Question #05a3c

1 Answer
Mark C.
Jan 15, 2018

Acceleration due to gravity, g is defined as being the rate of change in potential per unit distance or #g = (dV)/(dr#

Explanation:

Equally you can call it the force per unit mass, so #g = F/m# where force, F requires vector notation & spherical geometry so #vec(F) = -G(m_1m_2)/vec(r^2#

Thus #vec(g) = -G(m_1)/vec(r^2#

So #g = -6.67xx10^-11 (319 xx 6xx10^24)/(11.2 xx 6.37xx10^6)^2#

Giving #g = 25.1 m/s^2#

Another way of saying it is that the greater mass will increase g by 319 times and the increased radius will decrease it by #11.2^2# times. #319/11.2^2 = 2.54# and #2.54g = 24.9 m/s^2# so about correct!

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