Practice Test 7

A satellite of mass $m = 1.0 \times 10^3\ \text{kg}$ orbits Earth at an altitude of $h = 4.0 \times 10^5\ \text{m}$ above Earth’s surface. Use $M_E = 6.0 \times 10^{24}\ \text{kg}$, $R_E = 6.4 \times 10^6\ \text{m}$, and $G = 6.67 \times 10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$. Taking $r = R_E + h$, what is the magnitude of the gravitational force on the satellite?

A spacecraft of mass $m = 2.0 \times 10^3\ \text{kg}$ is in circular orbit at a distance $r = 1.28 \times 10^7\ \text{m}$ from Earth’s center (this is $2R_E$ where $R_E = 6.4 \times 10^6\ \text{m}$). Using $M_E = 6.0 \times 10^{24}\ \text{kg}$ and $G = 6.67 \times 10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$, what is the magnitude of Earth’s gravitational force on the spacecraft?