The later developments of Nike could get pretty high.
Does anyone have the math to calculate if the thrust could have been turned into enough speed for orbit? Maybe with less payload.
https://en.wikipedia.org/wiki/Project_Nike#Missiles
Don't really need the full math for this. The Nike Hercules weighted in at about 10,500 lb. The warhead assembly was about 1100 lb, so take that off. Max altitude was 150,000 ft, max speed was Mach 3.65, max range was 90 miles. "Space" is above 60 miles but atmospheric drag is still pretty high there, so rational satellite orbits are in the 100 mile + range.
But lets stick purely to the minimum space definition.
You need to achieve 60 miles altitude at 17,500 MPH or about Mach 25.
If you went straight up, with no payload, you might get well above the 150,000 foot altitude (~30 miles) but you are not going to fight gravity to double that. And, should you actually get to 60 miles, you will be a zero tangential velocity at bingo fuel so, not matter what height you have achieved, you simply fall back to earth not having achieved orbital velocity.
No. A Nike Hercules could not achieve orbit for any portion of that missile, payload or not.