WS MoreOrLess: How do we calculate the distance to the sun?
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What is the main topic discussed in this episode?
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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 are younger than others. I'm joined in the studio by two of them. Perhaps if you'd be so kind you could introduce yourselves.
I'm Annabelle and I'm 12. And I'm Serena and I'm 10.
And the fellow in the corner of the studio lurking, Andrew. I'm Andrew. And I'm 31. And you're an astronomer. I am. Welcome to More or Less Towers. Now, Sweeney and Annabelle, what can I do for you?
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.
Serena, this is a problem that's been getting you scratching your head.
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 two unknowns and zero knowns, so surely we can't know.
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?
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.
How did young listeners kick off the question about the Sun's distance?
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 round the Sun and how long it takes us to go round 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 round the Sun and Mars round 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 automatically. and work out the distance to the Sun.
So the only thing we're missing then is how do you know how far away Mars is?
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. Are you happy, Giles?
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?
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 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. Andrew, I have one final question. How far away is the sun? It is 150 million kilometres away.
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Chapters
4 chapters
1
What is the main topic discussed in this episode?
0:00–1:41
2
How did young listeners kick off the question about the Sun's distance?
1:41–6:52
3
How can we determine the Sun's distance and size using planetary orbits?
6:52–7:15
4
What role do Kepler's laws and Newtonian gravity play in measuring orbits?
7:15–9:27