Suppose that f is an inverse square force field below, where c is a constant.
f(r) = cr/|r|3
r = x i + y j + z k
(a) find the work done by f in moving an object from a point p1 along a path to a point p2 in terms of the distances d1 and d2 from these points to the origin.
(b) an example of an inverse square field is the gravitational field f = -(mmg)r/|r|3. use part (a) to find the work done by the gravitational field when the earth moves from aphelion (at a maximum distance of 1.52

Forces in our Universe

Step-by-step explanation:

a)

First of all we have,

and,

We need to define a function that allows us to find said change based on r, so one of the functions that shows that change is,

That is,

For this case F is a conservative field and the line integral is independent of the path. Thus, defining   and . So the amount of work on the movement of the object from P1 to P2 is,

2) The gravitational force field is given by,

The maximum distance from the earth to the sun is km and the minimum distance is km. The mass values of the bodies are given by m = kg, M = kg and the constant G is

In this way we raise the problem like this,