Captain James T. Kirk of Star Trek fame spent a large portion of his time mining for planets that contained heavy metals after leaving active duty. In order to accomplish this, he put his spaceship into an elliptical orbit around the planet and measured its density (= total mass/volume; a sphere's volume is equal to 4/3pi r^(3)), where r is its radius). Significant concentrations of important heavy metals were probably present on planets with densities higher than normal. The radius of the planet, the period of the orbit, the minimum and greatest distances of his ship from the planet's centre, or r_min and r_max, were the only measurements he took to arrive at this conclusion. The engines of the ship were deactivated during his journey in the elliptic orbit. Ignore any effects the local star might have on the motion. Kirk also knows the mass of his ship. Explain how he was able to determine the planet’s density using this method.
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