Opponents of the Thirty Meter Telescope appealed a Board of Land and Natural Resources decision to the Third Circuit Court in Hilo in May.
The petitioners say they want to force the board to uphold its public trust duties to protect Hawaii's natural and cultural resources as traditional and customary Hawaiian practices depend on these resources.
Kealoha Pisciotta, the president of Mauna Kea Anaina Hou, an organisation of Native Hawaiian traditional and cultural practitioners of Mauna Kea, said the question is whether the rules allow more development that would have an adverse and significant impact on the mountain's land and waters. She said the "answer is no."
The project to build the telescope was started by the University of California, California Institute of Technology and the Association of Canadian Universities for Research in Astronomy.
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Observatories and institutions in China, India and Japan have since signed on as partners.
Thirty Meter Telescope Corporation hopes to begin construction in April 2014 and start operations in 2021.
The telescope's segmented primary mirror would be nearly 100 feet or 30 meters long. TMT says this will give its telescope nine times the collecting area of the largest optical telescopes in use today, the twin W M Keck telescopes built on Mauna Kea in the 1990s.