Yes, the constellations on your Starfinder chart will shift in the sky if you observe from a location further south than 34° north latitude.
As you move southward in latitude, the entire night sky changes. Specifically:
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Visible Constellations: Some constellations that are visible in the northern hemisphere may dip below the horizon and become invisible, while others that are not seen at higher latitudes become visible.
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Celestial Pole: The North Celestial Pole, which is the point in the night sky directly above the Earth's North Pole, will appear lower in the sky as you travel south. Conversely, the South Celestial Pole will rise higher in the sky.
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Altitude of Stars: Stars located towards the celestial equator will appear higher in the sky as you move south. For instance, constellations like Orion, which are commonly seen from northern latitudes, will appear higher and more prominent in the sky when viewed from southern latitudes.
In summary, if you are observing from a location further south than 34° N, you can expect a noticeable change in the visible constellations and their positions in the night sky compared to observing from Los Angeles.