goleeya nirdeshaank paddhati

goleeya nirdeshaank (r, θ, φ) bhautiki mein aamtaur par prayog hote hain: trijya doori 'r', dhruveeya kon 'θ' (theeta) aur digansh kon 'φ' (faai). kabhi-kabhi 'r' ke sthaan par 'ρ' (ro) ka chinh istemaal hota hai
bhoogol mein istemaal hone waali akshaansh-rekhaansh (laitityood-laungityood) pranaali ek goleeya nirdeshaank paddhati hai

goleeya nirdeshaank paddhati (angreji: spherical coordinate system) teen aayaamon (daayameinshanon) vaale dik (space) mein prayog hone waali aisi nirdeshaank paddhati hoti hai jismein us dik mein maujood kisi bhi bindu ka sthaan teen ankon se nirdhaarit ho jaata hai:[1]

  • mool kendra se us bindu ki 'trijya doori' (radial distance) - iske liye aksar 'r' ya 'ρ' ka chinh prayog hota hai
  • shirobindu (jenith) ki disha se usaka 'dhruveeya kon' (polar angle) - iske liye aksar 'θ' ka chinh prayog hota hai
  • mool samatal se usaka 'digansh kon' (azimuth angle) - iske liye aksar 'φ' ka chinh prayog hota hai

jaahir hai ki aisi paddhati mein pehle se hi kisi mool kendra, shirobindu disha aur mool samatal ka chunaav kar lena aavashyak hai. is chunaav ke baad har bindu ka sthaan in teenon ankon - (r, θ, φ) - ke aadhaar par batalaaya ja sakta hai. kabhi-kabhi 'dhruveeya kon' ke sthaan par 'utkarsh ya ooainchaai kon' (elevation angle) ka prayog hota hai jo mool samatal se ooainchaai maapata hai.

bhaugolik prayog

bhoogol mein jagahon ka ankan karne waali akshaansh-rekhaansh (laitityood-laungityood) pranaali (yaani bhoogoleeya nirdeshaank pranaali) ek goleeya nirdeshaank pranaali ka udaaharan hai.[2] ismein:

  • 'mool kendra' pruthvi ke bilkul beech sthit kendreeya bindu hai
  • 'mool samatal' ek kaalpanik samatal hai jo bhoomadhya rekha se gujrakar pruthvi ko do baraabar ke uttari aur dakshini golaardhon (hemisfeeyaron) mein kaatata hai
  • 'ooainchaai kon' ka maap ek aisi kaalpanik rekha se kiya jaata hai jo pruthvi ke kendra se nikalkar inglaind ke grenich shahar se theek dakshin mein bhoomadhya rekha par sthit bindu se gujrati hai (yaani jahaaain madhyaahn rekha aur bhoomadhya rekha ek doosare ko kaatati hain).

is vyavastha mein kisi sthaan ki:

  • trijya doori usaki pruthvi ke kendra se ooainchaai hoti hai.
  • akshaansh (laitityood) usaka ooainchaai kon (eleveshan) hota hai. sthaan jitna bhoomadhya rekha se uttar ya dakshin ki or adhik doori par ho, yeh ank utana hi adhik hota hai aur bhaugolik dhruvon par badhkar apni adhiktam 90° ki sankhya par pahuainch jaata hai.
  • rekhaansh (laungityood) usaka digansh kon (aijimuth) hota hai. sthaan jitna madhyaahn rekha se poorv ya pashchim ki or adhik doori par ho, yeh ank utana hi adhik hota hai aur pruthvi ke theek ulti-taraf prashaant mahaasaagar mein badhkar apni adhiktam 180° ki sankhya par pahuainch jaata hai.

dhyaan rahe ki apne aakaar aur ghoornan (rotation) ki vajah se bhoomadhya rekha ka nirdhaaran to prakruti dvaara tay tha, lekin donon dhruvon ke beech chalne waali madhyaahn rekha (prime meridiyn) kaheen bhi ho sakti thi. yeh keval ek aitihaasik ittefaak hai ki usaka chunaav inglaind se nikalne ke liye kiya gaya aur vishvabhar mein sveekrut ho gaya.

inhein bhi dekhein

sandarbh

  1. Binocular Vision and Stereopsis, Ian P. Howard, Brian J. Rogers, pp. 236, Oxford University Press, 1995, ISBN 978-0-19-508476-4, ... the azimuth of a point is defined as the dihedral angle between a vertical plane passing through the point ...
  2. Relational Management and Display of Site Environmental Data, David Rich, pp. 246, CRC Press, 2002, ISBN 978-1-56670-591-2, ... The earth is roughly spherical, and the latitude-longitude system is used to describe locations in spherical coordinates. Latitude is measured in degrees (l/360th of the sphere) north or south of the equator. Longitude is measured in degrees east (positive) or west (negative) of the prime meridian, which passes through Greenwich, England ...