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dr.bob
167791.  Thu Apr 19, 2007 8:05 am Reply with quote

An alternative to Gray's explanation of Cavendish's experiment:

Quote:
Cavendish had two small balls. He dangled these from the ceiling on a thin bit of wire. He then took two much larger, more impressive balls and placed them close to the ones dangling from the ceiling. The gravity from the impressively large balls caused his two small balls to twist 'round slightly. Of course, dangling your balls from the ceiling is a very sensitive experiment, so he had to leave the room and peek back in through a hole in the wall to see how much his balls had twisted 'round.

By measuring the amount his small balls twisted, he was able to measure the gravity due to his impressively large balls. By comparing the gravity of his large balls to the gravity of the earth, and knowing the mass of his large balls, he was able to work out the mass of the earth.


Though I fully realise that the chances of Stephen getting all that out without interruption would be precisely zero.

 
Flash
167806.  Thu Apr 19, 2007 9:00 am Reply with quote

Can you just confirm my understanding that once you know the mass of the Earth you can deduce the mass of the Sun (by plugging the number into the formula for our orbit) and then use your newfound knowledge of the mass of the Sun to work out the masses of the other planets (same deal only backwards)?

 
Molly Cule
167817.  Thu Apr 19, 2007 9:22 am Reply with quote

For estimates we could mention estimating how far away a storm is by counting the time between the lightening and the thunder, I sometimes do that, I count the seconds between the lightening and thunder and thought, not really thinking that it could be right, that the number of seconds was the number of miles but seems its not that simple.... Every five seconds you count is one mile.

Quote:
The time between seeing a lightning flash and hearing the thunder it produces is a rough guide to how far away the lightning was. Normally, thunder can be heard up to 10 miles from the lightning that makes it. Lightning heats the air around it to as much as 60,000 degrees, producing sound waves by the quick expansion of the heated air. Since light travels at 186,000 miles per second, you see the lightning the instant it flashes. But sound, including thunder, travels about a mile in five seconds near the ground. If 15 seconds elapse between seeing a lightning bolt and hearing its thunder, the lightning was about three miles away. Lightning closer than about three miles away is a warning to take shelter immediately. Successive lighting strikes are often two to three miles apart. If the first stroke is three miles away, the next one could hit you.

 
Flash
167846.  Thu Apr 19, 2007 10:20 am Reply with quote

Good thinking

 
dr.bob
167850.  Thu Apr 19, 2007 10:39 am Reply with quote

Flash wrote:
Can you just confirm my understanding that once you know the mass of the Earth you can deduce the mass of the Sun (by plugging the number into the formula for our orbit) and then use your newfound knowledge of the mass of the Sun to work out the masses of the other planets (same deal only backwards)?


Pretty much. The only other piece of information you need to know is the distance between the Earth and the Sun (just knowing the mass of the Earth is not enough). However, you can figure that out by comparing it to the distance between the Earth and the Moon (which can be measured with a few different techniques including, these days, radar).

 
Gray
167862.  Thu Apr 19, 2007 11:12 am Reply with quote

You can't find the mass of a planet by seeing how far it is from the Sun. All masses of at the same distance will orbit at the same speed. The mass of the orbiting body is immaterial if you work out the force equation for orbit - m appears on both sides:

GMm/r^2 = mv^2/r

For example, satellites of lots of different masses can sit in the same orbit around Earth.

The only way you can work out the mass of a body is to look at the things orbiting IT, so you'd have to look at the other planets' moons to get their masses. Looking at the sun won't help. Plus it's bad for your eyes.

 
Flash
167866.  Thu Apr 19, 2007 11:16 am Reply with quote

OK, so when the wiki article says that Cavendish's experiment enabled the calculation of the masses of the other planets, it errs?

 
dr.bob
168009.  Fri Apr 20, 2007 3:33 am Reply with quote

Not necessarily. By working out the Gravitational Constant (the G in the equation provided by Gray up there), Cavendish made it possible to weigh the other planets by means of measuring how their moons orbit them.

That still leaves the problem of Mercury and Venus, though. Hmmm, I wonder how you weigh those.

Edit: Ah ha! It turns out you don't.

It seems that the masses of Venus and Mercury were not well known until pretty recently when we were able to chuck space probes at them and measure how these artificial moons orbited 'round those two planets.

 
Flash
168016.  Fri Apr 20, 2007 3:42 am Reply with quote

Well I call that quite interesting. Trying to think of a felicitous way to express the question, but it's something to the effect of:

Q: Why could Henry Cavendish weigh every planet except Venus and Mercury?

Which might lead us, in a misleading sort of a way, into this territory:

Q: What use is a plank in outer space?

post 143485

 
eggshaped
168019.  Fri Apr 20, 2007 3:47 am Reply with quote

But by your "Stephen won't be able to get the answer out" logic, surely this is worse - first he would have to describe the big-balls experiment, then the equation, then the fact that it doesn't work with planets sans lune.

 
dr.bob
168020.  Fri Apr 20, 2007 3:47 am Reply with quote

Flash wrote:
Q: Why could Henry Cavendish weigh every planet except Venus and Mercury?


That's a good way of phrasing the question.

Of course, Cavendish's work on the Gravitational Constant was necessary to weigh Venus and Mercury as well, but it wasn't possible during his lifetime so the question works.

(yes, I know you all realised that already. Just thinking aloud, really)

eggshaped wrote:
But by your "Stephen won't be able to get the answer out" logic, surely this is worse - first he would have to describe the big-balls experiment, then the equation, then the fact that it doesn't work with planets sans lune.


He may not necessarily need to explain the experiment with the big balls. He could just say "Cavendish measured the Gravitational Constant which allowed us to...."


Last edited by dr.bob on Fri Apr 20, 2007 3:49 am; edited 1 time in total

 
Gray
168021.  Fri Apr 20, 2007 3:47 am Reply with quote

There's a weird (though probably explicable using some emergent property of Kepler's laws) correspondence between the sizes of the orbits of the planets and the golden ratio 'phi'.

The orbits all lie very close to what successive ratios of their sizes would predict, except for a notable gap between Earth and Mars. This is, rather interestingly, where all the asteroids are, suggesting that they were all once part of a planet, of which huge lumps like Ceres are the remnant.

It's linked to what Euclid (I think) thought about the planets all lying at the edges of successive polyhedrons in space - the golden ratio is evident in that theory too, which is presumably how he noticed.

I can't find any sensible references of this, however - all the likely sites linked from google are rather 'woo' and packed full of spiritual energy or outright creationism.

 
eggshaped
168022.  Fri Apr 20, 2007 3:50 am Reply with quote

The asteroids are between Mars and Jupiter aren't they?

 
Gray
168024.  Fri Apr 20, 2007 3:51 am Reply with quote

Sorry, what am I thinking.

Too many astrology sites in my face...

 
eggshaped
168025.  Fri Apr 20, 2007 3:52 am Reply with quote

Quote:
He may not necessarily need to explain the experiment with the big balls. He could just say "Cavendish measured the Gravitational Constant which allowed us to...."


I guess, but why miss out on the chance to talk about big balls?

 

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