To understand how g is related to φ:
Similarly, it can be concluded that by multiplying both sides by test mass m.
$m$
thus $F$
symbol  $g$ 
$$ 
name  Field strength  Potential 
units  N kg^{1} or m s^{2}  J kg^{1} 
meaning  Force per unit mass  Potential energy per unit mass 
quantity  vector  scalar 
equation  $\mathrm{g}$ 
$\varphi $ 
relationship to mass  Force, $F$ 
Potential energy, $U$ 
graph  
computer model if M = 500.  6.67*500/(abs(r)*r)  6.67*500/abs(r) 
relationship between g and φ 
$g$
$g$ 

relationship between F and U 
$F$
$F$ 