## Posts Tagged ‘earth’

## The Earth is Round

…and it has been for a LONG time. At least, since the late 1000BCE. There’s been a weird misconception that in the time around 5th to 15th century, we all thought our Earth was flat. Then Columbus struck out on his boat and upon returning changed it all.

Truth is, many different scholarly Greeks had discovered, proved, calculated, however you want to call it, that our Earth was indeed a big blue ball. In fact, once this development sprouted out of Ancient Greece in the centuries before the Roman Empire even got off the ground, the ideals of a spherical Earth pervaded through Europe clear into modern day. The idea of a flat Earth between educated peoples in the days of Columbus was next to none.

But how on Earth did we figure out the Earth was round way back before satellites and computers? Well, one man named Ἐρατοσθένης (Eratosthenes) was able to get the answer using simple math that another Greek, Πυθαγόρας (Pythagoras), developed. If you remember your right-angle triangles you might already know where this is headed.

In his publication of “Περὶ τῆς ἀναμετρήσεως τῆς γῆς” (On the Measurement of the Earth) he explained the details of his method. Eratosthenes read that on the summer solstice at noon in the city of Syene, rays from the Sun would reach the bottom of the deepest well. In other words, the Sun would be directly overhead. He knew that on the same day in Alexandria, the sun was not directly overhead. Since he assumed that Alexandria was basically due north of Syene, he figured that the arc distance between the two locations was roughly 1/50 of a full circle (7°12′) north of the zenith at the same time.

How Eratosthenes figured out the distance from Alexandria to Syene is a somewhat unsettled. Some say he hired someone to measure the distance, others says that he estimated the distance from the average time required for a caravan of camels to travel the distance, and another that he walked the distance himself. However it was measured, the distance was determined to be about 5,000 stadia.

With all this, he foudn his final value of 700 stadia per degree, which would multiply out to a circumference of 252,000 stadia. There were at least two different units in common use at the time, equivalent to 157.5 m and about 185 m. That put Eratosthenes’s value between 39,690 km and 46,620 km. The circumference of the Earth around the poles is now measured to be around 40,008 km. If you average ou, this puts Eratosthene’s answer within roughly 7.8%! All with shadows and simple math.

This method, while hindered by low precision data, was very accurate and was accepted for hundreds of years afterwards. Even other astronomers/geographers used his method and other methods in its likeness to further maintain the accuracy of the Earth’s circumference.

## Relatable Distances

With this site my goal is to make some of the harder-to-grasp ideas in science easier to handle, so with this episode I wanted to appreciate some distances we have in our lives.

First, we all have heard of feet, meters, inches, kilometers, and most of us have at least heard about light-years, even if we haven’t used them ourselves; however, with light-years, we tend to loose our sense of estimation. It is hard for us humans to fully grasp a light-year, and what about an AU (astronomical unit) or a parsec (parallax arcsecond)? These measurements are employed with our neighbors in space. They describe great lengths across our universe, but what are these measurements?

Length |
in Kilometre |

1parsec | 3.0857×10^13km |

1light-year | 9.461×10^13km |

1AU | 1.4960×10^8km |

1km | 1000m |

1m | 1.0×10^-3km |

1 mile |
1 kilometre |

8 furlongs | 10 hectometre |

80 chains | 100 dekametre |

320 rods | 1000 metre |

8000 links | 10,000 decimetre |

5280 feet | 100,000 centimetre |

1760 yards | 1,000,000 millimetre |

Well, we’ll save how they were derived for a another time. Right now we’ll just focus on sheer distance.

Sorry, for you non-metric users. For a comparative table why I shy away from the Imperial/US system of measures here’s a sample of a mile divided down next to a kilometre.

So, now we know how far these new units, Parsec, AU, and Light-year, are in kilometers. But again, how long are these distances? One Parsec is equal to 30,857,000,000,000 kilometers? Think about what 30 quadrillion feels like in your mind. Roughly 6 million people in the Houston, TX city and surrounding metro areas, about 6.7 billion people living on the whole planet, a certain national debt is around 14.6 trillion dollars… but 30 quadrillion?

If we put some of these units to use we can get a better grasp of their magnitude. Let’s take a simple relationship our Earth and our star, the Sun. The easiest unit to place is an AU, which is one (1) astronomical unit. Well, that may not help too much, so let’s take the Sun, the Earth, and that 1 AU between us and shrink them down. If we shrunk our Earth down to a single grain of sand, the Sun would be almost the size of a DVD disc, and that 1 AU would only be 12.84 yds (about 6.5 people from head to toe.

And how about a Parsec? Well, 1 Parsec is 3.26156 light-year is 3.0857×10^13 km. The nearest star to ours is Proxima Centauri, 4.3 light-years away. Given our micro-scale universe it would be 1983.798 miles away. So you can place your DVD at city hall in Phoenix, AZ and you can put Proxima Centauri on capital hill in Washington, D.C.