Satish Dhawan Space Centre (SDSC) or Sriharikota Range (SHAR) is a rocket launch centre operated by Indian Space Research Organisation (ISRO). It is located in Sriharikota in Andhra Pradesh. Sriharikota Range was renamed in 2002 after ISRO's former chairman Satish Dhawan.

Answer this question: where is india's space rocket launching centre? Let's give stream of consciousness first:
The important part for answering this question is: It is located in Sriharikota in Andhra Pradesh.
So, the final answer is Sriharikota in Andhra Pradesh.