Synodic Frame Trajectory Plots¶

plot_synodic_3d renders 3D trajectories in a synodic (two-body rotating) frame: EMR (Earth-Moon Rotating), SER (Sun-Earth Rotating), GSE (Geocentric Solar Ecliptic), or a generic CelestialFrame.Synodic(origin, primary, secondary). Each input trajectory is converted to ECI and then transformed per-epoch into the requested frame via state_frame_to_frame. The frame's primary and secondary bodies are drawn as textured spheres at a single reference epoch, since a synodic frame keeps both bodies on the x-axis at all times.

plot_earth_moon_rotating_3d is an alias for plot_synodic_3d(trajectories, frame="EMR", ...); it accepts the same keyword arguments.

Input Requirement¶

plot_synodic_3d only accepts OrbitTrajectory objects, unlike plot_trajectory_3d and brahe's other plotting functions, which also accept propagators or raw arrays. Pass a KeplerianPropagator's or numerical propagator's .trajectory attribute directly.

Frame Selection¶

The frame parameter accepts:

A frame alias string: 'EMR', 'SER', or 'GSE'
Any other CelestialFrame name string accepted by CelestialFrame.from_string
A CelestialFrame.Synodic(origin, primary, secondary) instance for a custom two-body pair

See Synodic Reference Frames for the axis construction and physical definition of each frame. Passing a non-synodic frame raises ValueError.

Reference Epoch¶

reference_epoch sets the epoch at which the primary and secondary spheres are placed. It defaults to the first epoch of the first trajectory in trajectories, and must be supplied explicitly if trajectories is empty.

Example¶

The example below propagates a LEO trajectory with a KeplerianPropagator, then renders it in the Earth-Moon Rotating frame with plot_earth_moon_rotating_3d - the plot_synodic_3d(..., frame="EMR", ...) alias described above.

Plot Source

synodic_plot_plotly.py
#!/usr/bin/env python
# /// script
# dependencies = ["brahe", "plotly", "numpy"]
# FLAGS = ["NETWORK"]
# ///
"""
Synodic Frame Trajectory Plotting Example - Plotly Backend

This script demonstrates how to create an interactive 3D trajectory plot in
the Earth-Moon Rotating (EMR) frame using the plotly backend. Shows a LEO
orbit alongside the Earth and Moon, both fixed on the synodic x-axis.
"""

import os
import pathlib
import sys

import numpy as np

import brahe as bh

# Add plots directory to path for importing brahe_theme
sys.path.insert(0, str(pathlib.Path(__file__).parent.parent.parent))
from brahe_theme import save_themed_html

# Configuration
SCRIPT_NAME = pathlib.Path(__file__).stem
OUTDIR = pathlib.Path(os.getenv("BRAHE_FIGURE_OUTPUT_DIR", "./docs/figures/"))
os.makedirs(OUTDIR, exist_ok=True)

# Initialize EOP data and the DE440s ephemeris the EMR transform needs
bh.initialize_eop()
bh.load_common_spice_kernels()

# LEO orbit (51.6 deg inclination, ~500 km altitude)
epoch = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.TimeSystem.UTC)
oe = np.array([bh.R_EARTH + 500e3, 0.001, 51.6, 15.0, 30.0, 45.0])
state = bh.state_koe_to_eci(oe, bh.AngleFormat.DEGREES)

prop = bh.KeplerianPropagator.from_eci(epoch, state, 60.0)
prop.propagate_to(epoch + bh.orbital_period(oe[0]))

# Create the Earth-Moon Rotating 3D trajectory plot
fig = bh.plot_earth_moon_rotating_3d(
    [{"trajectory": prop.trajectory, "color": "red", "label": "LEO"}],
    backend="plotly",
)

# Save as interactive HTML (small file size, no large textures)
light_path, dark_path = save_themed_html(fig, OUTDIR / SCRIPT_NAME)
print(f"✓ Generated {light_path}")
print(f"✓ Generated {dark_path}")

print("\nSynodic plot generated successfully!")

Additional Bodies¶

The bodies parameter adds extra textured spheres beyond the frame's primary/secondary, each a dict with position (meters, in the synodic frame), radius (meters), texture, and name - the same shape as additional_bodies in plot_trajectory_3d.

Shared Parameters¶

units, view_azimuth, view_elevation, view_distance, sphere_resolution_lon, sphere_resolution_lat, backend, width, and height behave identically to plot_trajectory_3d.

Primary/secondary body textures are downloaded on first use from Solar System Scope:

Body textures: Solar System Scope, CC BY 4.0.