The force of gravity is the force exerted by the gravitational field of a massive object on any body within the vicinity of its surface. This force is dependent on three factors: the mass of the massive object, the mass of the smaller body, and the separation between the two, measured between their geometrical centers. Since planets are typically spherical, then their cores are taken to be their geometrical centers.
Strictly speaking, Newton’s Law of Universal Gravitation, from which the concept of the force of gravity is based on, does not stipulate a massive body and a smaller body. Instead it simply stipulates that the law affects two bodies regardless of whether one is really massive or not. However, since we commonly use the term ‘gravity’ in the context of massive celestial bodies, we defined the force of gravity accordingly in the first paragraph.
If we were to calculate the gravitational force, we would need one more factor, a gravitational constant with the value 6.673×10-11 N m2 kg-2
In our day to day lives, we can measure the force of gravity. Its more familiar term is ‘weight’. Thus, in most cases , your measured weight is actually a measurement of the force of the Earth’s gravity on you. The heavier you are, the greater is the force of gravity on you. There are exceptions, like when you are buoyed up by a fluid but that is for another text.
Allow me to add the mathematical relationship that defines the acceleration due to gravity or the gravitational force. Don’t worry, it’s going to simplify our understanding of this physical quantity. Here it is:
F = (G x m1 x m2) / r2
F = force of gravity
G = gravitational constant
m1 = mass of the first object (lets assume it’s of the massive one)
m2 = mass of the second object (lets assume it’s of the smaller one)
r = the separation between the two masses
Notice that the gravitational force is directly proportional to m1. Thus, all things being equal, a more massive planet would exert a larger gravitational force than a smaller planet. Hence, you’ll be ‘heavier’ on Jupiter than here on Earth.
Notice that the gravitational force is also directly proportional to m2. Thus, all things being equal again, you would weigh more than a puppy. I assume this is the easiest to imagine.
Finally, notice that the force of gravity is inversely proportional to the square of r. Thus, all things being equal again, you would feel heavier on the surface of the Earth than on say, a hot air balloon at high altitudes. Notice that since F is inversely proportional to the square of r, F would vary rapidly for a slight change in r. Thus, if you go even further from the Earth’s surface, say on a satellite, F would decrease rapidly and even become negligible.
There’s more about it at NASA. Here are a couple of sources there:
Here are two episodes at Astronomy Cast that you might want to check out as well:
Decelerating Black Holes, Earth-Sun Tidal Lock, and the Crushing Gravity of Dark Matter