يَسۡـَٔلُونَكَ عَنِ ٱلۡأَهِلَّةِ‌ۖ قُلۡ هِىَ مَوَٲقِيتُ لِلنَّاسِ وَٱلۡحَجِّ‌ۗ وَلَيۡسَ ٱلۡبِرُّ بِأَن تَأۡتُواْ ٱلۡبُيُوتَ مِن ظُهُورِهَا وَلَـٰكِنَّ ٱلۡبِرَّ مَنِ ٱتَّقَىٰ‌ۗ وَأۡتُواْ ٱلۡبُيُوتَ مِنۡ أَبۡوَٲبِهَا‌ۚ وَٱتَّقُواْ ٱللَّهَ لَعَلَّڪُمۡ تُفۡلِحُونَ O (سورة البقرة ۱۸۹)

"THEY ASK YOU ABOUT THE NEW MOONS. SAY: THEY ARE INDICATIVE OF TIME FOR THE PEOPLE, AND OF THE HAJJ. AND IT IS NOT RIGHTEOUSNESS THAT YOU COME INTO YOUR HOUSES FROM THEIR BACK SIDE BUT RIGHTEOUSNESS IS THAT ONE FEARS ALLAH. AND COME TO THE HOUSES THROUGH THEIR DOORS. AND FEAR ALLAH SO THAT YOU MAY BE SUCCESSFUL. (SURAH AL-BAQARAH:189)

Part 1

The words used by the Holy Quran with regard to the moon clearly indicate that lunar calendar is the preferred calendar in Islam, particularly in relation to those acts of worship that are specific to certain months or dates for example the months of Ramadan and Hajj, the days of Hajj, and Muharram and Ashura.
Continued...
From Ma'ariful Quran, by Mufti Muhammad Shafi RE


The Shariah has opted for the lunar calendar because it is based on something every sighted person  can see on the sky and be informed accordingly. Regardless of whether a person lives in the city, the jungle or the mountains, everyone can see for themselves when the lunar month starts and when it ends. This is in contrast with the solar calendar which depends on meteorological equipment and mathematical calculations which are not easily accessible to a lay person.

From Ma'ariful Quran, by Mufti Muhammad Shafi RE