NASA is planning an Asteroid Defense project called DART (Double Asteroid Redirection Test) – this is the closet device NASA has that is like the HARPOON device depicted in ASTEROIDS.
When I needed a device to destroy an asteroid in the story, I searched the web and found a 160-page NASA research paper written by Dr. Bong Wie of the Asteroid Deflection Research Center at Iowa State, University. I read the entire paper and used what I learned to create the HARPOON. When I contacted Dr. Wie and asked him to review what I had written he was very helpful.
Here is a link to the research paper: https://www.nasa.gov/sites/default/files/files/Bong_Wi_Final_Report.pdf
Here is a link to a news story about DART: https://www.mnn.com/earth-matters/space/blogs/nasa-test-new-asteroid-deflection-weapon