Melanderhjelm´s astronomical work was mainly in celestial mechanics, especially the theory for the motions in the Solar system and the Lunar orbit.
Other areas were studies of the atmospheres of the planets, the theory and calculation of the Equation of Time and studies of the Venus transitions of 1761 and 1769.
He published a text-book for the fundamental academical lectures in astronomy: Conspectus praelectionum academicarum continens fundamenta astronomiae (1779), used also in many foreign countries. It was later translated to Swedish and published as Astronomie (1795).
Melanderhjelm also took the initiative to the 1802 expedition to Lapland to measure a degree of a meridian to compare with Maupertuis´ values from 1736.
He was the secretary of the Royal Academy of Sciences in Stockholm from 1797.