A spacecraft is traveling directly toward Saturn, which exerts a gravitational f

Question

A spacecraft is traveling directly toward Saturn, which exerts a gravitational force of 7.7 units on it. Saturn's moon Titan exerts a force of 10.6 units on it, at a 40 degree to the left of the line between Saturn and the spacecraft. The moon Rhea exerts a force of 5 units, 80 degree to the right of this line. (a) Find ||F rightarow _STR||, the magnitude of the sum of the forces acting on the spacecraft ||F rightarow _STR|| = units. (b) Does the craft remain on course, or veer to the left or to the right? The craft will go in which direction? (c) If the engines have a thrust of 1 unit, is it possible to aim them in such a way as to correct the spacecraft's course? Is it possible?

Explanation / Answer

Find Forces in x and y direction:

Fx = 7.7 + 10.6cos40 + 5cos80

= 16.68 units

Fy = 0 + 10.6sin40 - 5sin80

= 1.89 units

||Fstr|| = sqrt(Fx^2 + Fy^2) = 16.78

Angle = 6.426 deg to the left of horizontal

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