Idan ka saka daidai atomic clocks biyu — daya a saman Duniya kuma daya a kan Wata — kuma ka durwa dansu bayan daidai ranar Duniya, Wata agogo za ya kasance gida ta kimanin 56.02 microseconds. Ba shi ne bukatun a clocks ba. Shi ne fundamental property na universe, tsara ta Albert Einstein's general theory na relativity kimanin shekaru da gida.
Gravitational Time Dilation Jajage
Einstein's general relativity, buga a cikin 1915, yana tsara gravity ba kamar strength ba kuma casuwa na spacetime. Massive objects kamar Duniya kuma Wata yana warkar da fabin spacetime a gefe nsu, kuma casuwa yana tasiri yadda lokaci yana gudu.
Keɓancen principle shine jinjiri: karfin gravity yana yi, yajin gudu lokaci. Wannan bukatun yana san gravitational time dilation. Duniya's surface gravity yana kimanin 9.8 m/s², yayin da Wata ba shi ne kamar 1.62 m/s² — kimanin sixth part kamar yadda karfin. Saboda karfin gravity a kan Wata bai zuwa ba, spacetime bai zuwa ba casuwa, kuma agogo yana gudu.
Nisan 56 Microsecond
Daidaitaccen adadin da ake gudu lunar agogo yana bukata da bambanci a gravitational potential tsakanin Duniya's surface kuma Wata's surface, kuma dan karkami para orbital velocity kuma Duniya's rotation.
Gravitational blueshift — agogo gudu a karfin gravity bai zuwa — yana saka kimanin +58.7 microseconds kowannen ranar. Kuma, Wata orbital velocity (kimanin 1.022 km/s) ya bukata dan karkami sauyi-dependent effect daga special relativity, da ba zuwa net gain ta kimanin 2.7 microseconds kowannen ranar. Jimillar sakamakon yana kimanin +56.02 microseconds kowannen ranar.
Wannan nisan an tabbata ta independent analyses karim, sansu work ta NASA's Jet Propulsion Laboratory kuma National Institute of Standards and Technology.
Ba Haka Theoretical — Yana Lissafi
Gravitational time dilation shine daya daidaitaccen predictions a dukkan physics. GPS satellites, wanda yana gudu kimanin 20,200 km altitude inda gravity bai zuwa ba, yana gida ta kimanin 45 microseconds kowannen ranar harangal Duniya's surface. Ba tare da lissafin wannan abin, GPS positions za su sauya ta kimanin 10 km kowannen ranar.
Ain physics amfani a kan Wata. Yayin da ba muka saka atomic clocks a kan saman Wata, bukatun yana lissafi daga abin da daidai equations. Gravitational time dilation formula yana yi predictions wanda an tabbata zuwa karim daya sai na triliyar.
Yace 56 Microseconds Yana Mahalarta
Para everyday human activities, 56 microseconds yana cikin abin da ba a iya ganin. Kuma para precision systems, yana tara sauri:
Bayan jiya, Wata agogo yana gida ta kimanin 1.7 milliseconds. Bayan shekara, offset yana yi karim kimanin 20 milliseconds. Tun da J2000.0 epoch (Janairu 1, 2000), jimillar sauyin ya karim kimanin dakika 0.5.
Para navigation, haske yana gudu kimanin 300 meters kowannen microsecond. 56-microsecond timing error yana dace da kimanin 16 meters matsayin uncertainty kowannen ranar. Para precision landings wanda Artemis missions bukatun — targeting specific sites a gefe na Wata south pole — wannan adadin drift yana zama unacceptable ba tare da lissafi ba.
Da shi shi ne daidai yace Coordinated Lunar Time (LTC) yana karu: da sanin time standard wanda yana lissafi relativistic bambanci kuma yana tiyaka dukkan lunar systems daidai.