Earth examples

Let’s define a small helper function:

def print_me(msg, val):

    print("{}: {}".format(msg, val))

An important concept are the reference ellipsoids, comprising information about the Earth global model we are going to use.

A very important reference ellipsoid is WGS84, predefined here:

print_me("WGS84", WGS84)

# WGS84: 6378137.0:0.00335281066475:7.292115e-05

# First field is equatorial radius, second field is the flattening, and the

# third field is the angular rotation velocity, in radians per second

Let’s print the semi-minor axis (polar radius):

print_me("Polar radius, b", WGS84.b())

# Polar radius, b: 6356752.31425

And now, let’s print the eccentricity of Earth’s meridian:

print_me("Eccentricity, e", WGS84.e())

# Eccentricity, e: 0.0818191908426

We create an Earth object with a given reference ellipsoid. By default, it is WGS84, but we can use another:

e = Earth(IAU76)

Print the parameters of reference ellipsoid being used:

print_me("'e' Earth object parameters", e)

# 'e' Earth object parameters: 6378140.0:0.0033528131779:7.292114992e-05

Compute the distance to the center of the Earth from a given point at sea level, and at a certain latitude. It is given as a fraction of equatorial radius:

lat = Angle(65, 45, 30.0)               # We can use an Angle for this

print_me("Distance to Earth's center, from latitude 65d 45' 30''", e.rho(lat))

# Distance to Earth's center, from latitude 65d 45' 30'': 0.997216343095

Parameters rho*sin(lat) and rho*cos(lat) are useful for different astronomical applications:

height = 650.0

print_me("rho*sin(lat)", e.rho_sinphi(lat, height))

# rho*sin(lat): 0.908341718779

print_me("rho*cos(lat)", e.rho_cosphi(lat, height))

# rho*cos(lat): 0.411775501279

Compute the radius of the parallel circle at a given latitude:

print_me("Radius of parallel circle at latitude 65d 45' 30'' (meters)", e.rp(lat))

# Radius of parallel circle at latitude 65d 45' 30'' (meters): 2626094.91467

Compute the radius of curvature of the Earth’s meridian at given latitude:

print_me("Radius of Earth's meridian at latitude 65d 45' 30'' (meters)", e.rm(lat))

# Radius of Earth's meridian at latitude 65d 45' 30'' (meters): 6388705.74543

It is easy to compute the linear velocity at different latitudes:

print_me("Linear velocity at the Equator (meters/second)", e.linear_velocity(0.0))

# Linear velocity at the Equator (meters/second): 465.101303151

print_me("Linear velocity at latitude 65d 45' 30'' (meters/second)", e.linear_velocity(lat))

# Linear velocity at latitude 65d 45' 30'' (meters/second): 191.497860977

Finally, let’s compute the distance between two points on the Earth:

  • Bangkok: 13d 14’ 09’’ North, 100d 29’ 39’’ East
  • Buenos Aires: 34d 36’ 12’’ South, 58d 22’ 54’’ West

Note

We will consider that positions ‘East’ and ‘South’ are negative

Here we will take advantage of facilities provided by Angle class:

lon_ban = Angle(-100, 29, 39.0)

lat_ban = Angle(13, 14, 9.0)

lon_bai = Angle(58, 22, 54.0)

lat_bai = Angle(-34, 36, 12.0)

dist, error = e.distance(lon_ban, lat_ban, lon_bai, lat_bai)

print_me("The distance between Bangkok and Buenos Aires is (km)", round(dist/1000.0, 2))

# The distance between Bangkok and Buenos Aires is (km): 16832.89

print_me("The approximate error of the estimation is (meters)", round(error, 0))

# The approximate error of the estimation is (meters): 189.0