How to Calculate Force of Gravity

Gravity is everywhere – both literally and in the everyday conscious doings of people around the planet. It is difficult or impossible to imagine living in a world free of its effects, or even in one where the effects were tweaked by a "small" amount – say, "only" about 25 percent. Well, imagine yourself going from not quite being able to jump high enough to touch a 10-foot-high basketball rim to being able to slam-dunk with ease; this is about what a 25-percent gain in leaping ability thanks to lessened gravity would provide a vast number of people!

One of the four fundamental physical forces, gravity influences every engineering enterprise humans have ever undertaken, especially in the realm of economics. Being able to calculate the force of gravity and solve related problems is a basic and essential skill in introductory physical science courses.

The Force of Gravity

No one can say exactly what gravity "is," but it is possible to describe it mathematically and in terms of other physical quantities and properties. Gravity is one of the four fundamental forces in nature, the others being the strong and weak nuclear forces (which operate at the intra-atomic level) and the electromagnetic force. Gravity is the weakest of the four, but has enormous influence on how the universe itself it structured.

Mathematically, the force of gravity in Newtons (or equivalently, kg m/s2) between any two objects of mass M1 and M2 separated by r meters is expressed as:

F_{grav} = \frac{GM_1M_2}{r^2}

where the universal gravitation constant G = 6.67 × 10-11 N m2/kg2.

Gravity Explained

The magnitude g of the gravitational field of any "massive" object (that is, a galaxy, star, planet, moon, etc.) is expressed mathematically by the relationship:

g = \frac{GM}{d^2}

where G is the constant just defined, M is the mass of the object and d is the distance between the object and the point at which the field is measured. You can see by looking at the expression for Fgrav that g has units of force divided by mass, since the equation for g is essentially the force of gravity equation (the equation for Fgrav) without accounting for the mass of the smaller object.

The variable g therefore has units of acceleration. Near the surface of the Earth, the acceleration owing to the Earth's gravitational force is 9.8 meters per second per second, or 9.8 m/s2. If you decide to go far in physical science, you will see this figure more times than you'll be able to count.

Force Due to Gravity Formula

Combining the formulae in the above two sections produces the relationship

F=mg

where g = 9.8 m/s2 on Earth. This is a special case of Newton's second law of motion, which is

F=ma

The gravity acceleration formula can be used in the usual way with the so-called Newtonian equations of motion that relate mass (m), velocity (v), linear position (x), vertical position (y), acceleration (a) and time (t) . That is, just as d = (1/2)at2, the distance an object will travel in time t in a line under the force of a given acceleration, the distance y an object will fall under the force of gravity in time t is yielded by the expression d = (1/2)gt2, or 4.9_t_2 for objects falling under the influence of Earth's gravity.

Tips

  • In introductory physics, when you are asked to solve gravity problems including free fall, you are asked to ignore the effects of air resistance. In practice, these effects are considerable, as you will learn if you pursue engineering or a similar field.

References

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.