Calculate the gravitational potential energy of a $9.50\mathrm{~kg}$ mass on the surface of the Earth.

Two $0.59 \mathrm{~kg}$ basketballs, each with a radius of $12 \mathrm{~cm}$, are just touching. How much energy is required to change the separation between the centers of the basketballs to $10.0 \mathrm{~m}$ ? (Ignore any other gravitational interactions.)

Two satellites orbit the Earth, with satellite $1$ at a greater altitude than satellite $2$. Calculate the orbital speed of a satellite that orbits at an altitude of two Earth radii above the surface of the Earth.

Two satellites orbit the Earth, with satellite $1$ at a greater altitude than satellite $2$. Which satellite has the greater orbital speed? Explain.

At some point along the direct path from the center of the Earth to the center of the Moon, the gravitational force of attraction on a spacecraft from the Moon becomes greater than the force from the Earth. How far from the center of the Earth does this occur?

An Asteroid with Its Own Moon The asteroid $243$ Ida has its own small moon, Dactyl. Outline a strategy to find the mass of $243$ Ida, given that the orbital radius of Dactyl is $89 \mathrm{~km}$ and its period is $19 \mathrm{hr}$. Use your strategy to calculate the mass of 243 Ida.

An Asteroid with Its Own Moon The asteroid $243$ Ida has its own small moon, Dactyl. Outline a strategy to find the mass of $243$ Ida, given that the orbital radius of Dactyl is $89 \mathrm{~km}$ and its period is $19 \mathrm{hr}$.

Two satellites orbit the Earth, with satellite $1$ at a greater altitude than satellite $2$. Calculate the orbital speed of a satellite that orbits at an altitude of one Earth radius above the surface of the Earth.

Two $0.59 \mathrm{~kg}$ basketballs, each with a radius of $12 \mathrm{~cm}$, are just touching. How much energy is required to change the separation between the centers of the basketballs to $1.0 \mathrm{~m}$ ? (Ignore any other gravitational interactions.)

The Martian moon Deimos has an orbital period that is greater than the other Martian moon, Phobos. Both moons have approximately circular orbits. Calculate the distance from the center of Mars to Deimos given that its orbital period is $1.10 \times 10^5 \mathrm{~s}$.

At what altitude above Earth's surface is the acceleration due to gravity equal to g/4?

The Martian moon Deimos has an orbital period that is greater than the other Martian moon, Phobos. Both moons have approximately circular orbits. Is Deimos closer to or farther from Mars than Phobos? Explain.

An Asteroid with Its Own Moon The asteroid 243 Ida has its own small moon, Dactyl.Another such system, asteroid 624 Hektor, has a mass of $7.9 \times 10^{18} \mathrm{~kg}$, with its moon orbiting at a radius of $623.5 \mathrm{~km}$ and a period of $2.965$ days. Calculate the mass of 243 Ida.

How long does a laser beam take to travel from the Earth to a reflector on the Moon and back? Take the distance from the Earth to the Moon to be $2.4 \times 10^{5}\ \mathrm{mi}.$ (This experiment was done when the Apollo flights of the early 1970s left laser reflectors on the lunar surface.