GeoLength

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`GeoLength`

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GeoLength[g]

gives the length of the geo path g.

Details and Options

The path g in GeoLength[g] can be any one-dimensional geo primitive, such as GeoPath, GeoCircle, or GeoVisibleRegionBoundary.
GeoLength[GeoPath[{p₁,p₂,…}]] computes the length of the path formed by geodesic segments joining the locations p_i.
JoinedCurve and GeoGroup can be used to combine multiple paths.
GeoLength[g] returns a Quantity object with units of length.
GeoLength[{g₁,g₂,…}] gives {GeoLength[g₁],GeoLength[g₂],…}.
Possible options of GeoLength include:
GeoModel Automatic model of the Earth or celestial body

UnitSystem $UnitSystem unit system to use in the result

Examples

open allclose all

Basic Examples (4)Summary of the most common use cases

Compute the total length of a geo path on the Earth:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-qzy371

Out[1]=1

Compute the total length of a path formed by geodesic segments:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-hqfrjt

Out[1]=1

Compute the total length of the rhumb lines joining the same points:

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-6bmwyl

Out[2]=2

Length of the Earth's equator:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-pj8662

Out[1]=1

Length of a full meridian:

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-cygb7y

Out[2]=2

Compute the perimeter of a geo disk:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-qn6xl0

Out[1]=1

Scope (3)Survey of the scope of standard use cases

Compute the length of different one-dimensional geo elements:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-zicct3

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-jlk5xz

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0cg5bnh6y-emi5c9

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0cg5bnh6y-mngr49

Out[4]=4

Length of the perimeter of a region with holes, as a single joined object:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-jxzqnl

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-pmf6rw

In[3]:=3

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https://wolfram.com/xid/0cg5bnh6y-habiu0

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0cg5bnh6y-1rz6mm

Out[4]=4

It can also be obtained by adding the lengths of the outer and inner curves:

In[5]:=5

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https://wolfram.com/xid/0cg5bnh6y-v3stdm

Out[5]=5

Paths of different types can be combined with GeoGroup:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-rcg7cd

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-6vatuw

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0cg5bnh6y-y60h42

Out[3]=3

Generalizations & Extensions (1)Generalized and extended use cases

GeoLength[Line[{p₁,p₂,…}]] is equivalent to GeoLength[GeoPath[{p₁,p₂,…}]] for geo locations p_i:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-kvdk3g

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-4oatbk

Out[2]=2

Options (2)Common values & functionality for each option

UnitSystem (1)

Use the units determined by the value of $UnitSystem:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-d9qs04

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-rfv5ov

Out[2]=2

Specify the unit system to use:

In[3]:=3

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https://wolfram.com/xid/0cg5bnh6y-rjvzdd

Out[3]=3

GeoModel (1)

Length of a geo path on the Earth:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-q3qy45

Out[1]=1

Length of the corresponding path on Mars:

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-yf20tf

Out[2]=2

Applications (2)Sample problems that can be solved with this function

Compute the length of the boundary of a country from its polygon:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-yc0eid

Out[1]=1

That value is shorter than the actual length of the boundary, due to approximations in the polygon:

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-2mxva3

Out[2]=2

The length of a segment of parallel, or the projection on a parallel of any geo path, is called departure:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-427wn1

Out[1]=1

Express it in nautical miles:

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-orb1au

Out[2]=2

Properties & Relations (1)Properties of the function, and connections to other functions

For a geo path defined by a list of points, GeoLength[GeoPath[list]] is equivalent to GeoDistance[list]:

In[1]:=1

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https://wolfram.com/xid/0cg5bnh6y-e0x622

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0cg5bnh6y-w42sxy

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0cg5bnh6y-2ahtfk

Out[3]=3

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