Existence of a class of irregular bodies with a higher convergence rate of Laplace series for the gravitational potential
The main form of the representation of a gravitational potential V for a celestial body T in the outer space is the Laplace series in solid spherical harmonics ( R / r ) n + 1 Y n ( R , θ , λ ) with R being the radius of enveloping T sphere. It is well known that Y n satisfy the inequality ⟨ Y n ⟩ &...
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| Veröffentlicht in: | Celestial mechanics and dynamical astronomy 2015-08, Vol.122 (4), p.391-403 |
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| container_title | Celestial mechanics and dynamical astronomy |
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| creator | Kholshevnikov, Konstantin V. Shaidulin, Vakhit Sh |
| description | The main form of the representation of a gravitational potential
V
for a celestial body
T
in the outer space is the Laplace series in solid spherical harmonics
(
R
/
r
)
n
+
1
Y
n
(
R
,
θ
,
λ
)
with
R
being the radius of enveloping
T
sphere. It is well known that
Y
n
satisfy the inequality
⟨
Y
n
⟩
<
C
n
-
σ
.
The angular brackets mark the maximum of a function’s modulus over a unit sphere. For bodies of irregular structure
σ
=
5
/
2
, and this value cannot be increased in general case. At the same time modern models of the geopotential show more rapid rate of decreasing of
Y
n
. We have found a class
T
of irregular bodies for which
σ
=
3
. The Earth and (at least a part of) other terrestrial planets, satellites, and asteroids most likely belong to this class. In this paper we describe
T
proving the above inequality for
σ
=
3
. |
| doi_str_mv | 10.1007/s10569-015-9622-7 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1730068957</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1730068957</sourcerecordid><originalsourceid>FETCH-LOGICAL-c415t-25a64309c8efe41276d09b982036aef05e8d0f8ca82b29ce48d7fb4e8887d6ba3</originalsourceid><addsrcrecordid>eNqNkcFu1DAQhi0EEkvhAbhZ4sIldOzEsX1EVSlIK3GBszVxJllXabzY3kLfHqfLAVVC4jQe6ftmxvoZeyvggwDQl1mA6m0DQjW2l7LRz9hOKC0b22nznO3AyraRVpmX7FXOtwCgwKode7j-FXKh1ROPE0fuF8x5e4aUaD4tmPgQx0CZ_wzlUIFDmA-UuI_rPaX5UUxYHu09Hhesfaa0CVNMvByIzwnvQ8ES4ooLP8a6rQRcXrMXEy6Z3vypF-z7p-tvV5-b_debL1cf943vhCqNVNh3LVhvaKJOSN2PYAdrJLQ90gSKzAiT8WjkIK2nzox6GjoyxuixH7C9YO_Pc48p_jhRLu4uZE_LgivFU3ZCtwC9sUr_BwpWGFuXV_TdE_Q2nlL9YKV6q1olWugqJc6UTzHnRJM7pnCH6cEJcFtu7pybq7m5LTe3HSHPTq7sOlP6a_I_pd9bEptz</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1695351304</pqid></control><display><type>article</type><title>Existence of a class of irregular bodies with a higher convergence rate of Laplace series for the gravitational potential</title><source>Springer Journals</source><creator>Kholshevnikov, Konstantin V. ; Shaidulin, Vakhit Sh</creator><creatorcontrib>Kholshevnikov, Konstantin V. ; Shaidulin, Vakhit Sh</creatorcontrib><description>The main form of the representation of a gravitational potential
V
for a celestial body
T
in the outer space is the Laplace series in solid spherical harmonics
(
R
/
r
)
n
+
1
Y
n
(
R
,
θ
,
λ
)
with
R
being the radius of enveloping
T
sphere. It is well known that
Y
n
satisfy the inequality
⟨
Y
n
⟩
<
C
n
-
σ
.
The angular brackets mark the maximum of a function’s modulus over a unit sphere. For bodies of irregular structure
σ
=
5
/
2
, and this value cannot be increased in general case. At the same time modern models of the geopotential show more rapid rate of decreasing of
Y
n
. We have found a class
T
of irregular bodies for which
σ
=
3
. The Earth and (at least a part of) other terrestrial planets, satellites, and asteroids most likely belong to this class. In this paper we describe
T
proving the above inequality for
σ
=
3
.</description><identifier>ISSN: 0923-2958</identifier><identifier>EISSN: 1572-9478</identifier><identifier>DOI: 10.1007/s10569-015-9622-7</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Aerospace Technology and Astronautics ; Astronomy ; Astrophysics and Astroparticles ; Classical Mechanics ; Convergence ; Dynamical Systems and Ergodic Theory ; Geophysics/Geodesy ; Gravitation ; Gravity ; Inequalities ; Laplace transforms ; Original Article ; Physics ; Physics and Astronomy ; Representations ; Spherical harmonics ; Terrestrial planets ; Texts</subject><ispartof>Celestial mechanics and dynamical astronomy, 2015-08, Vol.122 (4), p.391-403</ispartof><rights>Springer Science+Business Media Dordrecht 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c415t-25a64309c8efe41276d09b982036aef05e8d0f8ca82b29ce48d7fb4e8887d6ba3</citedby><cites>FETCH-LOGICAL-c415t-25a64309c8efe41276d09b982036aef05e8d0f8ca82b29ce48d7fb4e8887d6ba3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10569-015-9622-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10569-015-9622-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Kholshevnikov, Konstantin V.</creatorcontrib><creatorcontrib>Shaidulin, Vakhit Sh</creatorcontrib><title>Existence of a class of irregular bodies with a higher convergence rate of Laplace series for the gravitational potential</title><title>Celestial mechanics and dynamical astronomy</title><addtitle>Celest Mech Dyn Astr</addtitle><description>The main form of the representation of a gravitational potential
V
for a celestial body
T
in the outer space is the Laplace series in solid spherical harmonics
(
R
/
r
)
n
+
1
Y
n
(
R
,
θ
,
λ
)
with
R
being the radius of enveloping
T
sphere. It is well known that
Y
n
satisfy the inequality
⟨
Y
n
⟩
<
C
n
-
σ
.
The angular brackets mark the maximum of a function’s modulus over a unit sphere. For bodies of irregular structure
σ
=
5
/
2
, and this value cannot be increased in general case. At the same time modern models of the geopotential show more rapid rate of decreasing of
Y
n
. We have found a class
T
of irregular bodies for which
σ
=
3
. The Earth and (at least a part of) other terrestrial planets, satellites, and asteroids most likely belong to this class. In this paper we describe
T
proving the above inequality for
σ
=
3
.</description><subject>Aerospace Technology and Astronautics</subject><subject>Astronomy</subject><subject>Astrophysics and Astroparticles</subject><subject>Classical Mechanics</subject><subject>Convergence</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Geophysics/Geodesy</subject><subject>Gravitation</subject><subject>Gravity</subject><subject>Inequalities</subject><subject>Laplace transforms</subject><subject>Original Article</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Representations</subject><subject>Spherical harmonics</subject><subject>Terrestrial planets</subject><subject>Texts</subject><issn>0923-2958</issn><issn>1572-9478</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqNkcFu1DAQhi0EEkvhAbhZ4sIldOzEsX1EVSlIK3GBszVxJllXabzY3kLfHqfLAVVC4jQe6ftmxvoZeyvggwDQl1mA6m0DQjW2l7LRz9hOKC0b22nznO3AyraRVpmX7FXOtwCgwKode7j-FXKh1ROPE0fuF8x5e4aUaD4tmPgQx0CZ_wzlUIFDmA-UuI_rPaX5UUxYHu09Hhesfaa0CVNMvByIzwnvQ8ES4ooLP8a6rQRcXrMXEy6Z3vypF-z7p-tvV5-b_debL1cf943vhCqNVNh3LVhvaKJOSN2PYAdrJLQ90gSKzAiT8WjkIK2nzox6GjoyxuixH7C9YO_Pc48p_jhRLu4uZE_LgivFU3ZCtwC9sUr_BwpWGFuXV_TdE_Q2nlL9YKV6q1olWugqJc6UTzHnRJM7pnCH6cEJcFtu7pybq7m5LTe3HSHPTq7sOlP6a_I_pd9bEptz</recordid><startdate>20150801</startdate><enddate>20150801</enddate><creator>Kholshevnikov, Konstantin V.</creator><creator>Shaidulin, Vakhit Sh</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TG</scope><scope>7XB</scope><scope>88I</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABUWG</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>KL.</scope><scope>L7M</scope><scope>M2P</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>Q9U</scope></search><sort><creationdate>20150801</creationdate><title>Existence of a class of irregular bodies with a higher convergence rate of Laplace series for the gravitational potential</title><author>Kholshevnikov, Konstantin V. ; Shaidulin, Vakhit Sh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c415t-25a64309c8efe41276d09b982036aef05e8d0f8ca82b29ce48d7fb4e8887d6ba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Aerospace Technology and Astronautics</topic><topic>Astronomy</topic><topic>Astrophysics and Astroparticles</topic><topic>Classical Mechanics</topic><topic>Convergence</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Geophysics/Geodesy</topic><topic>Gravitation</topic><topic>Gravity</topic><topic>Inequalities</topic><topic>Laplace transforms</topic><topic>Original Article</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Representations</topic><topic>Spherical harmonics</topic><topic>Terrestrial planets</topic><topic>Texts</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kholshevnikov, Konstantin V.</creatorcontrib><creatorcontrib>Shaidulin, Vakhit Sh</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest One Sustainability</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ProQuest Science Journals</collection><collection>ProQuest advanced technologies & aerospace journals</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central Basic</collection><jtitle>Celestial mechanics and dynamical astronomy</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kholshevnikov, Konstantin V.</au><au>Shaidulin, Vakhit Sh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of a class of irregular bodies with a higher convergence rate of Laplace series for the gravitational potential</atitle><jtitle>Celestial mechanics and dynamical astronomy</jtitle><stitle>Celest Mech Dyn Astr</stitle><date>2015-08-01</date><risdate>2015</risdate><volume>122</volume><issue>4</issue><spage>391</spage><epage>403</epage><pages>391-403</pages><issn>0923-2958</issn><eissn>1572-9478</eissn><abstract>The main form of the representation of a gravitational potential
V
for a celestial body
T
in the outer space is the Laplace series in solid spherical harmonics
(
R
/
r
)
n
+
1
Y
n
(
R
,
θ
,
λ
)
with
R
being the radius of enveloping
T
sphere. It is well known that
Y
n
satisfy the inequality
⟨
Y
n
⟩
<
C
n
-
σ
.
The angular brackets mark the maximum of a function’s modulus over a unit sphere. For bodies of irregular structure
σ
=
5
/
2
, and this value cannot be increased in general case. At the same time modern models of the geopotential show more rapid rate of decreasing of
Y
n
. We have found a class
T
of irregular bodies for which
σ
=
3
. The Earth and (at least a part of) other terrestrial planets, satellites, and asteroids most likely belong to this class. In this paper we describe
T
proving the above inequality for
σ
=
3
.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10569-015-9622-7</doi><tpages>13</tpages></addata></record> |
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| ispartof | Celestial mechanics and dynamical astronomy, 2015-08, Vol.122 (4), p.391-403 |
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| language | eng |
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| source | Springer Journals |
| subjects | Aerospace Technology and Astronautics Astronomy Astrophysics and Astroparticles Classical Mechanics Convergence Dynamical Systems and Ergodic Theory Geophysics/Geodesy Gravitation Gravity Inequalities Laplace transforms Original Article Physics Physics and Astronomy Representations Spherical harmonics Terrestrial planets Texts |
| title | Existence of a class of irregular bodies with a higher convergence rate of Laplace series for the gravitational potential |
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