Sky Projection

Sky Projection#

Various tools for projecting positions onto the sky.

jorbit.astrometry.sky_projection.on_sky(x, v, time, observer_position, acc_func, acc_func_kwargs={}, ltt_position_fn=None, time_reference=0.0)[source]#

Compute the on-sky position of a particle from a given observer position.

This function computes the on-sky position of a particle at a given time, correcting for light travel time. By default it uses a 2nd-order Taylor expansion (position, velocity, acceleration) to propagate backward by the light travel time, where the acceleration is evaluated once at the observation time using acc_func. Three iterations of the light travel time correction are applied, which is sufficient for most cases.

For richer cases (e.g. a distant observer watching a close flyby, where higher-order terms in the polynomial expansion of position around the observation time matter), pass an explicit ltt_position_fn closure. When provided, this replaces both the on-the-fly acceleration evaluation and the constant-acceleration Taylor formula with a user-supplied propagator (typically built from IAS15 b-coefficients).

Note: you can vmap this function, but don’t pass multiple particles at once: each one needs its own light travel time correction.

Parameters:

  • x (Array) – Position of the particle, shape (3,).

  • v (Array) – Velocity of the particle, shape (3,).

  • time (float) – Time at which to compute the on-sky position, expressed as the relative_time offset (in days) against time_reference. The acceleration is evaluated at the absolute JD time + time_reference. Pass an absolute JD (TDB) here with time_reference=0.0 for standalone use.

  • observer_position (Array) – Position of the observer, shape (3,).

  • acc_func (Partial) – Acceleration function to use during light travel time correction. Must be a continuous function that can evaluate the positions of any fixed perturbers at arbitrary times. Ignored when ltt_position_fn is provided.

  • acc_func_kwargs (dict) – Additional arguments for the acceleration function.

  • ltt_position_fn (Partial | None) – Optional callable mapping a (negative) time offset dt to the particle’s position at time + dt. When provided, this is used inside the LTT iteration in place of the constant-acceleration Taylor expansion, and acc_func is not called. Default None preserves the original Taylor-based behavior.

  • time_reference (float) – Absolute JD (TDB) anchor that time is measured against. The acceleration is evaluated at time + time_reference. Defaults to 0.0 (i.e. time is treated as an absolute JD). Ignored when ltt_position_fn is provided.

Returns:

The right ascension and declination of the particle in radians, ICRS.

Return type:

tuple[float, float]

jorbit.astrometry.sky_projection.sky_sep(ra1, dec1, ra2, dec2)[source]#

Compute the angular separation between two points on the sky.

Following Astropy’s SkyCoord.separation, this uses the Vincenty formula.

Parameters:

  • ra1 (float) – Right ascension of the first position in radians.

  • dec1 (float) – Declination of the first position in radians.

  • ra2 (float) – Right ascension of the second position in radians.

  • dec2 (float) – Declination of the second position in radians.

Returns:

The angular separation in arcseconds.

Return type:

float

jorbit.astrometry.sky_projection.tangent_plane_projection(ra_ref, dec_ref, ra, dec)[source]#

Project a point on the sky onto a tangent plane at a reference point.

Somewhat overkill, rotates the positions to the equator to avoid any potential issues near the poles.

Parameters:

  • ra_ref (float) – Right ascension of the reference point in radians.

  • dec_ref (float) – Declination of the reference point in radians.

  • ra (float) – Right ascension of the point to project in radians.

  • dec (float) – Declination of the point to project in radians.

Returns:

The projected coordinates in arcseconds.

Return type:

Array