A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed (v0). Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If R $$=$$ radius of the Earth and ω be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.

Question

A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed (v0). Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If R $$=$$ radius of the Earth and ω be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.

Infinity Learn · Accepted Answer

Twest $$=2$$$$π$$$$Rv0+R$$ω and Teast $$=2$$$$π$$$$Rv0$$−Rω⇒⇒∆$$T=Teast$$ −Twest $$=2$$$$π$$$$RV0-R$$ω$$-2$$$$π$$$$RV0+R$$ω$$=2$$$$π$$R×$$2R$$ω$$v02$$−$$R2$$ω$$2=4$$πω$$R2v02$$−$$R2$$ω$$2$$

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