This is the third post in our series The Impact of Gravity on Life, a paper written by Dr. Emily R. Morey-Holton, NASA Ames Research Center, Moffett Field, California. Read the series in its entirety here in blog posts tagged Impact of Gravity on Life.
In 1665-1666, Sir Isaac Newton first developed the universal law of gravitation and the laws of motion, which form the basis for our understanding of planetary motion and spaceflight (Guillen, 1995).
The universal law of gravitation states that the attractive force between any two bodies is given by:
where M (of Earth) and m (of any object) and are the masses of the two attracting bodies, d is the distance between their centers of mass and Gu is the universal gravitational constant 6.67 x10-8 cm3/g•s2 (Pace, 1977). In other words, the force of gravity is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. Thus, each time the distance between the center of two masses doubles, the force is cut to 1/4 of the previous value.
Microgravity (10-6G) requires a significant distance between the two masses (~1000 earth radii or 6.37 x 106 km ). Low Earth orbit is only about 300 km above Earth. How, then, can we state that microgravity is found in low Earth orbit? The next paragraph suggests an answer to this apparent discrepancy.
A force is defined as equal to the mass of an object times its acceleration (i.e., F=ma). Equation
(1) can be rewritten as:
Thus, an object of any mass at the surface of the Earth accelerates toward the center of the Earth at approximately 9.8 m/sec2. This gravitational acceleration is 1-G. A spacecraft in orbit above Earth moves at a constant velocity in a straight trajectory (Fig, 2, above). Earth’s gravitational acceleration at that vehicle’s center of mass alters the direction of the spacecraft from a straight path into a circular orbit normal to the gravitational vector via centripetal acceleration. Centrifugal force, the apparent force in a rotating system, deflects masses radially outward from the axis of rotation and is equal and opposite centrifugal force per unit mass. Thus, a spacecraft in a circular orbit above Earth is in “free” fall around Earth. Centrifugal force counterbalances centripetal acceleration causing momentary resultant gravitational forces that range between 10-3 and 10-6G even though gravity per se is reduced only about 10% at the altitude of low Earth orbit (Klaus, 2001).
Gravity is one of the four fundamental physical forces of nature. The other three are the nuclear
strong and weak forces, and electromagnetic forces. Given the intensity of the forces (adapted from
NUCLEAR STRONG FORCE 100
ELECTROMAGNETIC FORCE 10-2
NUCLEAR WEAK FORCE 10-14
GRAVITATIONAL FORCE 10-40
One quickly sees that gravitational force is far weaker than other forces. How could such a weak force affect all living systems? A brief description of the various forces may help in understanding this apparent discrepancy. The strength of a force depends on the distance over which it is acting. The strong force holds together protons and neutrons in the nucleus of an atom and is effective over a relatively short distance. Electromagnetic force (EM) is the force between charged particles; whether the force is attractive or repulsive is determined by the charges between interacting particles. The strength of the force drops with the inverse of the distance between charges. The weak force is effective over an incredibly small distance and can be pictured as the force that causes the decaying processes of unstable nuclear particles through time. Gravitational force is the weakest of the four fundamental physical forces of nature. Similar to EM, this force gets smaller as the objects get further apart. Yet, you feel the force of gravity and not EM, because an object at rest on Earth is pressed against Earth’s surface by the force of gravity so that continuous loading is imposed upon the object. In orbit around Earth, objects have mass but almost no weight because the acceleration due to gravity is balanced by the centrifugal acceleration that keeps the object in orbit.