Final answer:
The algebraic expression for the planet's density when a satellite orbits very near its surface with a period is rho = GM / (4πR^3). Therefore the correct option is C) rho=GM/4πR3.
Step-by-step explanation:
To derive an algebraic expression for the density of a planet when a satellite orbits very near its surface with a period, we can use the following equation:
rho = GM / (4πR^3)
where rho is the density of the planet, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.
Newton's law of universal gravitation states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The gravitational force is always attractive, meaning it pulls objects towards each other. It's a fundamental force in the universe and plays a significant role in the motion of celestial bodies, such as planets orbiting around stars and the moon orbiting around Earth.