This shows more detail
http://saxbyphysics.com/AdvancedPhys...tialEnergy.pdf
This shows more detail
http://saxbyphysics.com/AdvancedPhys...tialEnergy.pdf
Some vocabulary technicalities:
According to current theory, G is constant. The force between two "point" masses m_1, m_2 that are a distance r apart is G m_1 m_2/ r_squared. Whether you include a minus sign in front of this formula depends on which mass you consider the force acting upon and which direction you call positive.
(The formula E = G m_1 m_2/r for potential energy is different than the formula for the force of attraction F = G m_1 m_2/ r_squared.. The formula e = m g h for potential energy is an approximation valid in distances near the surface of the earth, where (percentage wise) the value of r doesn't change much with changes in height. The constant g is a different constant than G )
A better name for "G" is "the gravitational constant". The term "acceleration due to gravity" is used for the constant denoted by a lower case g that is used in the formula e = m g h.As the object approaches the center of the earth, G (the acceleration due to gravity) decreases to zero (John's point) so we have 0/0.
It isn't G that changes, but yes, if we imagine a point object inside the earth and the earth as set of many point masses the net force on the object now involves some points in the earth that are pulling the object generally away from the earth's center and other points in the earth that are pulling the object toward the earth's center. So the total force on the object is no longer given by the formula that applies to only 2 point masses. (We can no longer consider the earth to be a point.) Acceleration on a mass is proportional to the net force on it, so the acceleration of the point mass is affected by its being inside the earth. Yes, the "acceleration due to gravity" changes if that phrase refers to the acceleration of the object. But it isn't the constant G that changes - and the constant g (which is also called "the acceleration due to gravity" ) isn't relevant since we are no longer talking about an object near the surface of the earth.
Last edited by Stephen Tashiro; 03-23-2021 at 2:26 PM.
Well, yes, G is constant. However, g is not a constant. It's different on the Moon, and different at various altitudes on Earth. The acceleration due to gravity is simply the ratio between the force on a test mass and it's mass. So at the center of a massive sphere g is zero. It increases linearly with distance from the center up to it's surface. Past the surface in then varies with the inverse square of the distance from the center of mass, just like the force equation you stated.
Beranek's Law:
It has been remarked that if one selects his own components, builds his own enclosure, and is convinced he has made a wise choice of design, then his own loudspeaker sounds better to him than does anyone else's loudspeaker. In this case, the frequency response of the loudspeaker seems to play only a minor part in forming a person's opinion.
L.L. Beranek, Acoustics (McGraw-Hill, New York, 1954), p.208.
Sounds good but what do you define as the surface? The diameter of earth is 12,742 km, I assume that's an average since the earth is neither perfectly round or uniform. So if a mass is 12,742.5 km from the center of the earth it could be 0.5km above the surface or 8.35km below the surface of the top of Everest. (Everest is 8.85 km high).
Beranek's Law:
It has been remarked that if one selects his own components, builds his own enclosure, and is convinced he has made a wise choice of design, then his own loudspeaker sounds better to him than does anyone else's loudspeaker. In this case, the frequency response of the loudspeaker seems to play only a minor part in forming a person's opinion.
L.L. Beranek, Acoustics (McGraw-Hill, New York, 1954), p.208.
This whole thread makes me glad I was a Political Science major.
Yeah, politics makes much more sense than science.
I never did get past a b c and x. Flunked out of Trig twice, but I do understand ZZZZZZZZZZZZZZZZZZZZZZZZZ.
Sorry, couldn't resist.
Rick Potter
DIY journeyman,
FWW wannabe.
AKA Village Idiot.