ant mass estimate.
• [07:43] — How ant mass is measured and average values.
• [08:28] — Historical speculation about the comparative mass of ants and humans.

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Summary Table: How Do We Calculate the Distance to the Sun?

| Step | Method / Principle | Key Data / Technique | |------|-----------------------------------|---------------------------------------| | 1 | Compare planetary orbits (Kepler’s laws) | Earth and Mars orbital years | | 2 | Measure Earth–Mars distance | Radar ranging (speed of light time delay) | | 3 | Calculate Sun–Earth distance | Combine orbit ratios with Mars measurement |

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Tone & Style

The episode is light, curious, and engaging—Tim Harford’s wry tone makes the technical discussion accessible, while the inclusion of young listeners keeps the questioning lively. Experts contribute clear, concise explanations without jargon, and running jokes (like the impossibility of measuring the sun with a tape measure) keep things friendly.

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In a Nutshell

• We know the distance to the sun through a chain of well-understood astronomical reasoning, precise planetary observations, and radar measurements—no tape measures required.
• The claim that all ants together weigh as much as all humans is based on broad assumptions and is likely not true today, though it may have been in the past.

For listeners interested in how we deduce the universe’s numbers (and why some numbers aren’t as solid as they seem), this episode delivers clear, fact-checked explanations and a healthy dose of skepticism.

Transcript

[BBC Announcer]

Thank you for downloading from the BBC. For details of our complete range of podcasts and our terms of use, go to bbcworldserveys.com podcasts

[Tim Harford]

hello, and welcome to More or Less on the BBC World Service. We're the programme which dances daringly with the data that surround us in the news and in life. And I'm Tim Harford. We always enjoy it when loyal listeners email us, and some loyal listeners and are younger than others. I'm joined in the studio by two of them. Well, perhaps if you'd be so kind, you could introduce yourselves.

[Annabelle]

I'm annabelle and I'm 12. And I'm Serena and I'm 10.

[Tim Harford]

And the fellow in the corner of the studio lurking? Andrew.

[Andrew Ponson]

I'm Andrew and I'm 31.

[Tim Harford]

And you're an astronomer?

[Andrew Ponson]

I am.

[Tim Harford]

Welcome to More or Less Towers. Now, Serena and Annabelle, what can I do for you?

[Annabelle]

Well, we were wondering how we can find out, or how people know how far away the sun is and how big it is. If we don't know how big it is and how far away it is. You need both to calculate, I think.

[Francis Ratniex]

Yes.

[Tim Harford]

Serena, this is a problem that's been getting you scratching your head.

[Annabelle]

Yes. And it doesn't really make sense because in algebra the unknowns can only be one less than the knowns. And so in this case there are 2 unknowns and 0 knowns. So surely we can't know.

[Tim Harford]

Well, Andrew, you've very kindly agreed to try to explain this. How do we know whether the sun is really dim and close or really bright and big and far away?

[Andrew Ponson]

Right. Well, bear with me, because it is a bit indirect. What we do is we start with the distance to a planet. So let's say Mars, and that's what's going to help us work out what the distance to the sun is. Then we use what we know about the way that planets orbit around the Sun. This was written down for the first time by Johannes Kepler and linked to gravity by Isaac Newton. So we now understand it very, very well. And it turns out that the amount of time it takes for a planet to go around the sun rises as the distance that that planet is from the sun also rises. And that link means that if we time how long it takes, say, Mars to go around the sun and how long it takes us to go around the sun, which is about two years for Mars and exactly one year for us, then we can use this link to work out, relatively speaking, how big is the orbit of Earth around the sun and Mars around the Sun? Then you add in what you know about how far it is from Earth to Mars. And this gives you all the information you need to solve this problem and work out the distance to the sun.

[Tim Harford]

So the only thing we're missing then is how do you know how far away Mars is?

[Andrew Ponson]

Yeah, I thought you might ask me that today. The best estimate that we have is from something called radar ranging. And the way this works is you may have heard of radar, it's used to track planes, for example. And it's just a massive version of that. The thing that you would see at the airport. We send big radio pulse towards Mars that bounces off Mars and comes back to us and then we receive it again here on Earth. And we measure the amount of time that passes between sending out the radio pulse and getting it back. And because we know how fast radio waves travel, they travel at the speed of light. We can work out from that exactly how far away Mars has to be.

[Tim Harford]

Are you happy, girls?

[Annabelle]

Well, I think I kind of understand the principle, but I'm still a bit confused at how you can find the exact distance to the sun. Or is that still unknown?

[Andrew Ponson]

The data we have tell us about the way the planets move around in the night sky is really, really accurate. And these Doppler pulses that we can use are also really, really accurate. So we think the estimate that we have is very good. And of course, we've used it to send spacecraft around the solar system as well. And so it's, it's been put to the test, really. Although we haven't flown anything into the sun with a tape measure, we've done lots of stuff that would come out quite wrong if we were wrong about the distance to the sun, if it was actually twice as far away or something. So it is a guess, but we have a lot of confidence in it.

[Tim Harford]

Now, Andrew, I have one final question. How far away is the sun?

[Andrew Ponson]

It is 150 million kilometres away.

[Tim Harford]

Wow, that's a very round number.

[Andrew Ponson]

Well, that's the number that I remember. I think it's 149,500,000 or something like that.

[Tim Harford]

What's a few hundred thousand kilometres between friends?

[Andrew Ponson]

Absolutely.

[Tim Harford]

Thanks to Serena, Annabelle, and a big

thanks too, to Andrew Ponson. He's an astrophysicist at University College London.

You're listening to More or Less with me, Tim Harford.

[Narrator]

One group of animals has truly colonized the Earth. They number more than 100 trillion, the ant. And you know, for every human on our planet, there were more than 14,000 of these. And if we were to weigh all of the ants in the world, they would weigh as much as all of the people.

[Tim Harford]

BBC's the Wonder of Animals and loyal listener Adam Richardson thought this sounded a bit dodgy. He's not the only one. He challenged us to find out the truth. So how heavy is an ant? Has anyone ever weighed them? How do you weigh an ant? Hannah Moore's been crawling about with her magnifying glass and her super sensitive set of scales and she can tell us now.

[Hannah Moore]

This claim was Originally made by Dr. Edward O Wilson, a professor at Harvard University, in his 1994 book, Journey to the Ants.

[Tim Harford]

I know his work. He's a top biologist, a leading antspert.

[Hannah Moore]

All the same, Adam insists we fact check. So I emailed Edward Wilson to ask how he calculated it and he wrote.

[Edward O. Wilson]

Here's the basis. An estimate made by an earlier ecologist that there are 10 to the power of 18 insects of all kinds. I'll add the guess that 100th of them, hence 10,000 trillion, are ants. Each human weighs roughly 1 million times as much as each ant on average. And there are 7.2 billion humans alive, hence maybe all the people and all the ants will weigh the same.

[Hannah Moore]

In case you're confused, Professor Wilson is rounding here. So 7.2 billion humans becomes roughly 10 billion humans for the purposes of this estimate.

[Tim Harford]

But E.O.

wilson says there are 10,000 trillion ants in the world. But on the BBC documentary it was claimed there are just 100 trillion.

[Hannah Moore]

That's the first problem. I've spoken to lots of antsperts this week from Bristol University's Ant Lab, the Bees, Wasps and Ants Recording Society, the Natural History Museum.

[Tim Harford]

No stone unturned.

[Hannah Moore]

That's the problem. There are too many stones to turn over. No one knows how many ants there are in the world.

[Tim Harford]

I suppose they are very small, but

let's see what we can do. According to Dr. Wilson, humans weigh on average a million times more than an ant. So what does the average human weigh?

[Hannah Moore]

62 kilograms. Let's call it 60 kilograms. Divide that by a million and you get 60 milligrams.

[Tim Harford]

So about a fifteenth of a gram, is that about right? I realise I have absolutely no idea how much an ant weighs.

[Hannah Moore]

Well, I've been looking into this and I found out that ants vary greatly in weight. There are about 13,000 species worldwide, ranging from less than one millimetre to 30 millimeters in length.

[Tim Harford]

Thirty millimetres. That's as long as a decent sized thumb. Monster ant.

[Hannah Moore]

They're actually called dinosaur ants, Tim.

[Tim Harford]

Anyway, that's so cool. Sorry, go on.

[Hannah Moore]

Anyway, experts agree the average ant weighs about 6 milligrams, making roughly 150 ants to the grammar.

[Tim Harford]

So that's a tenth the weight of Dr. Wilson's estimate. But hang on, how do you even weigh an ant? Well, I spoke to Francis Ratniex, he's professor of apiculture at the University of Sussex, and as you probably guessed, apiculture is something to do with ants and also bees.

[Francis Ratniex]

It's very easy to weigh an ant. You buy a small electronic balance, a few hundred pounds, maybe a thousand for a really fancy one, and you pop the ant on the balance. One way you can easily do it is by cooling the ant and that way it stops moving and you can put it on the balance and it doesn't run away.

[Tim Harford]

Now, did he think there was any truth to the statement that all the ants in the world weigh as much as all the humans?

[Francis Ratniex]

I don't think it's true now, but if we go back in time, I'm sure it was true at one point. If we go back several thousand years, I'm sure that the humans, who are much less numerous and also less fat than they are today, would have weighed less than the ants. So maybe two or 300 years ago, that was the point at which humans outweighed the ants.

[Tim Harford]

Francis Ratniex, professor of apiculture at the University of Sussex, and Hannah Moore.

Thank you, Hannah.

[Hannah Moore]

Thanks, Tim.

[Tim Harford]

Please send your comments or your questions to more or lessbc.co.uk and if you'd like a free download of this program, you are very welcome to it. Just go to bbcworldservice.com moreorless thank you for your company and until next week, Goodbye.

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