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Discussion Starter #1
I won't bother to explain the context, but today my boss said the following:

"We're 93 million miles from the sun. There are 365 days in a year. Speed equals distance over time. From that you can figure out how fast we're going!"

All I'll say is, my answer was a pretty close effort, considering I did it in my head, including the conversion from miles/hour to metres/second! INTPride.

I figured, since we're all intelli-boasting INTPs here, it would be fun to see what answers any of you fellow Maths nerds can come up with. Mine was close but I lost a zero somewhere along the way, so in a sense I had the right number but it was missing '0' on the end.

NO CHEATING! ALL IN YOUR HEAD! ANSWERS IN m/s!
If someone instantly spoils this I'll... well I'll do nothing :sad:
 

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Discussion Starter #2
And also.. not smart-arse comments about how, if we want to find out the speed of a fixed point on earth, you need to also consider the earth's spin, and where on its surface you are. That's just OTT and lame.

93 million miles from the sun. 365 days in a year. How fast is Earth going?

Answers in metres/second.
 

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You mean only how fast we're going around the sun?

Because the universe is also expanding more and more rapidly, so we're actually going much faster, in multiple directions at once.

Speed can only be determined relative to something else.

EDIT: Of course I wrote this before I saw your last post, although that doesn't answer my question. Just clarifying what you want...
 

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Discussion Starter #4
Ok...

A ball, in zero gravity, is attached to a stick by a totally inelastic cord, 93'000'000 miles in length.

The ball is then spun around the stick, with the cord extended to fell length, at a rate of 365 days per revolution.

Acceleration and deceleration is instant. No other forces acted on the ball.

How fast, in metres/second, did the ball travel?

:dry: Haha
 

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You have the radius of the Earth's orbit around the Sun. With that you can find the circumference of the orbit (circumference = diameter.π). With the circumference (the distance) and the time (365 days) you can find the speed (speed = distance/time). The rest is just basic conversion of the units. I don't see what's so difficult about it.
 

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Discussion Starter #6
Nothing specially difficult but I was proud of doing it all in my head and getting reasonably close, that's all! It was just a bit of fun!

The challenge was to figure out the actual answer in your head.
 

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Earths orbit is elliptical not circular.
147,098,074km the closest and 152,097,701km the furthest if someone wants to up the ante on the math problem.
edit: and a complete orbit takes 365.256363 days.
 

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Discussion Starter #9
Ugh. I knew this would happen. How un-fun.

I think the on-line INTP has a massive 'intelligence ego'.
 

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Ugh. I knew this would happen. How un-fun.

I think the on-line INTP has a massive 'intelligence ego'.
Show me one comment in here that indicates so.
 

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I'm curious about how good the circular approximation is. The Earth's orbit has a very small eccentricity of about 0.0167. The semimajor axis is 92,956,050 mi. From that you get the semiminor axis of 92,943,086.8 miles. The circumference of an ellipse is given by the incomplete elliptic integral of the second kind but the simplest approximation gives 505,787,362 miles. The period is about 365.256 days so you get 1,384,747.58 miles per day or 57,697.8158 mph. How close is that to what you got?
 

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Physics/mathematics in high school/university in the US state questions in miles and expect you to convert? I do realise they use metres for physics there but what a waste of time. I really want to know.
 

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Discussion Starter #13
Show me one comment in here that indicates so.
Since I specifically said it was just a bit of fun and only to be taken on a basic level, yet still everyone decides to highlight all these silly extra factors which make the question invalid or unanswerable with the given facts. It was a case of, "I'm so amazing that I'm gonna tell you all how I know this whole thing is flawed." Pretty typical INTP behaviour actually, haha.

Anyway, my answer came to 60'000mph, which I was pretty pleased with for doing it in my head. When I tried to convert it to metres/second I fucked up by losing a zero along the way and using the wrong conversion for miles to km, but still I was reasonably close, all things considered! I ended up with 2240m/s, which, if I stuck the lost zero back on, would be 22400m/s.

The real answer is around 29951m/s, so I'm please enough with what I did!
 

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Discussion Starter #14
Physics/mathematics in high school/university in the US state questions in miles and expect you to convert? I do realise they use metres for physics there but what a waste of time. I really want to know.
I don't get what you're saying here?

Basically my boss told me the earth was 93 million miles from the sun, so I took it from there, and for a laugh decided to try converting the speed into metres/second.

I'm pretty sure most/ALL scientific studies are metric. Just, like I said, my boss told me the figure in miles so I took it from there. I'm not American, by the way.
 

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Since I specifically said it was just a bit of fun and only to be taken on a basic level, yet still everyone decides to highlight all these silly extra factors which make the question invalid or unanswerable with the given facts. It was a case of, "I'm so amazing that I'm gonna tell you all how I know this whole thing is flawed." Pretty typical INTP behaviour actually, haha.

Anyway, my answer came to 60'000mph, which I was pretty pleased with for doing it in my head. When I tried to convert it to metres/second I fucked up by losing a zero along the way and using the wrong conversion for miles to km, but still I was reasonably close, all things considered! I ended up with 2240m/s, which, if I stuck the lost zero back on, would be 22400m/s.

The real answer is around 29951m/s, so I'm please enough with what I did!
That's a good order of magnitude estimate. Fermi would be proud. Now how many piano tuners are there in Chicago?
 

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My mental arithmetic is shockingly bad, I got.
33,000 meters/second

My bad approximations:
93 million miles -> 100 million miles

So 160 billion meters (radius)

2 * PI -> 6
6 * 160 billion is 960 billion -> 1000 billion (the circumference, meters)

1000/3 = 333, that's close enough to 365...
3 * 1000 billion / 1000 = 3 billion (meters per day)

100/4 = 25, that's close enough to 24...
4 * 3 billion / 100 = 120 million (meters per hour)

120 million / 60 = 2 million (meters per minute)

2 000 000 / 60 = 100 000 / 3 = 33 000 (meters per second)
 

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Well, first of all I don't remember the miles/km conversion by head(only use metric where I live), so I can't do everything without "cheating". Buut, yeah, considering all the rounding you'd have to make(pi, miles to km, distance between sun/earth, etc) the end result would probably be quite distant from the actual one, which makes this sound a bit pointless(besides the mental stimulation aspect, I guess...)

I mean, not that I don't appreciate math problems, it's just that answering this specific one reminds me a lot of everything I dislike about physics, chemistry, and other more "applied mathematics" subjects in school. "Multiply this variable by this constant, follow this equation, round and convert", I mean. What I like about math is the puzzle, the process, how you can completely understand a problem and get an absolute answer. Not the human calculator aspect of it...
 

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There are not actually 365 days in a year, it's 364.25. That's why we have leap year.
 

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There are not actually 365 days in a year, it's 364.25. That's why we have leap year.
It's not 364.25, a leap year is longer than a year. It's approximately 365.25, approximate because it's actually slightly less than that. This is why our current Gregorian calendar has exceptions to the 4 year rule to better approximate the actual value.

Leap year if divisible by 4
Unless divisible by 100
But still is if divisible by 400

e.g. 1900 wasn't a leap year, 2000 was


p.s. Love your avatar. <3
 

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It's not 364.25, a leap year is longer than a year. It's approximately 365.25, approximate because it's actually slightly less than that. This is why our current Gregorian calendar has exceptions to the 4 year rule to better approximate the actual value.

Leap year if divisible by 4
Unless divisible by 100
But still is if divisible by 400

e.g. 1900 wasn't a leap year, 2000 was


p.s. Love your avatar. <3
And yet that's not perfectly accurate. Damn universe, not being perfect for our units of measure!
 
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