[Verse 1] Eighteen forty-six, the sky held mystery Uranus wandered from its destined path Newton's laws were perfect, worked through history But something pulled the planet from its track The orbit curved away from calculations A force unseen was tugging at its course Either physics failed across the nations Or hidden mass applied a subtle force [Chorus] Perturbation shows the way When the numbers drift astray Numerical integration runs the dance Least squares finds the best solution Through the orbital confusion Algorithms gave Neptune its chance [Verse 2] Le Verrier sat with paper, pen, and math Perturbation analysis in hand He traced each deviation from the path To find what force could shift the wandering planet He modeled gravity's invisible pull Calculated where the phantom world must be His equations painted the picture full A planet hiding past what eyes could see [Chorus] Perturbation shows the way When the numbers drift astray Numerical integration runs the dance Least squares finds the best solution Through the orbital confusion Algorithms gave Neptune its chance [Bridge] Johann Galle aimed his telescope that night To coordinates that math had predicted Within one degree of calculated sight Neptune shone where algorithms depicted The triumph echoed through the halls of science Mathematical prediction proved its worth When observation met computational guidance A new world joined the family of our Earth [Chorus] Perturbation shows the way When the numbers drift astray Numerical integration runs the dance Least squares finds the best solution Through the orbital confusion Algorithms gave Neptune its chance [Outro] From Uranus dancing strangely in the void To Neptune's light through telescope revealed The mystery that once had us annoyed By mathematical precision was unsealed
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