1. [6pts]
The distance between the Sun and the Earth is 1 AU.
The distance between the Sun and Pluto is about 40 AU.
In order to directly compare these distances to that of the nearest star (Alpha or Proxima
Centauri) all the distances need to be expressed in the same units. The most convenient thing to do
here would be to convert 4 light years to AU:
4 light years x (9.46x1012 km/lt year) / (1.49x108 AU/km )
=2.54x105 AU (about 254,000 AU)
If we have a ship that can travel 1 AU in 1 month, then it will take 2.54x105 months, or
about 21,000 years, to travel to the nearest star.
2. [6pts]
Newton's 3rd Law is most applicable here. This is the one that says for every action there is
an equal but opposite reaction.
As hot gases (the exhuast plume) shoots out the back end of the rocket, the reaction
is for the rocket to move in the opposite direction. The rocket is propelled forward because the gases are pushing
on the vehicle itself, not anything else. This is true both during and after launch.
Some people made the argument that the rocket pushes off the ground, which then reacts by pushing on the rocket.
One might get this idea from seeing video footage of shuttle launches, for example, where you see a spectacular cloud of
gases slamming into the ground upon lift-off. However, before the gases hit the ground, they first push on the rocket
as they exit the back nozzle. Since the nozzle is directed downward, the rocket responds by moving upward.
Once the gases are free of the rocket, they keep expanding downward and outward, running into the launchpad, but
the ground didn't push the rocket into the air. Another problem with this argument is that, once the rocket has
lifted-off, there would be no more ground to push against. How then would the rocket be able to keep
accelerating upward?
Once the rocket is in the air, the exhaust gases are still pushing on the rocket, not the surrounding air.
As some of you realized, there is no air in space and yet rockets can still be accelerated!
3. [8pts] a. mass of the Sun: 1.99x1030 kg b. 0.73 x (1.99x1030 kg)=1.45 x 1030 kg c. 0.10 x (1.45 x 1030 kg) = 1.45 x 1029 kg d. 0.007 x (1.45 x 1029 kg) = 1.02 x 1027 kg e. In order to get the energy in Joules, you need to use the metric value of
the speed of light: c=3x108 m/s.
Einstein's equation says: f. The time for it will take for the hydrogen fuel to run out is the total amount
of energy available/the energy consumption rate: Some General Comments.
E=mc2 (energy = mass multiplied by the speed of light squared).
E = 1.02 x 1027 kg x (3x108 m/s)2= 9.15x1043 Joules
9.15x1043 Joules / 3.8x1026 Joule/sec = 2.4x1017 seconds
Converting into years:
2.4x1017 s/(3600 sec/hr x 24 hr/day x 365 days/yr) = 7.6x109 years
(or 7.6 billion years)
1. When you do a calculation, make sure you show as much work as possible. Showing all your steps also
helps you get more partial credit if you don't arrive at the correct final answer.
2. If a homework problem involves a calculation, feel free to work out the problem by hand.
Typing up equations and calculations is perfectly fine, but I understand that this can get tedious.
Just make sure that everything is legible!
3. When expressing a final number, please don't include more than a couple decimal places at most. Numbers in the
10th or umpteenth decimal place have no meaning, as values typically do not have such high precision!