It should. It’s the the Zeta Gundam theme, “Zeta ~Toki wo Koete”.
Y’see, the infamous Neil Sedaka had two of his songs adapted into the first opening and closing themes for the series; “Better Days Are Coming” (which is in the above video), and “Bad and Beautiful” which is “Hoshizora no Believe“. There was also an English version of “Mizu no Hoshi Ai wo Komete” but that was never recorded according to Wikipedia.
wussed out because they were apparently too cheap to pay for copyright royalties strategically decided to swap out the opening and ending themes for the US release of Zeta Gundam. To this day, fans are still pissed about it and even compare this to the slight BGM change in Aim for the Top!/Gunbuster‘s stateside release. Thankfully, the latter case isn’t as bad but one can only hope Bandai can just put out a proper release of the series with the themes intact.
Either way, I just thought this would be fun to listen to :P