mice_spkezr |
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## AbstractMICE_SPKEZR returns the state (position and velocity) of a target body relative to an observing body, optionally corrected for light time (planetary aberration) and stellar aberration. ## I/OGiven: targ the name of a target body. Optionally, you may supply the integer ID code for the object as an integer string, i.e. both 'MOON' and '301' are legitimate strings that indicate the Moon is the target body. The target and observer define a state vector whose position component points from the observer to the target. [1,c1] = size(target); char = class(target) or [1,1] = size(target); cell = class(target) et the ephemeris time(s), expressed as seconds past J2000 TDB, at which the state of the target body relative to the observer is to be computed. 'et' refers to time at the observer's location. [1,n] = size(et); double = class(et) ref the name of the reference frame relative to which the output state vector should be expressed. This may be any frame supported by the SPICE system, including built-in frames (documented in the Frames Required Reading) and frames defined by a loaded frame kernel (FK). When 'ref' designates a non-inertial frame, the orientation of the frame is evaluated at an epoch dependent on the selected aberration correction. [1,c2] = size(ref); char = class(ref) or [1,1] = size(ref); cell = class(ref) abcorr the aberration corrections to apply to the state of the target body to account for one-way light time and stellar aberration. [1,c3] = size(abcorr); char = class(abcorr) or [1,1] = size(abcorr); cell = class(abcorr) 'abcorr' may be any of the following: 'NONE' Apply no correction. Return the geometric state of the target body relative to the observer. The following values of 'abcorr' apply to the "reception" case in which photons depart from the target's location at the light-time corrected epoch et-lt and *arrive* at the observer's location at 'et': 'LT' Correct for one-way light time (also called "planetary aberration") using a Newtonian formulation. This correction yields the state of the target at the moment it emitted photons arriving at the observer at 'et'. The light time correction uses an iterative solution of the light time equation (see Particulars for details). The solution invoked by the "LT" option uses one iteration. 'LT+S' Correct for one-way light time and stellar aberration using a Newtonian formulation. This option modifies the state obtained with the "LT" option to account for the observer's velocity relative to the solar system barycenter. The result is the apparent state of the target---the position and velocity of the target as seen by the observer. 'CN' Converged Newtonian light time correction. In solving the light time equation, the "CN" correction iterates until the solution converges (three iterations on all supported platforms). The "CN" correction typically does not substantially improve accuracy because the errors made by ignoring relativistic effects may be larger than the improvement afforded by obtaining convergence of the light time solution. The "CN" correction computation also requires a significantly greater number of CPU cycles than does the one-iteration light time correction. 'CN+S' Converged Newtonian light time and stellar aberration corrections. The following values of 'abcorr' apply to the "transmission" case in which photons *depart* from the observer's location at 'et' and arrive at the target's location at the light-time corrected epoch et+lt: 'XLT' "Transmission" case: correct for one-way light time using a Newtonian formulation. This correction yields the state of the target at the moment it receives photons emitted from the observer's location at 'et'. 'XLT+S' "Transmission" case: correct for one-way light time and stellar aberration using a Newtonian formulation This option modifies the state obtained with the "XLT" option to account for the observer's velocity relative to the solar system barycenter. The position component of the computed target state indicates the direction that photons emitted from the observer's location must be "aimed" to hit the target. 'XCN' "Transmission" case: converged Newtonian light time correction. 'XCN+S' "Transmission" case: converged Newtonian light time and stellar aberration corrections. Neither special nor general relativistic effects are accounted for in the aberration corrections applied by this routine. Neither letter case or embedded blanks are significant in the 'abcorr' string. obs the name of a observing body. Optionally, you may supply the integer ID code for the object as an integer string, i.e. both 'MOON' and '301' are legitimate strings that indicate the Moon is the observing body. [1,c4] = size(target); char = class(target) or [1,1] = size(target); cell = class(target) the call: starg = ## ExamplesAny numerical results shown for this example may differ between platforms as the results depend on the SPICE kernels used as input and the machine specific arithmetic implementation. % % Load a set of kernels: an SPK file, a PCK % file and a leapseconds file. Use a meta % kernel for convenience. % cspice_furnsh( 'standard.tm' ) % % Define parameters for a state lookup: % % Return the state vector of Mars (499) as seen from % Earth (399) in the J2000 frame % using aberration correction LT+S (light time plus % stellar aberration) at the epoch % July 4, 2003 11:00 AM PST. % target = 'Mars'; epoch = 'July 4, 2003 11:00 AM PST'; frame = 'J2000'; abcorr = 'LT+S'; observer = 'Earth'; % % Convert the epoch to ephemeris time. % et = cspice_str2et( epoch ); % % Look-up the state for the defined parameters. % starg = ## ParticularsA sister version of this routine exists named cspice_spkezr that returns the structure field data as separate arguments. Aberration corrections ====================== In space science or engineering applications one frequently wishes to know where to point a remote sensing instrument, such as an optical camera or radio antenna, in order to observe or otherwise receive radiation from a target. This pointing problem is complicated by the finite speed of light: one needs to point to where the target appears to be as opposed to where it actually is at the epoch of observation. We use the adjectives "geometric," "uncorrected," or "true" to refer to an actual position or state of a target at a specified epoch. When a geometric position or state vector is modified to reflect how it appears to an observer, we describe that vector by any of the terms "apparent," "corrected," "aberration corrected," or "light time and stellar aberration corrected." The SPICE Toolkit can correct for two phenomena affecting the apparent location of an object: one-way light time (also called "planetary aberration") and stellar aberration. One-way light time ------------------ Correcting for one-way light time is done by computing, given an observer and observation epoch, where a target was when the observed photons departed the target's location. The vector from the observer to this computed target location is called a "light time corrected" vector. The light time correction depends on the motion of the target relative to the solar system barycenter, but it is independent of the velocity of the observer relative to the solar system barycenter. Relativistic effects such as light bending and gravitational delay are not accounted for in the light time correction performed by this routine. Stellar aberration ------------------ The velocity of the observer also affects the apparent location of a target: photons arriving at the observer are subject to a "raindrop effect" whereby their velocity relative to the observer is, using a Newtonian approximation, the photons' velocity relative to the solar system barycenter minus the velocity of the observer relative to the solar system barycenter. This effect is called "stellar aberration." Stellar aberration is independent of the velocity of the target. The stellar aberration formula used by this routine does not include (the much smaller) relativistic effects. Stellar aberration corrections are applied after light time corrections: the light time corrected target position vector is used as an input to the stellar aberration correction. When light time and stellar aberration corrections are both applied to a geometric position vector, the resulting position vector indicates where the target "appears to be" from the observer's location. As opposed to computing the apparent position of a target, one may wish to compute the pointing direction required for transmission of photons to the target. This also requires correction of the geometric target position for the effects of light time and stellar aberration, but in this case the corrections are computed for radiation traveling *from* the observer to the target. We will refer to this situation as the "transmission" case. The "transmission" light time correction yields the target's location as it will be when photons emitted from the observer's location at `et' arrive at the target. The transmission stellar aberration correction is the inverse of the traditional stellar aberration correction: it indicates the direction in which radiation should be emitted so that, using a Newtonian approximation, the sum of the velocity of the radiation relative to the observer and of the observer's velocity, relative to the solar system barycenter, yields a velocity vector that points in the direction of the light time corrected position of the target. One may object to using the term "observer" in the transmission case, in which radiation is emitted from the observer's location. The terminology was retained for consistency with earlier documentation. Below, we indicate the aberration corrections to use for some common applications: 1) Find the apparent direction of a target for a remote-sensing observation. Use 'LT+S' or 'CN+S' apply both light time and stellar aberration corrections. Note that using light time corrections alone ('LT' or 'CN') is generally not a good way to obtain an approximation to an apparent target vector: since light time and stellar aberration corrections often partially cancel each other, it may be more accurate to use no correction at all than to use light time alone. 2) Find the corrected pointing direction to radiate a signal to a target. This computation is often applicable for implementing communications sessions. Use 'XLT+S' or 'XCN+S' apply both light time and stellar aberration corrections for transmission. 3) Compute the apparent position of a target body relative to a star or other distant object. Use 'LT', 'CN', 'LT+S', or 'CN+S' as needed to match the correction applied to the position of the distant object. For example, if a star position is obtained from a catalog, the position vector may not be corrected for stellar aberration. In this case, to find the angular separation of the star and the limb of a planet, the vector from the observer to the planet should be corrected for light time but not stellar aberration. 4) Obtain an uncorrected state vector derived directly from data in an SPK file. Use 'NONE'. 5) Use a geometric state vector as a low-accuracy estimate of the apparent state for an application where execution speed is critical. Use 'NONE'. 6) While this routine cannot perform the relativistic aberration corrections required to compute states with the highest possible accuracy, it can supply the geometric states required as inputs to these computations. Use 'NONE', then apply relativistic aberration corrections (not available in the SPICE Toolkit). Below, we discuss in more detail how the aberration corrections applied by this routine are computed. Geometric case ============== spkezr_c begins by computing the geometric position T(et) of the target body relative to the solar system barycenter (SSB). Subtracting the geometric position of the observer O(et) gives the geometric position of the target body relative to the observer. The one-way light time, lt, is given by | T(et) - O(et) | lt = ------------------- c The geometric relationship between the observer, target, and solar system barycenter is as shown: SSB ---> O(et) | / | / | / | / T(et) - O(et) V V T(et) The returned state consists of the position vector T(et) - O(et) and a velocity obtained by taking the difference of the corresponding velocities. In the geometric case, the returned velocity is actually the time derivative of the position. Reception case ============== When any of the options "LT", "CN", "LT+S", "CN+S" is selected for `abcorr', spkezr_c computes the position of the target body at epoch et-lt, where `lt' is the one-way light time. Let T(t) and O(t) represent the positions of the target and observer relative to the solar system barycenter at time t; then `lt' is the solution of the light-time equation | T(et-lt) - O(et) | lt = ------------------------ (1) c The ratio | T(et) - O(et) | --------------------- (2) c is used as a first approximation to `lt'; inserting (2) into the right hand side of the light-time equation (1) yields the "one-iteration" estimate of the one-way light time ("LT"). Repeating the process until the estimates of `lt' converge yields the "converged Newtonian" light time estimate ("CN"). Subtracting the geometric position of the observer O(et) gives the position of the target body relative to the observer: T(et-lt) - O(et). SSB ---> O(et) | \ | | \ | | \ | T(et-lt) - O(et) | \ | V V V T(et) T(et-lt) The position component of the light time corrected state is the vector T(et-lt) - O(et) The velocity component of the light time corrected state is the difference T_vel(et-lt)*(1-d(lt)/d(et)) - O_vel(et) where T_vel and O_vel are, respectively, the velocities of the target and observer relative to the solar system barycenter at the epochs et-lt and `et'. If correction for stellar aberration is requested, the target position is rotated toward the solar system barycenter-relative velocity vector of the observer. The rotation is computed as follows: Let r be the light time corrected vector from the observer to the object, and v be the velocity of the observer with respect to the solar system barycenter. Let w be the angle between them. The aberration angle phi is given by sin(phi) = v sin(w) / c Let h be the vector given by the cross product h = r X v Rotate r by phi radians about h to obtain the apparent position of the object. When stellar aberration corrections are used, the rate of change of the stellar aberration correction is accounted for in the computation of the output velocity. Transmission case ================== When any of the options "XLT", "XCN", "XLT+S", "XCN+S" is selected, spkezr_c computes the position of the target body T at epoch et+lt, where `lt' is the one-way light time. `lt' is the solution of the light-time equation | T(et+lt) - O(et) | lt = ------------------------ (3) c Subtracting the geometric position of the observer, O(et), gives the position of the target body relative to the observer: T(et-lt) - O(et). SSB --> O(et) / | * / | * T(et+lt) - O(et) / |* / *| V V V T(et+lt) T(et) The position component of the light-time corrected state is the vector T(et+lt) - O(et) The velocity component of the light-time corrected state consists of the difference T_vel(et+lt)*(1+d(lt)/d(et)) - O_vel(et) where T_vel and O_vel are, respectively, the velocities of the target and observer relative to the solar system barycenter at the epochs et+lt and `et'. If correction for stellar aberration is requested, the target position is rotated away from the solar system barycenter- relative velocity vector of the observer. The rotation is computed as in the reception case, but the sign of the rotation angle is negated. Precision of light time corrections =================================== Corrections using one iteration of the light time solution ---------------------------------------------------------- When the requested aberration correction is "LT", "LT+S", "XLT", or "XLT+S", only one iteration is performed in the algorithm used to compute lt. The relative error in this computation | LT_ACTUAL - LT_COMPUTED | / LT_ACTUAL is at most (V/C)**2 ---------- 1 - (V/C) which is well approximated by (V/C)**2, where V is the velocity of the target relative to an inertial frame and C is the speed of light. For nearly all objects in the solar system V is less than 60 km/sec. The value of C is ~300000 km/sec. Thus the one-iteration solution for LT has a potential relative error of not more than 4e-8. This is a potential light time error of approximately 2e-5 seconds per astronomical unit of distance separating the observer and target. Given the bound on V cited above: As long as the observer and target are separated by less than 50 astronomical units, the error in the light time returned using the one-iteration light time corrections is less than 1 millisecond. The magnitude of the corresponding position error, given the above assumptions, may be as large as (V/C)**2 * the distance between the observer and the uncorrected target position: 300 km or equivalently 6 km/AU. In practice, the difference between positions obtained using one-iteration and converged light time is usually much smaller than the value computed above and can be insignificant. For example, for the spacecraft Mars Reconnaissance Orbiter and Mars Express, the position error for the one-iteration light time correction, applied to the spacecraft-to-Mars center vector, is at the 1 cm level. Comparison of results obtained using the one-iteration and converged light time solutions is recommended when adequacy of the one-iteration solution is in doubt. Converged corrections --------------------- When the requested aberration correction is 'CN', 'CN+S', 'XCN', or 'XCN+S', as many iterations as are required for convergence are performed in the computation of LT. Usually the solution is found after three iterations. The relative error present in this case is at most (V/C)**4 ---------- 1 - (V/C) which is well approximated by (V/C)**4. The precision of this computation (ignoring round-off error) is better than 4e-11 seconds for any pair of objects less than 50 AU apart, and having speed relative to the solar system barycenter less than 60 km/s. The magnitude of the corresponding position error, given the above assumptions, may be as large as (V/C)**4 * the distance between the observer and the uncorrected target position: 1.2 cm at 50 AU or equivalently 0.24 mm/AU. However, to very accurately model the light time between target and observer one must take into account effects due to general relativity. These may be as high as a few hundredths of a millisecond for some objects. Relativistic Corrections ========================= This routine does not attempt to perform either general or special relativistic corrections in computing the various aberration corrections. For many applications relativistic corrections are not worth the expense of added computation cycles. If however, your application requires these additional corrections we suggest you consult the astronomical almanac (page B36) for a discussion of how to carry out these corrections. ## Required ReadingFor important details concerning this module's function, please refer to the CSPICE routine spkezr_c. MICE.REQ SPK.REQ NAIF_IDS.REQ FRAMES.REQ TIME.REQ ## Version-Mice Version 1.0.3, 03-DEC-2014, EDW (JPL) Edited I/O section to conform to NAIF standard for Mice documentation. Discussion of light time corrections was updated. Assertions that converged light time corrections are unlikely to be useful were removed. -Mice Version 1.0.2, 07-NOV-2013 (EDW) I/O descriptions edits to conform to Mice documentation format. Added aberration algorithm explanation to Particulars section. -Mice Version 1.0.1, 22-DEC-2008, EDW (JPL) Header edits performed to improve argument descriptions. These descriptions should now closely match the descriptions in the corresponding CSPICE routine. -Mice Version 1.0.0, 16-DEC-2005, EDW (JPL) ## Index_Entriesusing body names get target state relative to an observer get state relative to observer corrected for aberrations read ephemeris data read trajectory data |

Wed Apr 5 18:00:36 2017