This mod is no longer needed since it has now been incorporated into the base game. Click on the rocket silo to enable auto-launch: https://us1.factorio.com/assets/img/blog/fff-187-03-rocket-silo-autolaunch.jpg
However, I have updated the mod for those that may need it. The research recipe has been edited to replace alien science with high tech science.
This is a 0.13+ release of the following mod: https://forums.factorio.com/viewtopic.php?f=93&t=15308
The mod adds a new radar that will automatically launch one rocket in the nearby rocket silos per completed radar scan as long as there is an item (satellite, ion canon, fish, etc.) in the cargo slot of the rocket. Accompanying technology has to be researched after the rocket silo before crafting the launch control radar. There will be an icon in the top left corner to display how many silos are currently under the influence of launch control.