## Principles of Space Navigation Using Pulsars

Transactions of IAA RAS, issue 52, 46–50 (2020)

**DOI**: 10.32876/ApplAstron.52.46-50

**Keywords**:
pulsar timing, pulsar time scale, space navigation

### Abstract

The available methods based on measuring the range of the signal propagation delay from the spacecraft to the ground base station and measuring the angular coordinates of the spacecraft by radio interferometry have a significant drawback associated with the deterioration of the accuracy of the radial coordinate due to the weakening of the response signal as $1/r^{4}$, where $r$ is the distance from the spacecraft to the earth's antenna, and the accuracy of the transversal coordinates as $1/r$. Nature has created sources of highly stable periodic signals – pulsars, the use of which does not have the disadvantages described above. Currently, the accuracy of recording pulsar pulses with the largest radio telescopes is made with submicrosecond accuracy. It is obvious that such accuracy can hardly be realized with an antenna installed on the spacecraft. However, even a microsecond measurement error is quite sufficient for distant interplanetary missions, because it allows to get to a pre-set point of the planet or its moons. The purpose and objective of the present paper is to determine the requirements for onboard spacecraft facilities to observe pulsars in the radio range, to determine the list of pulsars suitable for performing onboard navigation measurements, and to present a mathematical method for calculating the coordinates of the spacecraft by phase ranges and pseudo-distances relative to the barycenter of the Solar system. The paper considers several possible types of antennas: a multi-element phased array, a spherical mirror, and a deployable parabolic mirror with a single bipolarization irradiator. The advantages of the latter are shown by the method of mock-up and full-scale tests. Based on the observational characteristics of pulsars in the radio range, a list of reference pulsars is compiled and their parameters are given. The algorithm for determining the position of the spacecraft and corrections to the onboard scale in the barycentric reference system is described. The numerical simulation method for the elliptical Hofmann flight orbit to Mars shows that the accuracy of determining the coordinates of the spacecraft is 3 km. The error in determining the correction to the onboard time scale is of a few microseconds order. Conclusions: navigation of spacecraft by pulsars has an advantage in deep space, in the near-earth or the nearmoon space it is advisable to use other radio engineering methods that have a higher coordinate accuracy.

### Citation

`A. E. Rodin, V. V. Oreshko, V. A. Potapov. Principles of Space Navigation Using Pulsars // Transactions of IAA RAS. — 2020. — Issue 52. — P. 46–50.`

```
@article{rodin2020,
abstract = {The available methods based on measuring the range of the signal propagation delay from the spacecraft to the ground base station and measuring the angular coordinates of the spacecraft by radio interferometry have a significant drawback associated with the deterioration of the accuracy of the radial coordinate due to the weakening of the response signal as $1/r^{4}$, where $r$ is the distance from the spacecraft to the earth's antenna, and the accuracy of the transversal coordinates as $1/r$.
Nature has created sources of highly stable periodic signals – pulsars, the use of which does not have the disadvantages described above. Currently, the accuracy of recording pulsar pulses with the largest radio telescopes is made with submicrosecond accuracy. It is obvious that such accuracy can hardly be realized with an antenna installed on the spacecraft. However, even a microsecond measurement error is quite sufficient for distant interplanetary missions, because it allows to get to a pre-set point of the planet or its moons. The purpose and objective of the present paper is to determine the requirements for onboard spacecraft facilities to observe pulsars in the radio range, to determine the list of pulsars suitable for performing onboard navigation measurements, and to present a mathematical method for calculating the coordinates of the spacecraft by phase ranges and pseudo-distances relative to the barycenter of the Solar system.
The paper considers several possible types of antennas: a multi-element phased array, a spherical mirror, and a deployable parabolic mirror with a single bipolarization irradiator. The advantages of the latter are shown by the method of mock-up and full-scale tests.
Based on the observational characteristics of pulsars in the radio range, a list of reference pulsars is compiled and their parameters are given. The algorithm for determining the position of the spacecraft and corrections to the onboard scale in the barycentric reference system is described. The numerical simulation method for the elliptical Hofmann flight orbit to Mars shows that the accuracy of determining the coordinates of the spacecraft is 3 km. The error in determining the correction to the onboard time scale is of a few microseconds order.
Conclusions: navigation of spacecraft by pulsars has an advantage in deep space, in the near-earth or the nearmoon space it is advisable to use other radio engineering methods that have a higher coordinate accuracy.},
author = {A.~E. Rodin and V.~V. Oreshko and V.~A. Potapov},
doi = {10.32876/ApplAstron.52.46-50},
issue = {52},
journal = {Transactions of IAA RAS},
keyword = {pulsar timing, pulsar time scale, space navigation},
pages = {46--50},
title = {Principles of Space Navigation Using Pulsars},
url = {http://iaaras.ru/en/library/paper/2035/},
year = {2020}
}
```

```
TY - JOUR
TI - Principles of Space Navigation Using Pulsars
AU - Rodin, A. E.
AU - Oreshko, V. V.
AU - Potapov, V. A.
PY - 2020
T2 - Transactions of IAA RAS
IS - 52
SP - 46
AB - The available methods based on measuring the range of the signal
propagation delay from the spacecraft to the ground base station and
measuring the angular coordinates of the spacecraft by radio
interferometry have a significant drawback associated with the
deterioration of the accuracy of the radial coordinate due to the
weakening of the response signal as $1/r^{4}$, where $r$ is the
distance from the spacecraft to the earth's antenna, and the accuracy
of the transversal coordinates as $1/r$. Nature has created sources
of highly stable periodic signals – pulsars, the use of which does
not have the disadvantages described above. Currently, the accuracy
of recording pulsar pulses with the largest radio telescopes is made
with submicrosecond accuracy. It is obvious that such accuracy can
hardly be realized with an antenna installed on the spacecraft.
However, even a microsecond measurement error is quite sufficient for
distant interplanetary missions, because it allows to get to a pre-
set point of the planet or its moons. The purpose and objective of
the present paper is to determine the requirements for onboard
spacecraft facilities to observe pulsars in the radio range, to
determine the list of pulsars suitable for performing onboard
navigation measurements, and to present a mathematical method for
calculating the coordinates of the spacecraft by phase ranges and
pseudo-distances relative to the barycenter of the Solar system. The
paper considers several possible types of antennas: a multi-element
phased array, a spherical mirror, and a deployable parabolic mirror
with a single bipolarization irradiator. The advantages of the latter
are shown by the method of mock-up and full-scale tests. Based on
the observational characteristics of pulsars in the radio range, a
list of reference pulsars is compiled and their parameters are given.
The algorithm for determining the position of the spacecraft and
corrections to the onboard scale in the barycentric reference system
is described. The numerical simulation method for the elliptical
Hofmann flight orbit to Mars shows that the accuracy of determining
the coordinates of the spacecraft is 3 km. The error in determining
the correction to the onboard time scale is of a few microseconds
order. Conclusions: navigation of spacecraft by pulsars has an
advantage in deep space, in the near-earth or the nearmoon space it
is advisable to use other radio engineering methods that have a
higher coordinate accuracy.
DO - 10.32876/ApplAstron.52.46-50
UR - http://iaaras.ru/en/library/paper/2035/
ER -
```