How many times is the orbital period of an artificial satellite moving? "satellite photometry" The period of rotation of a satellite around the earth

2007

main idea

This site is dedicated to surveillance issues artificial earth satellites(Further satellite ). Since the beginning of the space age (October 4, 1957, the first satellite, Sputnik 1, was launched), humanity has created a huge number of satellites that circle the Earth in all kinds of orbits. Currently, the number of such man-made objects exceeds tens of thousands. This is mainly “space debris” - fragments of artificial satellites, spent rocket stages, etc. Only a small part of them are operational satellites.
Among them there are research and meteorological satellites, communications and telecommunications satellites, and military satellites. The space around the Earth is “populated” by them from altitudes of 200-300 km and up to 40,000 km. Only some of them are accessible for observation using inexpensive optics (binoculars, telescopes, amateur telescopes).

By creating this site, the authors set themselves the goal of collecting together information about methods of observing and filming satellites, showing how to calculate the conditions for their flight over a certain area, and describing the practical aspects of the issue of observation and filming. The site presents mainly original material obtained during observations by participants in the “Cosmonautics” section of the astronomy club “hν” at the Minsk Planetarium (Minsk, Belarus).

And yet, answering the main question - “Why?”, the following must be said. Among the various hobbies that people are interested in are astronomy and astronautics. Thousands of astronomy enthusiasts observe planets, nebulae, galaxies, variable stars, meteors and other astronomical objects, photograph them, and hold their own conferences and “master classes.” For what? It's just a hobby, one of many. A way to get away from everyday problems. Even when amateurs perform work of scientific significance, they remain amateurs who do it for their own pleasure. Astronomy and astronautics are very “technological” hobbies where you can apply your knowledge of optics, electronics, physics and other natural science disciplines. Or you don’t have to use it - and just enjoy contemplation. The situation with satellites is similar. It is especially interesting to monitor those satellites, information about which is not distributed in open sources- these are military reconnaissance satellites different countries. In any case, satellite observation is hunting. Often we can indicate in advance where and when the satellite will appear, but not always. And how he will “behave” is even more difficult to predict.

Thanks:

The described methods were created on the basis of observations and research in which members of the astronomy club "hν" of the Minsk Planetarium (Belarus) took part:

  • Bozbey Maxim.
  • Dremin Gennady.
  • Kenko Zoya.
  • Mechinsky Vitaly.

Members of the astronomy club "hν" also provided great assistance. Lebedeva Tatyana, Povalishev Vladimir And Tkachenko Alexey. Special thanks Alexander Lapshin(Russia), profi-s (Ukraine), Daniil Shestakov (Russia) and Anatoly Grigoriev (Russia) for help in creating paragraph II §1 “Satellite Photometry”, Chapter 2 and Chapter 5, and Elena (Tau, Russia) also for consultations and writing several calculation programs. The authors also thank Mikhail Abgaryan (Belarus), Yuri Goryachko (Belarus), Anatoly Grigoriev (Russia), Leonid Elenin (Russia), Victor Zhuk (Belarus), Igor Molotov (Russia), Konstantin Morozov (Belarus), Sergei Plaksa (Ukraine), Ivan Prokopyuk (Belarus) for providing illustrations for some sections of the site.

Some of the materials were received during the implementation of an order from the Geographic Information Systems Unitary Enterprise of the National Academy of Sciences of Belarus. The presentation of materials is carried out on a non-commercial basis in order to popularize the Belarusian space program among children and youth.

Vitaly Mechinsky, Curator of the “Cosmonautics” section of the “hν” astroclub.

Site news:

  • 09/01/2013: Significantly updated subparagraph 2 "Photometry of satellites during flight" p. II §1 - ​​information has been added on two methods of photometry of satellite tracks (method of photometric track profile and method of isophote photometry).
  • 09/01/2013: Subclause II §1 was updated - information on working with the "Highecl" program for calculating probable outbreaks from the GSS was added.
  • 01/30/2013: Updated "Chapter 3"-- added information on working with the "MagVision" program to calculate the drop in penetration from illumination from the Sun and Moon.
  • 01/22/2013: Updated Chapter 2. Added animation of satellites moving across the sky in one minute.
  • 01/19/2013: Subsection updated "Visual observations of satellites" paragraph 1 "Determination of satellite orbits" §1 of Chapter 5. Added information about heating devices for electronics and optics to protect against dew, frost and excessive cooling.
  • 01/19/2013: Added to "Chapter 3" information about the drop in penetration when illuminated by the Moon and twilight.
  • 01/09/2013: Added sub-item "Flashes from the lidar satellite "CALIPSO" subclause “Photography of flashes”, paragraph II “Photometry of satellites” §1 of Chapter 5. Information on the features of observing flashes from the laser lidar of the satellite “CALIPSO” and the process of preparing for them are described.
  • 11/05/2012: The introductory part of §2 of Chapter 5 has been updated. Information on the required minimum equipment for radio observations of satellites has been added, and a diagram has also been provided LED indicator signal level, which is used to set a safe input audio signal level for the recorder.
  • 11/04/2012: Sub-clause updated "Visual observations of satellites" paragraph 1 "Determination of satellite orbits" §1 of Chapter 5. Added information about the Brno star atlas, as well as about the red film on LCD screens electronic devices, used in observations.
  • 04/14/2012: Updated sub-item of the sub-item "Photo/video shooting of satellites" clause 1 "Determination of satellite orbits" §1 of Chapter 5. Added information about working with the "SatIR" program for identifying satellites in photographs with a wide field of view, as well as determining coordinates ends of satellite tracks on them.
  • 04/13/2012: Subsection updated "Astrometry of satellites on the received images: photos and videos" subsection "Photo/video shooting of satellites" clause 1 "Determination of satellite orbits" §1 of Chapter 5. Added information about working with the "AstroTortilla" program to determine the coordinates of the center of the field of view of images of areas of the starry sky.
  • 03/20/2012: Subclause 2 “Classification of satellite orbits by semimajor axis” §1 of Chapter 2 has been updated. Information has been added about the magnitude of GSS drift and orbital disturbances.
  • 03/02/2012: Added sub-item "Observing and filming rocket launches at a distance" subparagraph “Photo/video shooting of satellites”, paragraph I “Determination of satellite orbits” §1 of Chapter 5. Information on the features of observing the flight of launch vehicles at the launch stage is described.
  • "Converting astrometry to IOD format" subsection "Photo/video shooting of satellites" paragraph I "Determination of satellite orbits" §1 of Chapter 5. Added description of working with the program "ObsEntry for Window" for converting satellite astrometry into IOD format - an analogue of the "OBSENTRY" program, but for the OS Windows.
  • 02/25/2012: Subclause updated "Sun-synchronous orbits" paragraph 1 "Classification of satellite orbits by inclination" §1 of Chapter 2. Added information on calculating the inclination value i ss of a sun-synchronous satellite orbit depending on the eccentricity and semi-major axis of the orbit.
  • 09.21.2011: Subclause 2 “Photometry of satellites during a flight” has been updated, clause II “Photometry of satellites” §1 of Chapter 5. Information has been added about the synodic effect, which distorts the determination of the rotation period of satellites.
  • 09.14.2011: Sub-clause updated "Calculation of orbital (Keplerian) elements of the satellite's orbit based on astrometric data. One flyby" subclause "Photo/video shooting of satellites" of paragraph I "Determination of satellite orbits" §1 of Chapter 5. Information has been added about the "SatID" program for identifying a satellite (using received TLE) among satellites from a third-party TLE database, and also a method for identifying a satellite in program "Heavensat" based on the observed flyby near the guide star.
  • 09.12.2011: Updated sub-item "Calculation of orbital (Keplerian) elements of the satellite's orbit based on astrometric data. Several flights" of the sub-item "Photo/video shooting of satellites" of paragraph I "Determination of satellite orbits" §1 of Chapter 5. Added information about the TLE recalculation program -elements for the required date.
  • 09/12/2011: Added sub-item "Entry of an artificial satellite into the Earth's atmosphere" subsection “Photo/video shooting of satellites”, paragraph I “Determination of satellite orbits” §1 of Chapter 5. Information on working with the “SatEvo” program for predicting the date of entry of satellites into the dense layers of the Earth’s atmosphere is described.
  • "Flashes from geostationary satellites" subclause “Photography of flashes”, p. II “Photometry of satellites” §1 of Chapter 5. Information has been added about the period of visibility of GSS flashes.
  • 09/08/2011: Sub-clause updated "Change in the brightness of an satellite during its flight" subparagraph 2 "Photometry of satellites during the flight" paragraph II "Photometry of satellites" §1 of Chapter 5. Added information about the form of the phase function for several examples of reflective surfaces.
  • subparagraph 1 "Observation of artificial satellite flares" paragraph II "Satellite photometry" §1 of Chapter 5. Added information about the unevenness of the time scale along the image of the satellite track on the photodetector matrix.
  • 09/07/2011: Sub-clause updated "Photometry of satellites during flight" p. II "Photometry of satellites" §1 of Chapter 5. Added an example of a complex light curve of the satellite "NanoSail-D" (SCN:37361) and modeling of its rotation.
  • "Flashes from low-orbit satellites" subparagraph 1 "Observation of artificial satellite flares" paragraph II "Satellite photometry" §1 of Chapter 5. A photograph and photometric profile of the flare from the LEO satellite "METEOR 1-29" have been added.
  • 09/06/2011: Sub-clause updated "Geostationary and geosynchronous satellite orbits"§1 of Chapter 2. Added information on the classification of geostationary satellites, information on the shape of GSS trajectories.
  • 09/06/2011: Sub-clause updated "Shooting the passage of satellites: equipment for shooting. Optical elements" subclause “Photo/video shooting of satellites”, paragraph I “Determination of satellite orbits” §1 of Chapter 5. Added links to reviews of domestic lenses as applied to shooting satellites.
  • 09/06/2011: Sub-clause updated "Phase angle" Section II "Satellite Photometry" §1 Chapter 5. Added animation of satellite phase changes depending on the phase angle.
  • 13.07.2011: Completed completion of all chapters and sections of the site.
  • 07/09/2011: Finished writing the introductory part to paragraph II "Satellite Photometry"§1 Chapter 5.
  • 07/05/2011: Finished writing the introductory part to §2 "Radio observations of satellites" Chapters 5.
  • 07/04/2011: Sub-clause updated "Processing observations" p. I "Reception of satellite telemetry" §2 of Chapter 5.
  • 07/04/2011: Finished writing Section II "Obtaining cloud images"§2 Chapter 5.
  • 07/02/2011: Finished writing Section I "Reception of satellite telemetry"§2 Chapter 5.
  • 07/01/2011: Finished writing the subparagraph "Photo/video shooting of satellites" clause I §1 Chapter 5.
  • 06/25/2011: Finished writing Applications.
  • 06/25/2011: Finished writing the introductory part to Chapter 5: “What and how to observe?”
  • 06/25/2011: Finished writing the introductory part to §1 "Optical observations" Chapters 5.
  • 06/25/2011: Finished writing the introductory part to paragraph I "Determination of satellite orbits"§1 Chapter 5.
  • 06/25/2011: Finished writing Chapter 4: "About the time".
  • 01/25/2011: Finished writing Chapter 2: "What kind of orbits and satellites are there?".
  • 01/07/2011: Finished writing Chapter 3: "Preparing for Observations".
  • 01/07/2011: Finished writing Chapter 1: "How do satellites move?"

Goal: learn to calculate the period of revolution of a satellite around a planet depending on its mass, size and type of satellite.

Progress:

1. Draw the table presented at the bottom of the table into your notebook.

2. Calculate the orbital period for each satellite for each planet and present the result in the table on the page. It is known that a planet that is 2 times heavier than the Earth is 1.4 times larger in size, and a planet that is smaller than the Earth in mass is 0.8 times the size of the Earth. Data must be taken from the information window on the “Simulation of satellite motion” page. The radius of the Earth is taken to be 6400 km. The answer should be expressed in minutes, rounded to the nearest whole number.

3. Check the data you received. To do this, click the "Check Results" button.

4. If there are errors, correct them.

5. Write down the correct data obtained in a table in your notebook.

6. Draw a conclusion about how the satellite’s orbital period depends on the size of the planet and the type of satellite.

Page 1 of 2

171. Determine the period of revolution around the Sun of an artificial planet, if it is known that the semi-major axis of its elliptical orbit is 10 7 km greater than the semi-major axis of the earth's orbit.

172. The orbital period of Comet Halley around the Sun is T = 76 years. The minimum distance at which it passes from the Sun is 180 Gm. Determine the maximum distance at which Comet Halley moves away from the Sun. The radius of the Earth's orbit is taken equal to R 0 = 150 Gm.

173. Assuming the Earth’s orbit is circular, determine the linear speed v of the Earth’s movement around the Sun.

174. The orbital period of an artificial Earth satellite is 3 hours. Assuming its orbit is circular, determine at what height from the Earth’s surface the satellite is located.

175. A planet of mass M moves in a circle around the Sun with speed v (relative to the heliocentric frame of reference). Determine the period of revolution of this planet around the Sun.

176. Determine how many times the force of gravity on Earth is greater than the force of gravity on Mars if the radius of Mars is 0.53 of the radius of the Earth, and the mass of Mars is 0.11 of the Earth’s mass.

177. Determine the average density of the Earth, assuming that the gravitational constant, the radius of the Earth and the acceleration of gravity on the Earth are known.

178. Two material points of masses m 1 and m 2 are located at a distance R from each other. Determine the angular velocity of rotation with which they must rotate around a common center of mass so that the distance between them remains constant.

179. Two identical homogeneous balls made of the same material, touching each other, attract each other. Determine how the force of attraction will change if the mass of the balls is increased by n = 3 times due to an increase in their size.

180. Determine the height at which the acceleration of gravity is 25% of the acceleration of gravity on the surface of the Earth.

181. Assuming the density of the Earth to be constant, determine the depth at which the acceleration of gravity is 25% of the acceleration of gravity on the surface of the Earth.

182. At what height h is the acceleration of free fall less than half its value on the Earth’s surface.

183. A stationary artificial satellite of the Earth is a satellite that is constantly located above the same point of the equator. Determine the distance of such a satellite to the center of the Earth.

184. At the equator of a certain planet (planet density ρ = 3 g/cm 3), bodies weigh half as much as at the pole. Determine the period of revolution of the planet around its own axis.

185. Assuming that the radius of the Earth is known, determine at what height h above the Earth’s surface the gravitational field strength is equal to 4.9 N/kg.

186. Determine at what point (counting from the Earth) on the straight line connecting the centers of the Earth and the Moon, the gravitational field strength is zero. The distance between the centers of the Earth and the Moon is R, the mass of the Earth is 81 times the mass of the Moon.

187. There is a thin homogeneous rod of mass m and length l. For a point located on the same straight line with a rod at a distance a from its nearest end, determine: 1) the potential of the gravitational field of the rod; 2) the intensity of its gravitational field.

188. A thin homogeneous disk of radius R has mass m. Determine at point A, located on the axis of the disk at a distance h from it: 1) the potential of the gravitational field; 2) gravitational field strength. Forward

How many times does the period of revolution of an artificial satellite moving in a circular orbit at an altitude equal to the radius of the Earth exceed the period of revolution of a satellite in low-Earth orbit?

Problem No. 2.5.14 from the “Collection of problems for preparing for entrance exams in physics at USPTU”

Given:

\(h=R\), \(\frac(T_2)(T_1)-?\)

The solution of the problem:

Let us find the orbital period \(T_2\) of a satellite moving in a circular orbit at an altitude \(h=R\). It is clear that the force of universal gravity imparts to the satellite centripetal acceleration \(a_t\), therefore Newton’s second law will be written in the following form:

\[(F_(t2)) = m(a_(t2))\;\;\;\;(1)\]

The force of gravity is determined by the law of universal gravitation:

\[(F_(t2)) = G\frac((Mm))((((\left((R + h) \right))^2)))\;\;\;\;(2)\ ]

In order for the orbital period to appear in our formula, we need to express the centripetal acceleration \(a_(c2)\) through it. To do this, we write the formula for determining the acceleration \(a_(q2)\) through the angular velocity and the formula for connecting the latter with the period.

\[(a_(t2)) = (\omega ^2)\left((R + h) \right)\]

\[\omega = \frac((2\pi ))(T_2)\]

\[(a_(t2)) = \frac((4(\pi ^2)))(T_2^2)\left((R + h) \right)\;\;\;\;(3)\ ]

Let's substitute expressions (2) and (3) into equality (1):

Let's make an analogy for a satellite moving in low-Earth orbit. It is clear that its revolution period will be equal to:

\[(T_1) = 2\pi \sqrt (\frac(((R^3)))((GM)))\]

Now let’s substitute the condition \(h=R\) into the formula for determining the period \(T_2\) (in formula (4)):

\[(T_2) = 2\pi \sqrt (\frac((((\left((R + R) \right))^3)))((GM))) = 2\pi \sqrt (\frac ((8(R^3)))((GM))) \]

The required ratio is:

\[\frac(((T_2)))(((T_1))) = \sqrt 8 = 2\sqrt 2 = 2.83\]

Answer: 2.83 times.

If you do not understand the solution and you have any questions or you have found an error, then feel free to leave a comment below.

Satellite orbital period

"...Orbital period (of a satellite): the time interval between two successive passages by a satellite of a characteristic point of its orbit..."

Source:

<РЕГЛАМЕНТ РАДИОСВЯЗИ>(Extract)


Official terminology. Akademik.ru. 2012.

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