Final answer:
Gravitational forces are vectors, so to find the total force, you need to use vector addition rather than adding magnitudes. A free-body diagram and principles of vector addition are used to calculate the combined force, considering each force's magnitude and direction.
Step-by-step explanation:
When multiple gravitational forces act on a body, you cannot simply add the magnitudes of the gravitational forces to find the total force. This is because gravitational forces are vector quantities, which means they have both direction and magnitude. To calculate the total force, you need to find the vector sum of the forces. This requires using mathematical tools that account for the direction of each gravitational force as well as its magnitude.
One such tool is constructing a free-body diagram to visualize how forces are acting on the object. Then, using vector addition, you can calculate the net force on the body. For each force, you would need to identify its magnitude and direction. You can represent these forces as vectors and add them using the principles of vector addition -- typically by breaking them into their respective x and y components or by using trigonometry and geometry for angled forces.
To apply Newton's second law of motion (F=ma), you first need to determine the net force acting on the object and then use it to find the object's acceleration. This approach allows for an accurate description of the motion of celestial bodies, like stars in a cluster or satellites in orbit, where mutual gravitational effects are considered.