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Orbits Commands

The orbits command group provides calculations for: - Orbital period and semi-major axis - Mean motion - Anomaly conversions (mean, eccentric, true) - Sun-synchronous orbit design - Perigee and apogee velocities

All commands support constant expressions (e.g., R_EARTH+500e3).

Commands

orbital-period

Calculate the orbital period from semi-major axis.

Syntax: 

1
brahe orbits orbital-period <SEMI_MAJOR_AXIS> [OPTIONS]

Arguments: - SEMI_MAJOR_AXIS - Semi-major axis in meters (supports constants)

Options: - --gm <value> - Gravitational parameter (m³/s²). Default: GM_EARTH - --units [seconds|minutes|hours|days|years] - Output time units (default: seconds) - --format <fmt> - Output format string (default: f)

Examples:

LEO orbit period (500km altitude): 

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brahe orbits orbital-period "R_EARTH+500e3"
Output: 
1
# 5676.977164
(Period: ~94.6 minutes)

With different units: 

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brahe orbits orbital-period "R_EARTH+500e3" --units minutes
Output: 
1
# 94.616286

GEO orbit period (should be ~24 hours): 

1
brahe orbits orbital-period "R_EARTH+35786e3" --units hours
Output: 
1
# 23.934441

Moon's orbit (using GM_EARTH): 

1
brahe orbits orbital-period 384400e3 --units days
Output: 
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# 27.451894

Mars orbit (using GM_SUN): 

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brahe orbits orbital-period 227.9e9 --gm GM_SUN --units days
Output: 
1
# 686.794481

sma-from-period

Calculate semi-major axis from orbital period.

Syntax: 

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brahe orbits sma-from-period <PERIOD> [OPTIONS]

Arguments: - PERIOD - Orbital period (supports expressions)

Options: - --units [seconds|minutes|hours|days|years] - Input time units (default: seconds) - --gm <value> - Gravitational parameter (m³/s²). Default: GM_EARTH - --format <fmt> - Output format string (default: f)

Examples:

Find altitude for 90-minute orbit: 

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brahe orbits sma-from-period 90 --units minutes
Output: 
1
# 6652555.699659
(Semi-major axis: ~6653 km → altitude ~275 km)

Find GEO altitude (24-hour period): 

1
brahe orbits sma-from-period 24 --units hours
Output: 
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# 42241095.663660
(Semi-major axis: ~42164 km → altitude ~35786 km above Earth surface)

Calculate altitude: 

1
2
# SMA - R_EARTH = altitude
echo "scale=2; ($(brahe orbits sma-from-period 90 --units minutes) - 6378137) / 1000" | bc
Output: 
1
# 274.41

mean-motion

Calculate mean motion (radians per second).

Syntax: 

1
brahe orbits mean-motion <SEMI_MAJOR_AXIS> [OPTIONS]

Arguments: - SEMI_MAJOR_AXIS - Semi-major axis in meters (supports constants)

Options: - --gm <value> - Gravitational parameter (m³/s²). Default: GM_EARTH - --format <fmt> - Output format string (default: f)

Examples:

Mean motion for LEO (500km): 

1
brahe orbits mean-motion "R_EARTH+500e3"
Output: 
1
# 0.001107

anomaly-conversion

Convert between mean, eccentric, and true anomaly.

Syntax: 

1
brahe orbits anomaly-conversion <ANOMALY> <ECCENTRICITY> <INPUT_ANOMALY> <OUTPUT_ANOMALY> [OPTIONS]

Arguments: - ANOMALY - Anomaly value to convert (supports expressions) - ECCENTRICITY - Orbital eccentricity (supports expressions) - INPUT_ANOMALY - Input type: mean, eccentric, or true - OUTPUT_ANOMALY - Output type: mean, eccentric, or true

Options: - --as-degrees / --no-as-degrees - Use degrees (default: --no-as-degrees = radians) - --format <fmt> - Output format string (default: f)

Examples:

Mean anomaly to true anomaly (circular orbit): 

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brahe orbits anomaly-conversion 0.785 0.0 mean true
Output: 
1
# 0.785000
(For circular orbit, mean = eccentric = true)

Mean to true (eccentric orbit): 

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brahe orbits anomaly-conversion --as-degrees 45.0 0.1 mean true
Output: 
1
# 53.849399

True to mean anomaly: 

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brahe orbits anomaly-conversion --as-degrees 90.0 0.05 true mean
Output: 
1
# 84.272810

Eccentric to true anomaly: 

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brahe orbits anomaly-conversion --as-degrees 60.0 0.2 eccentric true
Output: 
1
# 70.528779

sun-sync-inclination

Calculate the inclination required for a sun-synchronous orbit.

Syntax: 

1
brahe orbits sun-sync-inclination <SEMI_MAJOR_AXIS> <ECCENTRICITY> [OPTIONS]

Arguments: - SEMI_MAJOR_AXIS - Semi-major axis in meters (supports constants) - ECCENTRICITY - Eccentricity (supports expressions)

Options: - --as-degrees / --no-as-degrees - Output in degrees (default: --as-degrees) - --format <fmt> - Output format string (default: f)

Examples:

Sun-sync inclination for 500km circular orbit: 

1
brahe orbits sun-sync-inclination "R_EARTH+500e3" 0.0
Output: 
1
# 97.401744
(Inclination: ~97.42°)

Sun-sync for 600km orbit: 

1
brahe orbits sun-sync-inclination "R_EARTH+600e3" 0.001
Output: 
1
# 97.787587

Sun-sync for 800km orbit: 

1
brahe orbits sun-sync-inclination "R_EARTH+800e3" 0.0
Output: 
1
# 98.603036

Output in radians: 

1
brahe orbits sun-sync-inclination "R_EARTH+500e3" 0.0 --no-as-degrees
Output: 
1
# 1.699981

perigee-velocity

Calculate orbital velocity at perigee (closest approach).

Syntax: 

1
brahe orbits perigee-velocity <SEMI_MAJOR_AXIS> <ECCENTRICITY> [OPTIONS]

Arguments: - SEMI_MAJOR_AXIS - Semi-major axis in meters (supports constants) - ECCENTRICITY - Eccentricity (supports expressions)

Options: - --format <fmt> - Output format string (default: f)

Examples:

Circular orbit velocity (500km): 

1
brahe orbits perigee-velocity "R_EARTH+500e3" 0.0
Output: 
1
# 7612.608558

Eccentric orbit perigee velocity: 

1
brahe orbits perigee-velocity "R_EARTH+500e3" 0.1
Output: 
1
# 8416.055421

GTO perigee velocity (highly eccentric): 

1
brahe orbits perigee-velocity "R_EARTH+24000e3" 0.73
Output: 
1
# 9169.158794

apogee-velocity

Calculate orbital velocity at apogee (farthest point).

Syntax: 

1
brahe orbits apogee-velocity <SEMI_MAJOR_AXIS> <ECCENTRICITY> [OPTIONS]

Arguments: - SEMI_MAJOR_AXIS - Semi-major axis in meters (supports constants) - ECCENTRICITY - Eccentricity (supports expressions)

Options: - --format <fmt> - Output format string (default: f)

Examples:

Circular orbit (apogee = perigee): 

1
brahe orbits apogee-velocity "R_EARTH+500e3" 0.0
Output: 
1
# 7612.608558

Eccentric orbit apogee velocity: 

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brahe orbits apogee-velocity "R_EARTH+500e3" 0.1
Output: 
1
# 6885.863526
(Lower velocity at apogee)

Compare perigee vs apogee: 

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echo "Perigee: $(brahe orbits perigee-velocity 'R_EARTH+500e3' 0.1) m/s"
echo "Apogee:  $(brahe orbits apogee-velocity 'R_EARTH+500e3' 0.1) m/s"
Output: 
1
2
# Perigee: 8416.055421 m/s
# Apogee:  6885.863526 m/s

See Also