RU2566379C1 - Method for determining value of atmospheric refraction under conditions of space flight - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: method is based on deviation of true and measured position of a star observed through earth atmosphere. Deviation is related to atmospheric refraction. For that purpose, measurements of angular distances between visible position of the known star, the beams of which are subject to refraction in atmosphere, and position of each of at least two stars located above atmosphere, the beams of which pass above atmosphere and are not subject to refraction, are performed simultaneously by means of a star instrument. A value of atmospheric refraction angle at measurement is determined as per the measured distances.

EFFECT: determination of an atmospheric refraction value for its use in an independent navigation system of a space vehicle in order to specify orbit parameters.

5 dwg

Description

The method for determining the amount of atmospheric refraction (ρ) in space flight conditions for determining the parameters of the orbit of a spacecraft is intended for use in motion control systems (SUD) and autonomous navigation (AN) of a spacecraft (SC).

During the spacecraft flight at significant distances from the Earth, for example, when flying from near-Earth orbit to the lunar orbit, it is necessary to clarify the orbit parameters, for which the spacecraft’s autonomous navigation system provides for the measurement of various navigation parameters.

The most famous navigation parameter, which is measured to clarify the parameters of the spacecraft orbit, is the angular distance at a given point in time between a known (recognized) star and the visible horizon of the planet. To measure this navigation parameter, a well-known method using a sextant is used, as was done during Apollon’s flights to the Moon. A description of the method for measuring this navigation parameter is given in the book “Navigation, Guidance and Stabilization in Space”, ed. "Engineering", Moscow, 1970, p. 235, dedicated to the Apollon spacecraft.

However, this method of measuring this navigation parameter has several disadvantages:

- the uncertainty of the position of the line of the visible horizon relative to the surface of the planet;

- the need for a certain orientation of the measuring plane of the sextant relative to the line of the visible horizon.

As an analogue of the method, the method proposed by the American scientist Kenneth R. can be used to measure the navigation parameter (to clarify the parameters of the orbit of the spacecraft) as the angle between the true direction to the star and the visible direction to the star whose light rays were refracted (deflected) in the Earth’s atmosphere (patent No. 3439427, USA).

However, the method for measuring such a navigation parameter in comic flight conditions proposed in US Pat. No. 3,439,427 requires:

- sophisticated precision equipment (gyroscopes),

- preliminary guidance of the axis of the measuring instrument (telescope) on the star before it is immersed in the atmosphere,

stabilization of this axis in inertial space either using a gyro-stabilized platform on which the telescope is mounted, or stabilization of the entire spacecraft,

- tracking the track of the star with fixing the measurement time,

- calculation of the angle of refraction by the size of the track,

- repeat measurements, for at least 6 stars, to determine the position of the spacecraft in orbit by classical methods for determining the orbit by 6 parameters.

The disadvantages of this method include a significant error, a relatively large measurement time, as well as the need for a large instrumentation to implement this method.

A prototype of the claimed method was not found.

The objective of the invention is the ability to determine the parameters of the orbit with high accuracy and speed while simplicity of the hardware.

To solve this problem, a navigation parameter is determined - the magnitude of the angle of refraction of a star entering beyond the planet’s atmosphere, for which they simultaneously measure the angular distances between the visible position of a known star whose rays are refracted in the atmosphere and two other known stars whose rays pass above the atmosphere and do not are refracted. For these measurements, for example, a star sensor can be used. The relative position of these three stars, the surface of the planet and the atmosphere in the angular field of the stellar instrument are shown in FIG. 1. Using the instrument at the same time (at the time when one of the stars is observed through the atmosphere), the angular distances between the 1st and 3rd stars — µ ′, are measured between the 2nd and 3rd stars — λ ′.

The angular distance between the 1st and 2nd stars is α, as well as the true (i.e., excluding atmospheric refraction) angular distances between the 1st and 3rd stars are μ and between the 2nd and 3rd stars - λ - constants (calculated by the coordinates of these three stars given in the star catalog).

The value of the angle of atmospheric refraction ρ is calculated by the formula below:

Where

α is the known angular distance between the first and second stars located above the Earth’s atmosphere, relative to which they take angular measurements relative to the third star, which extends beyond the Earth’s horizon,

µ is the known angular distance between the first star located above the upper boundary of the Earth’s atmosphere and the third star entering the Earth’s atmosphere without taking into account atmospheric refraction,

λ is the known angular distance between the second star located above the upper boundary of the Earth’s atmosphere and the third star entering the Earth’s atmosphere without taking into account atmospheric refraction,

µ ′ is the measured angular distance between the first star located above the upper boundary of the Earth’s atmosphere and the third star falling beyond the Earth’s atmosphere (i.e., taking into account atmospheric refraction),

λ ′ is the measured angular distance between the second star located above the upper boundary of the Earth’s atmosphere and the third star entering the Earth’s atmosphere (i.e., taking into account atmospheric refraction);

As an example, let us show the determination of the angle of refraction from the measurements with a spacecraft using a stellar instrument of the angular distances between three stars from the constellation Southern Cross, one of which extends beyond the Earth’s atmosphere. Geocentric coordinates of stars (era J2000):

1st star: β Southern Cross α ₁ = 191 ° 55′48 ′ ′, δ ₁ = -59 ° 41′19 ′ ′,

2nd star: γ of the Southern Cross α ₂ = 187 ° 47′28 ′ ′, δ ₂ = -57 ° 06′47 ′ ′,

3rd star: α of the Southern Cross α ₃ = 186 ° 38′58 ′ ′, δ ₃ = -63 ° 05′56 ′ ′,

The 3rd star sets behind the Earth’s atmosphere.

True angular distances between stars (excluding atmospheric refraction) are:

between the 1st and 2nd stars, the angle α = 3.6571 °,

between the 1st and 3rd stars, the angle µ = 4.24237 °,

between the 2nd and 3rd stars, the angle λ = 6.01256 °.

The measured angular distances between the third star entering the atmosphere and the stars above the atmosphere were:

between the 1st and 3rd stars, the angle µ ′ = 4.378 °,

between the 2nd and 3rd stars, the angle λ ′ = 6.169 °.

Substituting the calculated and measured values into the formula, we obtain the value of the angle of refraction ρ = 9.39486′≈2.73 mrad.

The relative position of the spacecraft and the beam path from the star (lines ed, db, bc, cKA) are shown in FIG. 2. The height H corresponds to the segment ab lying on a line coinciding with the radius of the Earth, and the point b corresponds to the maximum immersion of the ray from the star observed from the spacecraft's point. The dependence of the angle of refraction ρ on the height H is known (tabular values for different wavelengths of optical radiation, geographical latitudes and seasons). An example of a graph of the dependence of the angle of refraction ρ on height H for a wavelength of 0.850 μm and mid-latitudes is shown in FIG. 3. According to this graph, the value of the angle of refraction ρ≈2.73 mrad calculated above in the example corresponds to the height of the beam from the star above the Earth’s surface H≈13 km.

The position of the spacecraft in orbit in the geocentric coordinate system is determined by the angle θ between the spacecraft vectors — the center of the planet and the spacecraft — the first star shown in FIG. 2, and the angle η between the spacecraft vectors is the center of the planet and the spacecraft is the second star. The angles θ and η in the projection of spherical triangles onto a plane are shown in FIG. 4, as well as in FIG. 5 in the planes of 1 star. - KA-O and 2 stars. - KA-O. The calculation of the angles θ and η is performed according to the formulas:

and

,

,

Where

θ is the angle between the direction of the first star above the atmosphere and the direction of the local vertical for the spacecraft,

η is the angle between the direction of the second star above the atmosphere and the direction of the local vertical for the spacecraft,

R is the radius of the planet,

H ₀ - spacecraft orbit,

h is the height of the refracted ray from the third star, for the angle of refraction ρ.

As an example, we calculate the angles θ and η using the above formulas for the following initial data: R = 6371 km, H ₀ = 300 km, ρ = 0.006 rad, h = 30 km, µ = 4.6 °, µ ′ = 4.59 °, λ = 6.6 °, λ ′ = 6.58 °. After substituting the initial data in the above formulas, we obtain:

θ≈73.656 ° and η≈73.962 °.

Similar measurements at another moment in time and in another direction (in azimuth), as described above, make it possible to determine the second position of the spacecraft's point in orbit, and, therefore, to refine the parameters of the orbit.

Thus, the task is solved. In figures 1-5 shows:

1 star - 1st famous star observed over the planet’s atmosphere,

2 stars - The 2nd famous star observed over the atmosphere of the planet,

3 stars - 3rd famous star observed through the atmosphere of the planet (true position without refraction),

3 ′ sound - The 3rd known star, observed through the atmosphere of the planet (visible position, taking into account refraction),

A is the atmosphere of the planet

P is the solid surface of the planet,

α is the angular distance between the 1st and 2nd known stars observed above the planet’s atmosphere,

λ is the angular distance between the 2nd star and the true position of the 3rd star,

λ ′ is the angular distance between the 2nd star and the visible position of the 3rd star,

µ is the angular distance between the 1st star and the true position of the 3rd star,

µ ′ is the angular distance between the 1st star and the visible position of the 3rd star,

ρ is the angle of refraction of the beam from the 3rd star at the time of measurement,

R is the radius of the planet,

But - the height of the orbit,

KA - spacecraft,

h is the maximum height of the refracted ray above the surface of the planet,

θ is the angle between the directions of the spacecraft - the 1st star and the spacecraft - O (center of the planet),

η is the angle between the directions of the spacecraft - the 2nd star and the spacecraft - O (center of the planet).

The advantages of the described method in comparison with the analogue are:

1. Reduction of error.

The duration of the measurements affects the accuracy of the method. For example, if the measurement time is ~ 1 ms (which is enough for a modern stellar instrument), then during this time the spacecraft will shift in orbit by ~ 7.5 m, at an orbital speed of 7.5 km / s. This bias will constitute a positioning error for a single measurement cycle. In subsequent measurements, this error can be taken into account and minimized. In the case of the analogue mentioned above, where the star’s track is measured, the duration of the measurement is determined by the length of the star’s track on the sensitive element of the measuring instrument, whose axis is stabilized. Thus, when a star ray is immersed in the atmosphere to a depth of ~ 20 km (from the surface to the beam), the angular track size of the refracted star is ~ 5 ′. When the angular velocity of stellar approach (in the orbit plane) is ~ 4 ′ / s, and if we assume that above 50 km the refraction angle is practically ~ 0, then the measurement time will be:

T _rev. = arctan [(50 km - 20 km) / 2300 km] / (4 ′ / s) ≈10 s,

which corresponds to an orbital displacement of ~ 75 km. Those. the error of the claimed method (7.5 m) is significantly less than the error of the analogue (75 km). In total, to fully determine the position of the spacecraft in orbit for a method adopted as an analogue, at least 6 measurements are needed, which accordingly leads to an increase in the error and complexity of its accounting.

2. Reduction of measurement time.

The duration of the measurement process, including at least 6 measurements, for the method considered as an analogue is at least 60 s, which is several times longer than the required time for the claimed method ~ 1 ms.

3. The simplicity of the hardware.

For the claimed method, a modern star sensor can be used, in the memory of which a star catalog with the coordinates of the stars is stored, and having a processor for processing the measurement results. The position of the spacecraft is determined by the results of measurements in the computer complex of the spacecraft.

For the method indicated as an analogue, the following components are required:

- measuring instrument - telescope in a gimbal suspension,

- a telescope pointing system for a given star,

- a stabilization system to maintain the direction of the axis of the telescope to the star in the process of measuring the track of the star (due to refraction) on the sensitive element of the telescope,

- a processor for processing measurement results and calculating the position of the spacecraft

- A control system for interfacing and coordinated operation of all constituent components.

As you can see, in the case of an analogue, the instrumentation for solving the problem exceeds the instrumentation for the claimed method in terms of nomenclature (quantitative composition of components), and therefore, in volume, mass, dimensions, power consumption, i.e. those parameters that are of great importance for spacecraft.

Literature

1. “Navigation, guidance and stabilization in space”, ed. "Engineering", Moscow, 1970,

2. Patent No. 3439427, USA.

Claims (1)

A method for determining the angle of atmospheric refraction in a space flight, characterized in that the angular distances between one star observed through the atmosphere and each of at least two stars above the atmosphere are simultaneously measured, and the angle of atmospheric refraction is determined from the measured distances moment of measurement according to the formula:

,
Where
ρ is the angle of atmospheric refraction,
α is the known angular distance between the first and second stars located above the planet’s atmosphere, relative to which they take angular measurements relative to the third star, which goes beyond the planet’s horizon,
µ is the known angular distance between the first star located above the upper boundary of the planet’s atmosphere and the third star entering the planet’s atmosphere without taking into account atmospheric refraction,
λ is the known angular distance between the second star located above the upper boundary of the planet’s atmosphere and the third star entering the planet’s atmosphere without taking into account atmospheric refraction,
µ ′ is the measured angular distance between the first star located above the upper boundary of the planet’s atmosphere and the third star falling beyond the planet’s atmosphere (i.e., taking into account atmospheric refraction),
λ ′ is the measured angular distance between the second star located above the upper boundary of the planet’s atmosphere and the third star entering beyond the planet’s atmosphere (i.e., taking into account atmospheric refraction).

Images