The millennium eagle passes between a pair of asteroids, as shown. If the mass of the spaceship is 2.50 x 10⁷kg and the mass of each asteroid is 3.50 x 10¹¹kg, find the net gravitational force exerted on the millennium eagle at point (A) and point (B). Treat the asteroids and the spaceship as if they were point objects
F = G(m₁m₂)/r²
The Attempt at a Solution
This is not really a question I need help answering as the solution is laid out by the author. My question is more about the fundamentals of doing this type of problem.
As you can see in part (A) found the value of R using the Pythagorean theorm and then added up the components to find the net force acting.
I wanted to try and solve it a different way. So I decided to fist calculate the components and then just add them up. This seemed easier and more straightforward to me as it requires less steps.
F1 = F1x + F1y
F2 = F2x + F2y
When calculating the F1x and F1y I got ridiculously different answers than what F1x and F1y is in the book.
Using the universal gravitational law I got
F1x = (6.67x10^-11)(2.50x10^7)(3.50x10^11)/(3000^2)N = 64.8N
As you can see this Is not what I am supposed to get for F1x..
Its seems like my strategy will not work. Is there a reason why? Can somebody please explain this? Thanks!