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 frustrating 10 meters away. Your spacesuit has no jet...
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 frustrating 10 meters away. Your spacesuit has no jet pack and you have no air to spare. All you have is your wrench. How do you return to your ship? State the corresponding physical principle
2. Suppose Earth had a second moon, called Swisscheese, with an average orbital distance double the Moon’s and a mass about the same as the Moon’s.
a. (3 points) How does Swisscheese’s orbital period compare to that of the Moon? In a few words, justify your answer and state the corresponding law and/or principle.
b. (5 points) In a few words, describe how tides would differ due to the presence of this second moon. Consider the cases when the two moons are on the same side of Earth, on opposite sides of Earth, and 90◦ apart in their orbits. Justify your answer!
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.
As the previous answer noted, there are a couple of ways to explain part 1 of the question. The previous answer said that you could throw the wrench in the opposite direction that you want to travel in order to make it back to your space ship. This would definitely work, and it can be explained with Newton's Laws of Motion. Newton's third law says that for every force that is applied, there is also an equal and opposite force applied. In this situation, you apply a force to the wrench in order to throw it, and the wrench applies a force of equal size on you. It is important to note that the wrench and you will not be moving at the same rate. The same size force was applied to you and the wrench, but your mass is likely much greater than the wrench's mass. The rate of acceleration for you and the wrench can be calculated using Newton's second law. It states that the acceleration of an object depends on the force applied to the object and the mass of the object. The equation looks like this: Acceleration = Force/Mass. Your greater mass means that your acceleration will be less than that of the wrench. Throwing the wrench will move you the 10 meters back to your ship, but you might not move that quickly. You will eventually get there, though. Since you are in a vacuum, there is not fluid friction between you and the space craft. Once you are moving, you will keep moving in that direction and at that speed. This is Newton's first law. Make sure your wrench throw is accurate because you won't be able to slow down or change directions.