SQLDeveloper needs to run under a Java version greater than 7 and less than 8. Installing the most up-to-date JDK gets you at least version 1.8.0_131 (as of 26 April, 2017). You can find older versions of Java from their Download Archives where I was able to find version 1.7.0_80.
Alas, even after installing this version, SQLDeveloper “sees” the newer version that I also have installed on my Macbook Pro and not the required JDK. Luckily one Paulo Pedroso on the stackOverflow posted a solution which was to edit the file
/Applications/SQLDeveloper.app/Contents/MacOS/sqldeveloper.sh
(I used nano) to the line that reads
export JAVA_HOME-‘/use/libexec/java_home -v 1.7’
and simply change the 1.7 to 1.7.0_80.
Yup, that’s it.