1. (4 point) You are alone in space and your tether brakes and you are floating motionless relative to your spaceship, which is located a...

1) There might be various possible answers to this question. One way to return to your spaceship is by throwing the wrench in the direction opposite to the direction between your and the ship. This will get you moving in the direction of the spaceship.

The physical principle involved here is the conservation of the linear momentum. The original momentum of "you-and-the-wrench" system, relative to the spaceship, is zero. If you through the wrench away from...

1) There might be various possible answers to this question. One way to return to your spaceship is by throwing the wrench in the direction opposite to the direction between your and the ship. This will get you moving in the direction of the spaceship.

The physical principle involved here is the conservation of the linear momentum. The original momentum of "you-and-the-wrench" system, relative to the spaceship, is zero. If you through the wrench away from the spaceship, you will give it momentum equal to the mass of the wrench times the velocity of the wrench. The harder you throw the wrench, the greater its velocity and the momentum. 

Because momentum is conserved, since wrench is now given momentum pointing away from the ship, you will then be given momentum equal to that of the wrench and pointing toward the ship. This means you will start moving in the direction of the ship and your momentum will equal your mass times your velocity. Because you are more massive than the wrench, your speed will be smaller than that of the wrench. However, because you are in space, where is no air, there will be no resistance to your motion. So after you throw the wrench you will continue moving with the same speed in the same direction, and eventually reach the ship. This is according to the first Newton's law, also known as the principle of inertia, which states that in the absence of forces an object continues to move with the given velocity (with the same speed and in the same direction.)

2a) To find the orbital period of Swisscheese, you need the third Kepler's Law, the law of orbits. It states that for two planets orbiting around the same star, or another planet, the square of orbital period equals the cube of the radius of the orbit. This is independent of the mass of the orbiting planets, and follows directly from the Newton's law of gravity.

So if the average orbital distance of Swisscheese is double that of the moon, the square of its orbital period is eight times greater, and the orbital period itself is greater by a factor equal to the square root of eight, or approximately 2.83.