NEET Physics — Gravitation

What does Kepler’s third law imply about the relationship between orbital period and distance?

A moon orbits a planet with a period of 9 days and radius $6 \times 10^8 \, \text{m}$. What is the planet’s mass? ($G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2, 1 \, \text{day} = 86400 \, \text{s}$)

A satellite orbits Earth at $7 R_E$ from the center. What is its orbital speed? ($g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m}$)

A planet orbits the Sun with a period of 7 years. If Earth’s orbital radius is $1.5 \times 10^{11} \, \text{m}$, what is its semi-major axis?

What is the gravitational force on a $12 \, \text{kg}$ mass $10 \, \text{m}$ from the center of a spherical shell of mass $600 \, \text{kg}$ and radius $8 \, \text{m}$? ($G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$)