Why g cancels in the slip condition:
Uphill: μ · mgcosθ ≥ mgsinθ + c_rr · mgcosθ
→ μ ≥ tanθ + c_rr
Downhill: μ · mgcos|θ| ≥ mgsin|θ| − c_rr · mgcos|θ|
→ μ ≥ tan|θ| − c_rr (steep downhill can still cause slips!)
g gone in both cases! Mars or Earth — same traction physics.