# Furlongs per fortnight

Furlongs per fortnight is a problem set with a contained quiz that focuses on the fundamentals of observational and deductive astronomy. In the activity Energy phantoms you learned about the value of distance, or displacement, and motion, speed, velocity, and acceleration. Here, you can practice and test yourself on converting from units that may or have occurred in the literature to units popular today.

## Astronomical units

Notation: let the symbol $R_{\oplus }$ indicate the Earth's radius.
Notation: let the symbol $R_{J}$ indicate the radius of Jupiter.
Notation: let the symbol $R_{\odot }$ indicate the solar radius.

## Physical units

Both physics and astronomy use units and dimensions to describe observations.
Units of Physics and Astronomy :
| Dimension | Astronomy | Symbol | Physics | Symbol | Conversion |
| time | 1 day | d | 1 second | s | 1 d = 86,400 s |
| time | 1 "Julian year" | J | 1 second | s | 1 J = 31,557,600 s |
| distance | 1 astronomical unit | AU | 1 meter | m | 1 AU = 149,597,870.691 km |
| angular distance | 1 parsec | pc | 1 meter | m | 1 pc ~ 30.857 x 10$^{12}$ km |

## Theoretical units

Perhaps the first step in deciphering ancient presumably astronomical records is determining what the unit is.
Def.
* a series of interconnected rings or links usually made of metal,
* a series of interconnected links of known length, used as a measuring device,
* a long measuring tape,
* a unit of length equal to 22 yards. The length of a Gunter's surveying chain. The length of a cricket pitch. Equal to 20.12 metres. Equal to 4 rods. Equal to 100 links.
* a totally ordered set, especially a totally ordered subset of a poset,
* iron links bolted to the side of a vessel to bold the dead-eyes connected with the shrouds; also, the channels, or
* the warp threads of a web
is called a chain.
Def. a period of fourteen nights; two weeks is called a fortnight.
Def. a unit of length equal to 220 yards or exactly 201.168 meters, now only used in measuring distances in horse racing is called a furlong.
Def.
* a trench cut in the soil, as when plowed in order to plant a crop or
* any trench, channel, or groove, as in wood or metal
is called a furrow.
Def. the distance that a person can walk in one hour, commonly taken to be approximately three English miles (about five kilometers) is called a league.
Def. a period of seven nights; a week is called a sennight.
Def.
* any period of seven consecutive days,
* a period of seven days beginning with Sunday or Monday,
* a subdivision of the month into longer periods of work days punctuated by shorter weekend periods of days for markets, rest, or religious observation such as a sabbath, or
* seven days after (sometimes before) a specified date
is called a week.

## Problem 1

A local farmer has spotted what she believes is an astronomical object moving in the sky at night.
As the ox-plow travels using the apparently fixed points of light in the night sky, the object has covered 0.214 furlongs in her field over 1.631 fortnights.
Her field is 16.421 furlongs from horizon to horizon in the direction the object is traveling. The amount of the total sky (360° if the Earth were not in the way) her field actually views in 10.123°.
How many arcseconds has the astronomical object traversed in the night sky?
How fast is the object traveling in degrees/hour?
If after the first night of travel, the object appears to cover about 0.250 less distance, is the object accelerating or decelerating and by how much in kilometers/sec$^2$?
If the object turns out to be 0.313 of the mean distance to the Moon away, what are its actual speed and acceleration in km and sec?

## Problem 2

Like the farmer in problem 1, a sailor aboard an oil tanker heading northeast across the mid-Atlantic has noticed an apparent astronomical entity traveling north against the fixed stars. Using another nearby ship, the sailor estimates that relative to those stars the entity has traveled 20,000 leagues due north along the surface of the ocean.
Using the radius of the Earth to the North Pole, how many arcseconds has the entity traversed, if the period of movement is a tunti?
What is the entity's speed in km/sec?
What is its speed in arcsecs per minute?
At the end of the observing period, the sailor notices the entity make a 22° change in direction to the east in about four diba'igaans.
If after the change in direction the entity is observed to be traveling at the same speed, what acceleration has been applied to the entity?

## Problem 3

An astronaut on the surface of the Moon is observing the Earth at night. While watching the Earth she notices a source of visible white light traveling perpendicular to the direction of the Earth's rotation.
In the time it takes North America to rotate into view from just before it's visible the source travels a linear arc approximately equivalent to the arc from the Tropic of Cancer to the Tropic of Capricorn.
About how many arcminutes has the source traveled?
If it is as far away as the Earth from the Moon, what is its speed in km/hr?
Relative to the Earth's rotational axes, is the object traveling northward or southward?

## Hypotheses

* A speed requires a standardized distance (not necessarily a meter) divided by a standardized time (not necessarily an hour).