What is the direction of the gravitational force that acts on an object

Each of the following figures shows two rocks in outer space. Which figure correctly shows the direction of the gravitational force exerted on each rock? (a), (b), (c), (d), or (e).

Okay, so here we’re told that we have two rocks in outer space. That means there are no other masses anywhere nearby these rocks. Therefore, we can assume that the gravitational force exerted on each rock is due only to the other of the two rocks. In order to figure out which of these five diagrams correctly shows the direction of the forces acting on each rock, we can recall a principle about gravitational force. That is, gravitational force is always attractive.

This means that if we have two masses, say one mass here and the other mass here, the force of gravity will cause this mass to be attracted to the other one. And this second mass to be attracted to the first. That is, the force vectors we could show on each mass lie along a line between the two masses. This is always true when objects exert gravitational forces on one another. Those attractional forces lie along a line between the two objects’ respective centers of mass.

Looking at our answer options, we see option (a) agreeing with the rule we just described. If the center of mass of the reddish-brown rock is here and the center of mass of the yellowish rock is right here, then we can see that the two gravitational force vectors lie along the line between these points. And what’s more, they point in such a way that indicates these forces as attractive. That is, the rocks will tend to move toward one another.

Before we confirm that option (a) is the correct answer, let’s look at the remaining choices. For option (b), if we draw a straight line between the two centers of mass, we see the forces don’t lie along this line. So, that means option (b) won’t be our choice. Then, looking at option (c), here the force vectors do lie along this line. But we notice that the force on the reddish-brown rock is pointed in the wrong direction. The implication here is that the golden-colored rock is somehow repelling the reddish-brown one. But we know that gravity doesn’t act that way. We’ll cross off option (c) then as well.

Looking at option (d), this fails for the same reason option (b) did. The force vectors do not lie along the line connecting these rocks’ centers of mass. And lastly, for option (e), the vectors are along this line. But now, they both imply a repulsive force rather than an attractive one. But gravity is always attractive. So, we’ll cross out option (e) too.

This confirms our earlier assessment that it’s figure (a) that correctly shows the direction of the gravitational force exerted on each rock.

Isaac Newton's First Law of Motion states, "A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force." What, then, happens to a body when an external force is applied to it? That situation is described by Newton's Second Law of Motion. 

According to NASA, this law states, "Force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration." This is written in mathematical form as F = ma

F is force, m is mass and a is acceleration. The math behind this is quite simple. If you double the force, you double the acceleration, but if you double the mass, you cut the acceleration in half. 

Newton published his laws of motion in 1687, in his seminal work "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy) in which he formalized the description of how massive bodies move under the influence of external forces. 

Newton expanded upon the earlier work of Galileo Galilei, who developed the first accurate laws of motion for masses, according to Greg Bothun, a physics professor at the University of Oregon. Galileo's experiments showed that all bodies accelerate at the same rate regardless of size or mass. Newton also critiqued and expanded on the work of Rene Descartes, who also published a set of laws of nature in 1644, two years after Newton was born. Descartes' laws are very similar to Newton's first law of motion.

Acceleration and velocity

Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is viewed from a moving inertial reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other.

The bold letters F and a in the equation indicate that force and acceleration are vector quantities, which means they have both magnitude and direction. The force can be a single force or it can be the combination of more than one force. In this case, we would write the equation as ∑F = ma

The large Σ (the Greek letter sigma) represents the vector sum of all the forces, or the net force, acting on a body. 

It is rather difficult to imagine applying a constant force to a body for an indefinite length of time. In most cases, forces can only be applied for a limited time, producing what is called impulse. For a massive body moving in an inertial reference frame without any other forces such as friction acting on it, a certain impulse will cause a certain change in its velocity. The body might speed up, slow down or change direction, after which, the body will continue moving at a new constant velocity (unless, of course, the impulse causes the body to stop).

There is one situation, however, in which we do encounter a constant force — the force due to gravitational acceleration, which causes massive bodies to exert a downward force on the Earth. In this case, the constant acceleration due to gravity is written as g, and Newton's Second Law becomes F = mg. Notice that in this case, F and g are not conventionally written as vectors, because they are always pointing in the same direction, down.

The product of mass times gravitational acceleration, mg, is known as weight, which is just another kind of force. Without gravity, a massive body has no weight, and without a massive body, gravity cannot produce a force. In order to overcome gravity and lift a massive body, you must produce an upward force ma that is greater than the downward gravitational force mg. 

Newton's second law in action

Rockets traveling through space encompass all three of Newton's laws of motion.

If the rocket needs to slow down, speed up, or change direction, a force is used to give it a push, typically coming from the engine. The amount of the force and the location where it is providing the push can change either or both the speed (the magnitude part of acceleration) and direction.

Now that we know how a massive body in an inertial reference frame behaves when it subjected to an outside force, such as how the engines creating the push maneuver the rocket, what happens to the body that is exerting that force? That situation is described by Newton’s Third Law of Motion. 

In what direction is the force of gravity acting?

What is the direction of the gravitational force acting on the left object?