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# Is there a measuring system that accurately determines the extent of a stars' gravitational limits based on size?

Question #126529. Asked by george48. (Aug 05 12 8:44 PM)

sportsherald

It isn't clear to me whether this question relates to the units that are used, or to the accuracy of the measurements. Either way, it appears that we are talking about gravitational field strength, known as "g" (not the same as "gram," however):

"Gravitational field strength at a point is defined as the gravitational force per unit mass at that point.

Newton's law of gravitation:
The (mutual) gravitational force F between two point masses M and m separated by a distance r is given by

F = GMm (where G: Universal gravitational constant)
r2

or, the gravitational force of between two point masses is proportional to the product of their masses & inversely proportional to the square of their separation.

Gravitational field strength at a point is the gravitational force per unit mass at that point. It is a vector and its S.I. unit is N kg-1.

By definition , g = F / m

By Newton Law of Gravitation, F = GMm / r2

Combining, magnitude of g = GM / r2

Therefore g = GM / r2, M = Mass of object "creating" the field" -from http://www.xtremepapers.com/revision/a-level/physics/gravitation.php

While most of these units are standard SI units, the calculations rely on "G." the gravitational constant, which does have some uncertainty around it:

"The constant of proportionality, G, is the gravitational constant.

The gravitational constant is a physical constant that is difficult to measure with high accuracy.[3] In SI units, the 2010 CODATA-recommended value of the gravitational constant (with standard uncertainty in parentheses) is:
G = 6.67384 (80) * 10^-11 m^3 kg^-1 s^-2 = 6.67384(80) * 10^-11 N (m/kg)^2

with relative standard uncertainty 1.2×10?4." -from http://en.wikipedia.org/wiki/Gravitational_constant

 Aug 05 12, 11:46 PM
nautilator

The equation for gravitational attraction for two objects is F = G*M1*M2/d^2. That works for any and all objects.
http://www.ajdesigner.com/phpgravity/newtons_law_gravity_equation_force.php

You may instead want the classification system where we decide if a star is a red giant, dwarf, potential black hole, etc. If so, there is the Hertzsprung-Russell Diagram (for example, http://aspire.cosmic-ray.org/labs/star_life/hr_diagram.html) which correlates stars based on their size, mass, temperature, etc. Most stars fall into the main sequence, but we also have classes like the dwarf stars and giant stars.

If you are looking for any one specific outcome, there are equations that show whether or not a star will fit it. For example, in order to become a black hole, a star has to be dense enough that its radius falls below a certain threshold. That radius can be found by R = 2*G*M/c^2, with G being the gravitational constant (6.67E^-11).
http://www.physicsforidiots.com/blackholes.html

 Aug 06 12, 12:04 AM

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