Astronomy supports Ikhtilaaf AlMataale since the First Hilal Sighting (“Lunar Date Line” for a month) can occur anywhere Around the Globe for a particular month, and divides the world into different parts which see the Hilal on different days. See figure below for Hilal visibility model using Mooncalc written by Dr. Monzur Ahmed of UK.

So much of the populated world should start Ramadan, Eid ul Fitr etc. within about 24 hours, but TWO Solar dates because of the artificially fixed International (Solar) date line. Note that even at one moment of time there are two Solar dates in the world. E.g. if it is Sunday evening in America, it is Monday morning in Indonesia!

visMap 2003-11-23

Later I also found the following very illustrative Fatwa of Sheikh Al Uthaimeen (RH) Ref: Al-Aqalliyaat Al-Muslimah - Page 84, Fatwa No.23, supporting Ikhtilaaf AlMataale from the Qur’aan, Hadith, and Qiyas (Analogy).
Fatwa: Should we fast and end our fast according to the sighting of the new moon in Saudi Arabia?

Prof. Muhammad Ilyas of Malaysia, a pioneer in the calculations of Hilal prediction, Masha’Allaah has hence proposed for civil use, a Tri-zonal Hejiri calendar: dividing the earth into 3 zones: Americas; Europe-Africa-West Asia; Asia-Pacific and calculating Hilal visibility separately for each region. This Tri-Zonal Calendar concept has also gained support in the Jordanian Astronomical Society (Mohammed Odeh and elsewhere Alhamdulillaah. Please see MoonCalc program by Dr Monzur Ahmed for details. Thus for example, sometimes Hilal sighting in North America can be One Date Before Hilal sighting in Saudi Arabia, e.g. see projection from MoonCalc in Illustration 8 [above]. Also see for more details.

Also see Arab News: Monday 11 September 2006:
Beginning of Ramadan: Following the Saudi Moon Sighting. Edited by Adil Salahi