Gravitational Models Comparison

In this tutorial, we'll compare various Gravitational Models.

Setup

Let's import the necessary libraries:

import numpy as np

import pandas as pd

import plotly.graph_objs as go

from ostk.physics import Environment
from ostk.physics.time import Instant
from ostk.physics.environment.gravitational import Earth as EarthGravitationalModel

<frozen importlib._bootstrap>:241: FutureWarning: pybind11-bound class 'ostk.physics.coordinate.frame.provider.Dynamic' is using an old-style placement-new '__init__' which has been deprecated. See the upgrade guide in pybind11's docs. This message is only visible when compiled in debug mode.

Computation

environment = Environment.default()
earth = environment.access_celestial_object_with_name("Earth")

Let's set up some gravitational models:

gravitational_models = [
    EarthGravitationalModel(EarthGravitationalModel.Type.Spherical),
    EarthGravitationalModel(EarthGravitationalModel.Type.WGS84),
    EarthGravitationalModel(EarthGravitationalModel.Type.EGM84),
    EarthGravitationalModel(EarthGravitationalModel.Type.EGM96),
]

And evaluate them at various altitudes:

altitudes = list(range(0, 1000000, 100000))

instant = Instant.J2000()

positions = [
    np.array([float(earth.get_equatorial_radius().in_meters() + altitude), 0.0, 0.0])
    for altitude in altitudes
]

def evaluate_field_values(gravitational_model, positions):
    field_values = [
        np.transpose(gravitational_model.get_field_value_at(position, instant))[0]
        for position in positions
    ]

    return field_values

field_valuess = [
    evaluate_field_values(gravitational_model, positions)
    for gravitational_model in gravitational_models
]
print(field_valuess)
print(altitudes)

[[np.float64(-9.798285471812783), np.float64(-9.498117084672169), np.float64(-9.211533740415616), np.float64(-8.937727860123543), np.float64(-8.675950994401918), np.float64(-8.42550870321693), np.float64(-8.18575594562386), np.float64(-7.9560929221730206), np.float64(-7.735961319898761), np.float64(-7.524840915948707)], [np.float64(-9.814241041880868), np.float64(-9.513108776825897), np.float64(-9.225633270500504), np.float64(-8.951000633607185), np.float64(-8.688456744928928), np.float64(-8.437302058356305), np.float64(-8.196886929018294), np.float64(-7.9666074000230305), np.float64(-7.74590139862987), np.float64(-7.534245296986336)], [np.float64(-9.814307141616844), np.float64(-9.513178979811148), np.float64(-9.225699538056165), np.float64(-8.95106240934248), np.float64(-8.688514829376778), np.float64(-8.437357149910085), np.float64(-8.196939440406812), np.float64(-7.966657554394403), np.float64(-7.745949325710143), np.float64(-7.534291088893372)], [np.float64(-9.814284387550872), np.float64(-9.513160999207878), np.float64(-9.22568814318402), np.float64(-8.951055205359841), np.float64(-8.688510334843228), np.float64(-8.437354343587772), np.float64(-8.196937668392207), np.float64(-7.9666564151497585), np.float64(-7.745948576059298), np.float64(-7.534290581611349)]]
[0, 100000, 200000, 300000, 400000, 500000, 600000, 700000, 800000, 900000]

field_dfs = [
    pd.DataFrame(
        [
            [altitude, field.tolist()]
            for [altitude, field] in zip(altitudes, field_values)
        ],
        columns=["$altitude [m]$", "$g_x$"],
    )
    for field_values in field_valuess
]

# field_dfs = [pd.DataFrame([[altitude, field.tolist()] for [altitude, field] in zip(altitudes, field_values)], columns=['$altitude [m]$', '$g_x$', '$g_y$', '$g_z$']) for field_values in field_valuess]

Display

Table:

field_dfs[0]

	$altitude [m]$	$g_x$
0	0	-9.798285
1	100000	-9.498117
2	200000	-9.211534
3	300000	-8.937728
4	400000	-8.675951
5	500000	-8.425509
6	600000	-8.185756
7	700000	-7.956093
8	800000	-7.735961
9	900000	-7.524841

Scatter plot:

figure = go.Figure(
    data=[
        go.Scatter(
            x=field_df["$altitude [m]$"],
            y=field_df["$g_x$"],
            name=model.get_type().name,
        )
        for model, field_df in zip(gravitational_models, field_dfs)
    ]
)

figure.show("svg")

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