Besselian Epoch to Julian Epoch

R2026b

Transform position and velocity components from discontinued Standard Besselian Epoch (B1950) to Standard Julian Epoch (J2000)

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Besselian Epoch to Julian Epoch block

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Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The Besselian Epoch to Julian Epoch block transforms two 3-by-1 vectors of Besselian Epoch position $$({\overline{r}}_{B1950})$$, and Besselian Epoch velocity $$({\overline{v}}_{B1950})$$ into Julian Epoch position $$({\overline{r}}_{J2000})$$, and Julian Epoch velocity $$({\overline{v}}_{J2000})$$. For more information on the transformation, see Algorithms.

Ports

Input

r_B1950 — Position

3-by-1 vector

Position in Standard Besselian Epoch (B1950), specified as a 3-by-1 vector.

Data Types: double

v_B1950 — Velocity

3-by-1 vector

Velocity in Standard Besselian Epoch (B1950), specified as a 3-by-1 vector.

Data Types: double

Output

r_J2000 — Position

3-by-1 vector

Position in Standard Julian Epoch (J2000), returned as a 3-by-1 vector.

Data Types: double

v_J2000 — Velocity

3-by-1 vector

Velocity in Standard Julian Epoch (J2000), returned as a 3-by-1 vector.

Data Types: double

Algorithms

The transformation is calculated using:

$$\left[\begin{array}{l}{\overline{r}}_{J2000}\\ {\overline{v}}_{J2000}\end{array}\right]=\left[\begin{array}{cc}{\overline{M}}_{rr}& {\overline{M}}_{vr}\\ {\overline{M}}_{rv}& {\overline{M}}_{vv}\end{array}\right]\left[\begin{array}{l}{\overline{r}}_{B1950}\\ {\overline{v}}_{B1950}\end{array}\right]$$

where $$({\overline{M}}_{rr},{\overline{M}}_{vr},{\overline{M}}_{rv},M_{vv})$$ are defined as:

$${\overline{M}}_{rr}\left[\begin{array}{ccc}0.9999256782& -0.0111820611& -0.0048579477\\ 0.0111820610& 0.9999374784& -\text{0}\text{.0000271765}\\ 0.0048579479& -\text{0}\text{.0000271474}& 0.9999881997\end{array}\right]$$

$${\overline{M}}_{vr}=\left[\begin{array}{ccc}0.00000242395018& -\text{0}\text{.00000002710663}& -0.00000001177656\\ 0.00000002710663& 0.00000242397878& -0.00000000006587\\ 0.00000001177656& -0.00000000006582& 0.00000242410173\end{array}\right]$$

$${\overline{M}}_{rv}=\left[\begin{array}{ccc}-0.000551& -0.238565& 0.435739\\ 0.238514& -0.002667& -0.008541\\ -0.435623& 0.012254& 0.002117\end{array}\right]$$

$${\overline{M}}_{vv}=\left[\begin{array}{ccc}0.99994704& -0.01118251& -0.00485767\\ 0.01118251& 0.99995883& -0.00002718\\ 0.00485767& -0.00002714& 1.00000956\end{array}\right]$$

References

[1] "Supplement to Department of Defense World Geodetic System 1984 Technical Report: Part I - Methods, Techniques and Data Used in WGS84 Development," DMA TR8350.2-A.

Extended Capabilities

C/C++ Code Generation
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Version History

Introduced before R2006a