# Relationship between gravitational force and distance

### Why do mass and distance affect gravity?

many other objects. The strength of the gravitational force between two objects depends on two factors, mass and distance. The Mass of the Objects The more. This illustrates the inverse relationship between separation distance and the force of gravity (or in this case, the weight of the student). The student weighs less at. Gravity is a fundamental underlying force in the universe. The amount of gravity that something possesses is proportional to its mass and distance between it and another object. This relationship was first published by Sir Issac Newton. His law .

The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death.

## Space Environment

This experiment will be discussed later in Lesson 3. Using Newton's Gravitation Equation to Solve Problems Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance. As a first example, consider the following problem. The solution of the problem involves substituting known values of G 6.

The solution is as follows: This would place the student a distance of 6. Two general conceptual comments can be made about the results of the two sample calculations above.

First, observe that the force of gravity acting upon the student a. This illustrates the inverse relationship between separation distance and the force of gravity or in this case, the weight of the student. The student weighs less at the higher altitude. However, a mere change of 40 feet further from the center of the Earth is virtually negligible. A distance of 40 feet from the earth's surface to a high altitude airplane is not very far when compared to a distance of 6.

This alteration of distance is like a drop in a bucket when compared to the large radius of the Earth. As shown in the diagram below, distance of separation becomes much more influential when a significant variation is made.

The second conceptual comment to be made about the above sample calculations is that the use of Newton's universal gravitation equation to calculate the force of gravity or weight yields the same result as when calculating it using the equation presented in Unit 2: What happens to the forces between the two objects?

Again using inverse square law, we get distance squared to go up by a factor of 9. The force decreases by a factor of 9 and becomes 1. If you wanted to make a profit in buying gold by weight at one altitude and selling it at another altitude for the same price per weight, should you buy or sell at the higher altitude location?

What kind of scale must you use for this work? To profit, buy at a high altitude and sell at a low altitude. Explanation is left to the student. Check Your Understanding 4. Your weight is nothing but force of gravity between the earth and you as an object with a mass m. As shown in the above graph, changing one of the masses results in change in force of gravity. The planet Jupiter is more than times as massive as Earth, so it might seem that a body on the surface of Jupiter would weigh times as much as on Earth.

But it so happens a body would scarcely weigh three times as much on the surface of Jupiter as it would on the surface of the Earth. Explain why this is so. The effect of greater mass of Jupiter is partly off set by its larger radius which is about 10 times the radius of the earth. This means the object is times farther from the center of the Jupiter compared to the earth. Inverse of the distance brings a factor of to the denominator and as a result, the force increases by a factor of due to the mass, but decreases by a factor of due to the distance squared.

The net effect is that the force increases 3 times. Planetary and Satellite Motion After reading this section, it is recommended to check the following movie of Kepler's laws. Kepler's three laws of planetary motion can be described as follows: Law of Orbits Kepler's First Law is illustrated in the image shown above. The Sun is not at the center of the ellipse, but is instead at one focus generally there is nothing at the other focus of the ellipse.

The planet then follows the ellipse in its orbit, which means that the Earth-Sun distance is constantly changing as the planet earth goes around its orbit. For purpose of illustration we have shown the orbit as rather eccentric; remember that the actual orbits are much less eccentric than this. Law of Areas Kepler's second law is illustrated in the preceding figure.

The line joining the Sun and planet sweeps out equal areas in equal times, so the planet moves faster when it is nearer the Sun. Thus, a planet executes elliptical motion with constantly changing angular speed as it moves about its orbit. The point of nearest approach of the planet to the Sun is termed perihelion; the point of greatest separation is termed aphelion.

Hence, by Kepler's second law, the planet moves fastest when it is near perihelion and slowest when it is near aphelion. Law of Periods In this equation P represents the period of revolution for a planet in some other references the period is denoted as "T" and R represents the length of its semi-major axis. The subscripts "1" and "2" distinguish quantities for planet 1 and 2 respectively. The periods for the two planets are assumed to be in the same time units and the lengths of the semi-major axes for the two planets are assumed to be in the same distance units.

Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. Thus, we find that Mercury, the innermost planet, takes only 88 days to orbit the Sun but the outermost planet Pluto requires years to do the same. The Seasons There is a popular misconception that the seasons on the Earth are caused by varying distances of the Earth from the Sun on its elliptical orbit.

**Newtonian Gravity: Crash Course Physics #8**

This is not correct. One way to see that this reasoning may be in error is to note that the seasons are out of phase in the Northern and Southern hemispheres: Seasons in the Northern Hemisphere The primary cause of the seasons is the This means that as the Earth goes around its orbit the Northern hemisphere is at various times oriented more toward and more away from the Sun, and likewise for the Southern hemisphere, as illustrated in the following figure.

Thus, we experience Summer in the Northern Hemisphere when the Earth is on that part of its orbit where the N.

### The Universe Adventure - Gravitational Equation

Hemisphere is oriented more toward the Sun and therefore the Sun rises higher in the sky and is above the horizon longer, and the rays of the Sun strike the ground more directly. Likewise, in the N. Hemisphere Winter the hemisphere is oriented away from the Sun, the Sun only rises low in the sky, is above the horizon for a shorter period, and the rays of the Sun strike the ground more obliquely. In fact, as the diagram indicates, the Earth is actually closer to the Sun in the N.

Hemisphere Winter than in the Summer as usual, we greatly exaggerate the eccentricity of the elliptical orbit in this diagram.

G is the "gravitational coupling constant", which sets the size of the force between two massive objects separated by a given distance. Because gravity is the weakest of the 4 fundamental forces of nature, G is hard to measure experimentally with any precision.

Newton did not know the value of G, but he was able to pose his problems in ways that G drops out mathematically, thus to him it was just a constant of proportionality. The first experimental measurment of G was done by British physicist Henry Cavendish in experiments performed between andusing a torsion balance to measure the force of gravity between two weights in the laboratory. However, Cavendish's explicit goal for this experiment was to accurately measure the density - and hence the Mass - of the Earth, and he never once mentions G in his work or explicitly derives a value for it.

Like Newton, Cavendish posed his problems so that G canceled mathematically. We'll do much the same in this class, which is why you'll never need to know G operationally for exams or homework problems. It was not until much later almost 75 years later that his experimental data was used by others to derive a value for G.

## Homework Help: Relationship between distance and gravitational force

It was not until the later part of the 19th century that astronomers needed to know G so they could, among other things, compute the densities of celestial bodies like the Moon and Sun. Stand on the Earth and drop an apple. What is the force of the Earth on the apple?

This means that the acceleration due to gravity is independent of the mass of the apple, just like Galileo had shown earlier. Equal and Opposite Reactions But, Newton's Third Law of Motion states that all forces come in equal yet opposite pairs What force does the the apple apply in return upon the Earth? The Mass of the Earth We can directly measure the acceleration of gravity at the surface of the Earth by dropping objects and timing their fall e.

This is an example of one of the powerful implications of Newton's Law of Gravity: It gives us a way to use the motions of objects under the influence of their mutual gravitation to measure the masses of planets, stars, galaxies, etc.