Physics
posted by Paige on .
Suppose the Earth was only half the size it is now (half the mass and half the radius), what would "g" be?

Newtons law:
g= G Me/r^2
Now, if one halves the radius, mass is not half.
Mass=density*volume=density 4/3 PI r^3 so if radius goes down by 1/2, then mass goes to 1/8 Me
So your question is really confusing. 
Newton's law of universal gravitation:
where force equals the universal constant of gravity multiplied by mass of the earth and mass of an object divided by the raduis squared
F = G((m1*m2)/(r^2))
Force equals the mass of an object multiplied by the acceleration or 'g'
mg = G((m1*m2)/(r^2))
Mass of the object would cancel out on both sides since infact we do not have a second mass
g = G((m1)/(r^2))
The universal constant of gravity as Newton discovered is:
G = 6.67 * 10^11 m^3/kg*s^2
The mass of the Earth is:
mass of the earth = 5.98 * 10^24 kg
The radius of the Earth is:
radius of the earth = 6.38 * 10^6 m
The mass then needs to be divided in half:
5.98 * 10^24 kg/2 = 2.94 * 10^24 kg
The radius then needs to be divided in half:
6.38 * 10^6 m/2 = 3.19 * 10^6 m
The equation for the acceleration or 'g' is:
g = 6.67 * 10^11 m^3/kg*s^2((2.94 * 10^24 kg)/(3.19 * 10^6 m^2))
Leaving 'g' as:
g = 19.27 m/s^2