Each of the following diagrams shows a spaceship somewhere along the way between

Question

Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distance is marked to make it easier to see how the locations compare. Assume the spaceship has the same mass throughout the trip (that is, it is not burning any fuel). Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest. The following diagrams are the same as those from Part A. This time, rank the five positions of the spaceship from left to right based on the strength of the gravitational force that the Moon exerts on the spaceship, from strongest to weakest. The following diagrams show five pairs of asteroids, labeled with their relative masses (M) and distances (d) between them. For example, an asteroid with M=2 has twice the mass of one with M=1 and a distance of d= 2 is twice as large as a distance of d = 1. Rank each pair from left to right based on the strength of the gravitational force attracting the asteroids to each other, from strongest to weakest.

Explanation / Answer

Part A: The gravitational force on an object is based on the mass andthe inverse of distance2. This means that the more distance betweenthe two objects, the less gravitational force. The only two objectstaken into account in this part are the spaceship and Earth. Theposition of the moon does not matter, only the space between thespaceship and the Earth. Frame#1 - The spaceship is 3rd in nearness to the Earth Frame#2 - The spaceship is 4th in nearness to the Earth Frame#3 - The spaceship is 5th in nearness to the Earth Frame#4 - The spaceship is 2nd in nearness to theEarth Frame#5 - The spaceship is 1st in nearness to theEarth The closer they are to the Earth the stronger thegravity. Strongest to Weakest: Frame: 5-4-1-2-3 Part B: This part is the complete reverse of the Part A. Therefore thefurther it is away from the Earth the closer it is to the moon. Thestrength of gravitational pull is just backwards from Part A, inreference to the moon. Strongest to Weakest: Frame: 3-2-1-4-5 Part C: Since gravitational pull is greater the closer and bigger theobjects are, we can easily rank them based on these concepts. It isalso worthwhile to remember that distance plays thebigger role due to the fact that its value is squared. Equation for gravity: where G = gravitational constant m1 = first astroid m2 = second astroid d = distance between them To determine the order simply plug the values into theequation for gravity, disregarding the G since it is aconstant. Frame#1 = (1)(1)/(22) = 1/4 Frame#2 = (1)(2)/(22) = 1/2 Frame#3 = (1)(2)/(12) = 2 Frame#4 = (2)(2)/(12) = 4 Frame#5 = (1)(1)/(12)= 1 The higher the value the stronger the gravitationalpull. Strongest to weakest: Frame#: 4-3-5-2-1

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