Astrology has been in existence for thousands of years . It is a gift given to us by our sages who studied planets and its effects. However as time passed by, the accuracy of predictions went down and along with that went down the trust of people. It is purely based on science, learning it and understanding it, is the real challenge.
Vastu is the ancient science of architecture. It is basically space management keeping directions in mind in such a way that we have blissful dwelling for whatever purpose the building is.
Internet is full of articles and arguements on this topic. This is a topic on which we will never have full proof justification. Science believes in only something that can be proved. However if outcome of an event remains same everytime that doesn't mean scientifically it is proved. However it can be conveniently "taken for granted" if outcomes is same. Likewise only possible proof of palmistry is evaluation of one's own hand from a professional skilled palmist.