The gravitational law and Huygens's centripetal law are the same

Huygens published his centripetal law Fc = mpl*vm^2/sma in 1659.
The formula Fg = G*(M*mpl/sma^2) produces the same results.

mpl vm sma Fc Fg
MER 3.30E+23 47873 57,909,231,029 1.31E+22 1.31E+22
VEN 4.87E+24 35021 108,209,525,401 5.52E+22 5.52E+22
EAR 5.97E+24 29786 149,598,319,494 3.54E+22 3.54E+22
MAR 6.42E+23 24131 227,943,771,564 1.64E+21 1.64E+21
JUP 1.90E+27 13070 778,342,761,465 4.17E+23 4.16E+23
SAT 5.68E+26 9672 1,426,714,892,866 3.73E+22 3.71E+22
URA 8.68E+25 6835 2,870,633,540,862 1.41E+21 1.40E+21
NEP 1.02E+26 5478 4,498,393,012,162 6.83E+20 6.72E+20
PLU 1.25E+22 4749 5,906,438,090,764 4.77E+16 4.76E+16

Fc = centripetal force
Fg = gravitational force
mpl = mass of a planet
vm = orbital velocity in m
sma = semi major axis in m
G = gravitational constant = 6.674E-11
M = Mass of the sun = 1.9885E+30