What is the origin of this? Does anybody other than Tamilian use it? Is there any scientific reason for this belief?
Once in a while somebody raises this doubt about rahu kalam in this forum and such discussions have happened many times in the past. Hope you will spend some time looking into the archives.
In a nut shell, rahu kalam is a distinct southern contribution to the immense storehouse of hindu superstitions, but the beauty is it is pandemic; when the southies went in large numbers to Delhi and other northern cities/areas rahukalam also spread there. So now it has an All-India status.
About its origin nothing can be said clearly; but some medieval astrological text, most probably from some Kerala or Tamilnadu Pandit, must have launched Rahu, YamakanDakan, guLikan, mAndi, dhUma, indrachaapa, (a.k.a Chaapa; kOdanda; kArmuka), parivEsha. (paridhi), vyateepaata. (paata), upakEtu. (dhwaja; Sikhi), Pranapada ..
to rule over some time period during day and night (separately) according to the day of the week. The easiest of all these "upagrahas" as denoted by some authorities, "baadhaka grahas", "dhooma grahas" by others, etc., is rahu as far as calculation goes.
The time period allotted seems to be quite arbitrary and since it is based on an equally non-astronomical base of the days of the week, the whole thing is pure bunkum, imho. But many people are so much taken in by this RK, it has accumulated its own potential energy to survive.
The time period has been expressed as one-and-a-half hour blocks but strictly speaking the duration of daytime (local sunrise to local sunset) has to be divided by 8 and the one-eighth portion should be taken as the rahu block. If we denote this by say H, then out of the 8 Hs available on that day, the rahukaalam will be the block indicated below:
Today, 29-11-2011, the sunrise/set in Trivandrum are 6-23-46 and 17-57-06.
Duration of daytime= 11-33-20
Being Tuesday, RK for today will be from 15-03-46 to 16-30-26 hrs. in Trivandrum. But if you take northern latitudes, the results will vary widely.