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Relativistic Effects

General relativistic corrections to satellite acceleration.

Note

For conceptual explanations and examples, see Relativistic Effects in the Learn section.

Relativistic Acceleration

accel_relativity builtin 

accel_relativity(x_object: ndarray) -> ndarray

Calculate acceleration due to special and general relativity.

Parameters:

Name Type Description Default
x_object ndarray

State vector of the object in ECI frame. Units: [m; m/s]

 required

Returns:

Type Description
ndarray

np.ndarray: Acceleration due to relativistic effects. Units: (m/s²)
Example 
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import brahe as bh
import numpy as np

x_object = np.array([bh.R_EARTH + 500e3, 0.0, 0.0, 0.0, 7500.0, 0.0])
a_rel = bh.accel_relativity(x_object)

Arbitrary Central Body

accel_relativity_for_body builtin 

accel_relativity_for_body(x_object: ndarray, gm: float) -> ndarray

Calculate acceleration due to special and general relativity for an object orbiting a central body with an arbitrary gravitational parameter.

Generalizes accel_relativity to non-Earth central bodies. accel_relativity is equivalent to calling this with gm = GM_EARTH.

Parameters:

Name Type Description Default
x_object ndarray

State vector of the object in the central body's inertial frame. Units: [m; m/s]

 required
gm float

Gravitational parameter of the central body. Units: (m^3/s^2)

 required

Returns:

Type Description
ndarray

np.ndarray: Acceleration due to relativistic effects. Units: (m/s²)
Example 
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import brahe as bh
import numpy as np

x_object = np.array([bh.R_MOON + 100e3, 0.0, 0.0, 0.0, 1600.0, 0.0])
a_rel = bh.accel_relativity_for_body(x_object, bh.GM_MOON)

See Also