Definitions & Notes

This section contains pedantic definitions, explanations, principles, etc., as it relates to the Places Visited page. If any of this bores or angers you, just ignore it. Everything will be okay.

General Principles

Off on a Tangent considers the world as it is, which is not always the way it ought to be. Maps and place names are meant to reflect the reality “on the ground”—who controls an area and what name they have given it.

All de facto sovereign states are treated equally without regard for international recognition, legal or moral legitimacy, or de jure claims by other states. The presence of a particular state or particular border on the maps and lists is not an endorsement.

Definitions

For Places on Earth

• First-level places are listed in alphabetical order; these include:
  • Sovereign States: Exert stable de facto control of defined areas and are not subject to another states’ domestic or foreign policies, regardless of international recognition or de jure claims by other states.
  • Multinational Areas: Cooperatively governed by multiple sovereign states under treaties, United Nations mandates, or other agreements.
  • Unclaimed Areas: Not under stable de facto control of any sovereign states and not subject to serious de jure claims.
  • Disputed Areas: Not under stable de facto control by any single sovereign state because of active conflicts, overlapping claims, etc.
• Second-level places are listed in alphabetical order; these include:
  • Dependencies: Partially or wholly subject to a sovereign state’s domestic or foreign policies; geographically distant areas are shown as dependencies even if they are legally integral to the state.
• Additional definitions:
  • Uninhabited Areas: No permanent residential settlements and no self-sustaining economy, but may have transient populations, research outposts, military bases, and other facilities.
  • Visited: I have set foot on its ground or a fixed structure, traveled on its land in a ground conveyance, observed it from a low-altitude aircraft or close-passing boat or ship where observing the place was part of the purpose of the journey, or entered its interior waters.

For Planets & Satellites

• First-level objects are listed in order of their mean orbital distance from the sun; these include:
  • Planets: Natural objects orbiting the sun (Sol) that have a mean diameter of at least 2,000 kilometers.
  • Binary Planets: Pairs of natural objects orbiting the sun (Sol) that are in a mutual gravitational relationship when (1) the sum of their mean diameters is at least 2,000 kilometers, (2) their barycenter is in open space between them, and (3) the less massive object’s mass is at least two-thirds of the larger object’s mass.
• Second-level objects are listed in order of category; these include:
  • Large Moons: Natural planetary satellites that have a mean diameter of at least 1,000 kilometers; ordered by mean orbital distance from the planet.
  • Space Stations: Artificial planetary satellites that are permanently or semi-permanently inhabited by humans; ordered by date of first habitation.
• Additional definitions:
  • For planets and large moons:
    • Uninhabited: No permanent human residential settlements, no self-sustaining economy, and no known indigenous intelligent life.
    • Visited: I have set foot on its surface or a fixed structure, traveled on its surface in a ground conveyance, entered its atmosphere, completed a full orbit, or passed through its gravity well if observing the planet or moon was part of the purpose of the pass.
  • For space stations:
    • Uninhabited: Not applicable (a “space station” with no inhabitants is just a satellite).
    • Visited: I have docked or attached to it with a vehicle or entered its habitable environment.

Notes

On Place Names

As a general rule, the short English-language name preferred by a sovereign state’s government is used.

If the preferred name is complicated or confusing, a commonly-understood alternate may be used. Appelations like “Republic of” and “Kingdom of” are omitted unless necessary to differentiate from similarly named states.

On Places With Unusual Statuses

Most of the world’s first-level places are de facto sovereign states (whether we like it or not). There are four places in other categories:

• Antarctica – multinational area
• Bir Tawil – unclaimed area
• Donbas & Southern Dnieper Regions– disputed area
• Spratly Islands – disputed area

On Additional Claimed U.S. Territories

The U.S. government claims two territories it does not possess; both are uninhabited islands in the western Caribbean:

• Bajo Nuevo Bank – de facto territory of Colombia
• Serranilla Bank – de facto territory of Colombia

On U.S. American Indian Reservations

Within the United States are numerous American Indian nations and reservations. They are generally considered “domestic dependent nations” with a degree of sovereignty over their internal affairs. They are generally subject to U.S. federal law, but not to state laws.

Reservations could be depicted as a separate class of U.S. dependencies and their territories could be “cut out” of the states they are located in. This would make the map (and the list of places) extremely complicated, so I did not even attempt it . . . it’s not clear if this would be a more “correct” depiction anyway.

For the time being, I am treating American Indian reservations as something akin to extraterritorial property (see next section)—they are within the states, and their land “belongs” to the states, but it is set-apart under a special legal structure.

On Extraterritoriality

Extraterritoriality is not depicted on the map or lists. Embassies, military bases, and other properties are sometimes set apart from a host country’s sovereign control by agreement, lease, or treaty, but the land remains part of the host country.

On Territorial Changes

If sovereignty over a given territory changes, the map will be updated accordingly. The list of places visited will be modified on the basis of the current sovereign over each physical place, even if they were under a different sovereign at the time of my visit.

On the Definition of “Planet”

Off on a Tangent defines “planet” differently than the International Astronomical Union (IAU). For details, refer to the Special Statement on Planets and Moons.

On the International Space Station

The International Space Station (ISS) is a space station built and operated by Canada, the European Space Agency (ESA), Japan, Russia, and the United States. Each habitable module of the space station is subject to the laws of the state that owns it.

On Flags for Planets & Moons

Planets and large moons do not have official flags (as far as we know), so I created some. They follow a defined design pattern:

• Basic characteristics:
  • Nominal design resolution is 640x480px (4:3 ratio).
  • Black field (background) representing outer space.
  • Colored circles represent planets and large moons.
  • The colors, sizes, and positions of the circles are determined as described below, but may be adjusted on a case-by-case basis for improved contrast, visual balance, or aesthetics.
• For planets:
  • A colored circle representing the planet is centered in the field (nominal coordinates 320x240px).
  • The nominal diameter of the planet’s circle is set using the planet diameter calculation methodology described below.
  • The color of the planet’s circle is set using the color calculation methodology described below.
  • The planet’s astronomical symbol is placed in the center of its circle, black with an opacity value of 50%, and scaled to fit within the space of a nominal 150px circle.
• For large moons:
  • The colored circle and symbol representing the moon’s planet (see above) is placed at the center of the bottom-left quadrant (nominal coordinates 160x360px). It may overrun the field.
  • A colored circle representing the moon is placed in the top-right quadrant; its position is set using the moon position calculation methodology described below.
  • The nominal diameter of the moon’s circle is 150px.
  • The color of the moon’s circle is set using the color calculation methodology described below.
  • If the planet has more than one large moon, a Roman numeral representing the number in the set is placed in the bottom-right quadrant, white with an opacity value of 50%. Its nominal height is 75px, its vertical position is centered at 360px, and its horizontal position is centered beneath the moon’s circle.

The planet diameter calculation methodology scales the sizes of circles representing planets on a logarithmic scale. This means that bigger planets get bigger circles and smaller planets get smaller ones, but they are not literally [or linearly] to-scale:

• The maximum nominal diameter of a circle representing a planet is 420px.
• To calculate the nominal diameter of a particular planet, n_d,
  • take the natural logarithm of the planet’s mean diameter in kilometers, ln(d_cur),
  • divide by the natural logarithm of the largest planet’s (Jupiter’s) mean diameter in kilometers, ln(d_max),
  • multiply by 420, then round the result down to the nearest integer.
• Equation form of nominal diameter calculation:

$$\begin{array}{c}\begin{array}{ccc}\hfill n_d& =& [\frac{\ln (d_{\mathit{cur}})}{\ln (d_{\mathit{max}})}\times 420]\hfill \end{array}\\ \cdots \\ \begin{array}{ccc}\hfill d_{\mathit{cur}}& =& \text{this planet’s mean diameter (km)}\hfill \\ \hfill d_{\mathit{max}}& =& \text{largest planet’s mean diameter (km)}\hfill \\ \hfill \text{Result}{n}_d& =& \text{nominal diameter in pixels,}\le 420\hfill \end{array}\end{array}$$

The color calculation methodology selects a color to represent the planet or large moon. The color of objects other than Earth is mathematically derived from its visible color (spectra) and brightness (albedo).

• For Earth:
  • Use HEX color #87ceeb (standard web color “sky blue”).
• For other objects:
  • The target brightness value, b, is a percentage between 0.5 (50%) and 1.0 (100%) in relative proportion to the object’s measured geometric albedo a (or 1.0 if the albedo is greater than 1.0). To calculate it,
    • multiply the object’s geometric albedo by 0.5,
    • then add 0.5 to the result.
  • Then, to calculate a target color,
    • use photo editing software (such as Adobe Photoshop) to isolate the object from a color photograph,
    • convert the isolated image to LAB color space and set the brightness of all pixels to the target brightness, b (see above),
    • apply an “average” filter to the image
    • determine the HEX color of the result with the “eyedropper” tool or equivalent.
• Equation form of target brightness calculation:

$$\begin{array}{c}\begin{array}{ccc}\hfill b& =& 0.5a+0.5\hfill \end{array}\\ \cdots \\ \begin{array}{ccc}\hfill a& =& \text{object’s geometric albedo,}\ge 0.0,\le 1.0\hfill \\ \hfill \text{Result}b& =& \text{target brightness,}\ge 0.5,\le 1.0\hfill \end{array}\end{array}$$

The moon position calculation methodology computes a central coordinate for placing a planet’s large moons’ circles in the upper right quadrants of their flags based on their numerical order within the set.

• To calculate the offset multiplier, m,
  • take the moon’s number within the planet’s list of large moons, i_cur,
  • then subtract the planet’s total number of large moons, i_max, divided by two and rounded down to the nearest integer.
• To calculate the nominal position of the moon’s center,
  • for the horizontal, p_x, multiply the multiplier by 20px and add the result to 480px,
  • and for the vertical, p_y, multiply the multiplier by -10px and add the result to 120px.
• Equation form of these calculations:

$$\begin{array}{c}\begin{array}{ccc}\hfill m& =& i_{\mathit{cur}}-\lfloor \frac{i_{\mathit{max}}}{2}\rfloor \hfill \\ \hfill p_x& =& 480+(20m)\hfill \\ \hfill p_y& =& 120-(10m)\hfill \end{array}\\ \cdots \\ \begin{array}{ccc}\hfill i_{\mathit{cur}}& =& \text{large moon’s number within the set}\hfill \\ \hfill i_{\mathit{max}}& =& \text{planet’s number of large moons}\hfill \\ \hfill \text{Result}m& =& \text{multiplier value}\hfill \\ \hfill \text{Result}{p}_x& =& \text{nominal horizontal position}\hfill \\ \hfill \text{Result}{p}_y& =& \text{nominal vertical position}\hfill \end{array}\end{array}$$

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