Problem Solving and Estimation challenge problem 1 http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/introduction-to-mechanics/problem-solving-and-estimation/MIT8_01SC_problems02_soln.pdf
I'm trying to understand what happens between steps 1.9 and 1.10-does this look right? (I reversed Earth and Europa)
(1.9) F_e/F_E = (R_E^2/R_e^2) * (M_e/M_E)
Can I do this?
F_e/F_E = m*g_e/m*g_E = g_e/g_E
g_e/g_E = (R_E^2/R_e^2) * (M_e/M_E)
replace M with density * volume and assuming density is the same:
(1.10) g_e/g_E = R_e/R_E
sorry for not using latex....

Question

Problem Solving and Estimation challenge problem 1 http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/introduction-to-mechanics/problem-solving-and-estimation/MIT8_01SC_problems02_soln.pdf
I'm trying to understand what happens between steps 1.9 and 1.10-does this look right? (I reversed Earth and Europa)
(1.9)  F_e/F_E  = (R_E^2/R_e^2) * (M_e/M_E)
Can I do this?
F_e/F_E = m*g_e/m*g_E = g_e/g_E
g_e/g_E = (R_E^2/R_e^2) * (M_e/M_E) 
replace M with density * volume and assuming density is the same:
(1.10) g_e/g_E = R_e/R_E
sorry for not using latex....