Use the figure: a comet is $8.0\ast 10^{10}\text{m}$ from the star at A and $4.0\ast 10^{11}\text{m}$ at B. At both points v is perpendicular to the star line, and gravity gives no torque. How do speed and angular momentum compare?

Use the figure: an asteroid has the same mass at C and D; C is $3.0\ast 10^{10}\text{m}$ from the star and D is $6.0\ast 10^{10}\text{m}$. Velocities are perpendicular to the star line. Which energy comparison is correct?

Use the figure: point P is $1.2\ast 10^8\text{m}$ from the planet and point Q is $3.6\ast 10^8\text{m}$ away. Each velocity is perpendicular to the radius line. If angular momentum is conserved, what is $v_P/v_Q$?

Use the figure: at E a probe is $2.0\ast 10^{11}\text{m}$ from the star and moving at $5.0\ast 10^4\text{m}/\text{s}$. At F it is $5.0\ast 10^{11}\text{m}$ away. The velocity is perpendicular to the radius at both points. What is $v_F$?

Use the figure: point G is $4.0\ast 10^7\text{m}$ from the planet and point H is $1.0\ast 10^8\text{m}$ away. The orbiting object's velocity is perpendicular to the radius at each point. Which statement is consistent with gravity alone?

Use the figure: point N is $7.5\ast 10^{10}\text{m}$ from the star and point M is $1.5\ast 10^{11}\text{m}$ away. At which point are both the gravitational force magnitude and the orbital speed greater?

Use the figure: X is $9.0\ast 10^6\text{m}$ from the planet, and Y is $1.8\ast 10^7\text{m}$ away. At both points the velocity is perpendicular to the radius. If angular momentum is conserved, which relation must hold?

Use the figure: I and J are equal distances from the star on the same elliptical orbit. With no nonconservative work and no torque about the star, how do their speeds and angular momenta compare?

A satellite moves in a circular orbit of radius $7.0\times 10^6\text{m}$ about Earth, mass $5.97\times 10^{24}\text{kg}$. Take $G=6.67\times 10^{-11}\text{N}\cdot {\text{m}}^2/{\text{kg}}^2$. What is its orbital speed?

A moon circles Mars at speed $3.4\times 10^3\text{m}/\text{s}$. Mars has mass $6.42\times 10^{23}\text{kg}$, and $G=6.67\times 10^{-11}\text{N}\cdot {\text{m}}^2/{\text{kg}}^2$. What is the circular orbital radius?

A planet follows a circular orbit of radius $1.50\times 10^{11}\text{m}$ around a star of mass $1.99\times 10^{30}\text{kg}$. Take $G=6.67\times 10^{-11}\text{N}\cdot {\text{m}}^2/{\text{kg}}^2$. What is the orbital speed?

A satellite's circular orbital speed around Earth is $7.7\times 10^3\text{m}/\text{s}$. Earth's mass is $5.97\times 10^{24}\text{kg}$, and $G=6.67\times 10^{-11}\text{N}\cdot {\text{m}}^2/{\text{kg}}^2$. What orbital radius gives that speed?

A planet's angular momentum about the Sun stays constant during its elliptical orbit. What physical reason accounts for that?

Which statement is Kepler's second law, and what does it imply for speed on an elliptical orbit?

For a satellite, gravity is radial but velocity is usually not. Which torque statement about the central body's center is correct?

A comet sweeps out equal areas in equal time intervals as it orbits a star with only gravity acting. Which conservation law explains that area rule?

A comet moves from the far end of its elliptical orbit inward toward the Sun, with no engines or drag. Which statement describes its energy as it approaches?

After passing closest approach, a probe moves outward on its elliptical orbit with only gravity acting. What happens to its kinetic energy, gravitational potential energy, and total energy?

A satellite is in a circular orbit with U = -GMm/r and $v=\sqrt{GM/r}$. What is its total mechanical energy E = K + U?

A comet gains $3.0\times 10^8\text{J}$ of kinetic energy while falling inward, and no nonconservative work is done. What is the change in its gravitational potential energy?