A proton has a velocity of 1 × 10^5 m/s at point A and a velocity of 3 × 10^5 m/s at point B. If the voltage at point A is 1000 volts, what is the voltage at point B?

a) How much work do you have to do on a 100-kg payload to move it from Earth's surface to a height of 1000 km?

b) How much additional work must you do to put this payload into orbit at this altitude?

The 75,000 kg space shuttle used to fly in a 250-km-high circular orbit. It needed to reach a 610-km-high circular orbit to service the Hubble Space Telescope. How much energy was required to boost it to the new orbit?

A 4000 kg lunar lander is in orbit 50 km above the surface of the moon. It needs to move out to a 300-km-high orbit in order to link up with the mother ship that will take the astronauts home. How much work must the thrusters do?

(III) Show that to slow down a spacecraft (perhaps to put it into orbit around a planet or moon) $v_{0_x}$ must be in the same direction as $\overrightarrow{u}$ and have magnitude greater than u. Show that this means the spacecraft will then pass in front of Jupiter. Draw a new diagram to replace Fig. 8–25b for this situation.

For an object of mass $m$ orbiting a much larger mass $M$ in a stable circular orbit of radius $r$, what is the total mechanical energy of the object?

3) What is the standard unit of measurement for $K=\frac{1}{2}m{v}^2$ (kinetic energy) in the context of circular orbits?

Approximately how much mass does the Sun lose every second due to nuclear fusion in its core?

A magnitude $7.0$ earthquake releases approximately how much energy, expressed in terms of the equivalent energy released by the atomic bomb dropped on Hiroshima (about $6\times {10}^{13}$ joules)?