When calculating gravity, we measure from ____

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gravity, also called gravitation, in mechanics, the universal force of attraction acting between all matter. It is by far the weakest known force in nature and thus plays no role in determining the internal properties of everyday matter. On the other hand, through its long reach and universal action, it controls the trajectories of bodies in the solar system and elsewhere in the universe and the structures and evolution of stars, galaxies, and the whole cosmos. On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth’s mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects. At Earth’s surface the acceleration of gravity is about 9.8 metres (32 feet) per second per second. Thus, for every second an object is in free fall, its speed increases by about 9.8 metres per second. At the surface of the Moon the acceleration of a freely falling body is about 1.6 metres per second per second.

The works of Isaac Newton and Albert Einstein dominate the development of gravitational theory. Newton’s classical theory of gravitational force held sway from his Principia, published in 1687, until Einstein’s work in the early 20th century. Newton’s theory is sufficient even today for all but the most precise applications. Einstein’s theory of general relativity predicts only minute quantitative differences from the Newtonian theory except in a few special cases. The major significance of Einstein’s theory is its radical conceptual departure from classical theory and its implications for further growth in physical thought.

The launch of space vehicles and developments of research from them have led to great improvements in measurements of gravity around Earth, other planets, and the Moon and in experiments on the nature of gravitation.

Newton argued that the movements of celestial bodies and the free fall of objects on Earth are determined by the same force. The classical Greek philosophers, on the other hand, did not consider the celestial bodies to be affected by gravity, because the bodies were observed to follow perpetually repeating nondescending trajectories in the sky. Thus, Aristotle considered that each heavenly body followed a particular “natural” motion, unaffected by external causes or agents. Aristotle also believed that massive earthly objects possess a natural tendency to move toward Earth’s centre. Those Aristotelian concepts prevailed for centuries along with two others: that a body moving at constant speed requires a continuous force acting on it and that force must be applied by contact rather than interaction at a distance. These ideas were generally held until the 16th and early 17th centuries, thereby impeding an understanding of the true principles of motion and precluding the development of ideas about universal gravitation. This impasse began to change with several scientific contributions to the problem of earthly and celestial motion, which in turn set the stage for Newton’s later gravitational theory.

Who was the first scientist to conduct a controlled nuclear chain reaction experiment? What is the unit of measure for cycles per second? Test your physics acumen with this quiz.

The 17th-century German astronomer Johannes Kepler accepted the argument of Nicolaus Copernicus (which goes back to Aristarchus of Samos) that the planets orbit the Sun, not Earth. Using the improved measurements of planetary movements made by the Danish astronomer Tycho Brahe during the 16th century, Kepler described the planetary orbits with simple geometric and arithmetic relations. Kepler’s three quantitative laws of planetary motion are:

The planets describe elliptic orbits, of which the Sun occupies one focus (a focus is one of two points inside an ellipse; any ray coming from one of them bounces off a side of the ellipse and goes through the other focus).
The line joining a planet to the Sun sweeps out equal areas in equal times.
The square of the period of revolution of a planet is proportional to the cube of its average distance from the Sun.

During this same period the Italian astronomer and natural philosopher Galileo Galilei made progress in understanding “natural” motion and simple accelerated motion for earthly objects. He realized that bodies that are uninfluenced by forces continue indefinitely to move and that force is necessary to change motion, not to maintain constant motion. In studying how objects fall toward Earth, Galileo discovered that the motion is one of constant acceleration. He demonstrated that the distance a falling body travels from rest in this way varies as the square of the time. As noted above, the acceleration due to gravity at the surface of Earth is about 9.8 metres per second per second. Galileo was also the first to show by experiment that bodies fall with the same acceleration whatever their composition (the weak principle of equivalence).

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Barry Lienert, a geophysicist at the University of Hawaii, provides the following explanation.

We start by determining the mass of the Earth. Issac Newton's Law of Universal Gravitation tells us that the force of attraction between two objects is proportional the product of their masses divided by the square of the distance between their centers of mass. To obtain a reasonable approximation, we assume their geographical centers are their centers of mass.

Because we know the radius of the Earth, we can use the Law of Universal Gravitation to calculate the mass of the Earth in terms of the gravitational force on an object (its weight) at the Earth's surface, using the radius of the Earth as the distance. We also need the Constant of Proportionality in the Law of Universal Gravitation, G. This value was experimentally determined by Henry Cavendish in the 18th century to be the extemely small force of 6.67 x 10-11 Newtons between two objects weighing one kilogram each and separated by one meter. Cavendish determined this constant by accurately measuring the horizontal force between metal spheres in an experiment sometimes referred to as "weighing the earth."

Calculating the Sun's Mass

Knowing the mass and radius of the Earth and the distance of the Earth from the sun, we can calculate the mass of the sun (right), again by using the law of universal gravitation. The gravitational attraction between the Earth and the sun is G times the sun's mass times the Earth's mass, divided by the distance between the Earth and the sun squared. This attraction must be equal to the centripetal force needed to keep the earth in its (almost circular) orbit around the sun. The centripetal force is the Earth's mass times the square of its speed divided by its distance from the sun. By astronomically determining the distance to the sun, we can calculate the earth's speed around the sun and hence the sun's mass.

Once we have the sun's mass, we can similarly determine the mass of any planet by astronomically determining the planet's orbital radius and period, calculating the required centripetal force and equating this force to the force predicted by the law of universal gravitation using the sun's mass.

Additional details are provided by Gregory A. Lyzenga, a physicist at Harvey Mudd College in Claremont, Calif.

The weight (or the mass) of a planet is determined by its gravitational effect on other bodies. Newton's Law of Gravitation states that every bit of matter in the universe attracts every other with a gravitational force that is proportional to its mass. For objects of the size we encounter in everyday life, this force is so minuscule that we don't notice it. However for objects the size of planets or stars, it is of great importance.

In order to use gravity to find the mass of a planet, we must somehow measure the strength of its "tug" on another object. If the planet in question has a moon (a natural satellite), then nature has already done the work for us. By observing the time it takes for the satellite to orbit its primary planet, we can utilize Newton's equations to infer what the mass of the planet must be.

MASS of asteroid Mathilde was calculated by measuring gravitational perturbations in the course of the passing NEAR spacecraft.

For planets without observable natural satellites, we must be more clever. Although Mercury and Venus (for example) do not have moons, they do exert a small pull on one another, and on the other planets of the solar system. As a result, the planets follow paths that are subtly different than they would be without this perturbing effect. Although the mathematics is a bit more difficult, and the uncertainties are greater, astronomers can use these small deviations to determine how massive the moonless planets are.

Finally, what about those objects such as asteroids, whose masses are so small that they do not measurably perturb the orbits of the other planets? Until recent years, the masses of such objects were simply estimates, based upon the apparent diameters and assumptions about the possible mineral makeup of those bodies.

Now, however, several asteroids have been (or soon will be) visited by spacecraft. Just like a natural moon, a spacecraft flying by an asteroid has its path bent by an amount controlled by the mass of the asteroid. This "bending" is measured by careful tracking and Doppler radio measurement from Earth. Recently, the NEAR spacecraft flew by the asteroid Mathilde, determining for the first time its actual mass. It turned out to be considerably lighter and more "frothy" in structure than had been expected, a fact that is challenging planetary scientists for an explanation.

Originally published on March 16, 1998.