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Newton's universal formula for calculating Gravity: Fg = G Mm / r²

which states that two objects attract each other with a force equal to the product of their masses

divided by the square of their separation,

times a constant of proportionality (G), where G = 6.6742(10) x 10^-11

makes it possible to calculate the mean acceleration due to gravity (g)

for any planet

in the case of Earth

g = G*Me / Re²

earth's radius (Re] = 6 378 137 m

this radius squared = 40 680 631 590 769

earth's mass (Me) = 5 977 347 368 296 994 158 859 250.7577676 kg

G = 0,0000000000667421 m³ kg^-1 s-²

applying these values to the above formula

5 977 347 368 296 994 158 859 250.7577676

/ 40 680 631 590 769

= 146 933 494 750.68959472357028022792

*0.0000000000667421

= 9.80665

therefore 1 g = 9.80665 m/s²

from this point a dimensional analysis can be made

on the premise that

d = integral of v dt over time interval

since gravity is constant acceleration

v = g*t

d = g*t²/2

as illustrated in following table

exact values from rest to 0.2 seconds - in 0.01 s intervals

0 ..............................0 .................... 0

0.0980665 ................. 0.01 ............... 0.0004903325

0.196133 ................... 0.02 ............... 0.00196133

0.2941995 ................. 0.03 ............... 0.0044129925

0.392266 ................... 0.04 ............... 0.00784532

0.4903325 ................. 0.05 ............... 0.0122583125

0.588399 ................... 0.06 ............... 0.01765197

0.6864655 ................. 0.07 ............... 0.0240262925

0.784532 ................... 0.08 ............... 0.03138128

0.8825985 ................. 0.09 ............... 0.0397169325

0.980665 .................. 0.10 ................ 0.04903325

1.0787315 ................. 0.11 ............... 0.0593302325

1.176798 ................... 0.12 ............... 0.07060788

1.2748645 ................. 0.13 ............... 0.0828661925

1.372931 ................... 0.14 ............... 0.09610517

1.4709975 ................. 0.15 ............... 0.1103248125

1.569064 ................... 0.16 ............... 0.12552512

1.6671305 ................. 0.17 ............... 0.1417060925

1.765197.................... 0.18 ............... 0.15886773

1.8632635 ................. 0.19 ............... 0.1770100325

1.96133 .................... 0.20 ............... 0.196133

exact values from rest to 2 seconds - in 0.1 s intervals

0 .............................0 ..................... 0

0.980665 .................. 0.1 .................. 0.04903325

1.96133 .................... 0.2 .................. 0.196133

2.941995 .................. 0.3 .................. 0.44129925

3.92266 .................... 0.4 .................. 0.784532

4.903325 .................. 0.5 .................. 1.22583125

5.88399 .................... 0.6 .................. 1.765197

6.864655 .................. 0.7 .................. 2.40262925

7.84532 .................... 0.8 .................. 3.138128

8.825985 .................. 0.9 .................. 3.97169325

9.80665 ................... 1 ..................... 4.903325

10.787315 ................ 1.1 .................. 5.93302325

11.76798 .................. 1.2 .................. 7.060788

12.748645 ................ 1.3 .................. 8.28661925

13.72931 .................. 1.4 .................. 9.610517

14.709975 ................ 1.5 .................. 11.03248125

15.69064 .................. 1.6 .................. 12.552512

16.671305 ................ 1.7 .................. 14.17060925

17.65197 .................. 1.8 .................. 15.886773

18.632635 ................ 1.9 .................. 17.70100325

19.6133 ................... 2 ..................... 19.6133

at 1 g

an object will (from rest) fall 1 m in 0.452 s ---- reaching a velocity of 4.4326058 m/s

an object will (from rest) reach a velocity of 1 m/s in 0.10197162129779282425700927431896 s

and will (during this interval) travel a distance of 0.050985810648896412128504637158521 m

which states that two objects attract each other with a force equal to the product of their masses

divided by the square of their separation,

times a constant of proportionality (G), where G = 6.6742(10) x 10^-11

makes it possible to calculate the mean acceleration due to gravity (g)

for any planet

in the case of Earth

g = G*Me / Re²

earth's radius (Re] = 6 378 137 m

this radius squared = 40 680 631 590 769

earth's mass (Me) = 5 977 347 368 296 994 158 859 250.7577676 kg

G = 0,0000000000667421 m³ kg^-1 s-²

applying these values to the above formula

5 977 347 368 296 994 158 859 250.7577676

/ 40 680 631 590 769

= 146 933 494 750.68959472357028022792

*0.0000000000667421

= 9.80665

therefore 1 g = 9.80665 m/s²

from this point a dimensional analysis can be made

on the premise that

d = integral of v dt over time interval

since gravity is constant acceleration

v = g*t

d = g*t²/2

as illustrated in following table

exact values from rest to 0.2 seconds - in 0.01 s intervals

__Velocity m/s.........Time (s)..........Distance (m)__0 ..............................0 .................... 0

0.0980665 ................. 0.01 ............... 0.0004903325

0.196133 ................... 0.02 ............... 0.00196133

0.2941995 ................. 0.03 ............... 0.0044129925

0.392266 ................... 0.04 ............... 0.00784532

0.4903325 ................. 0.05 ............... 0.0122583125

0.588399 ................... 0.06 ............... 0.01765197

0.6864655 ................. 0.07 ............... 0.0240262925

0.784532 ................... 0.08 ............... 0.03138128

0.8825985 ................. 0.09 ............... 0.0397169325

0.980665 .................. 0.10 ................ 0.04903325

1.0787315 ................. 0.11 ............... 0.0593302325

1.176798 ................... 0.12 ............... 0.07060788

1.2748645 ................. 0.13 ............... 0.0828661925

1.372931 ................... 0.14 ............... 0.09610517

1.4709975 ................. 0.15 ............... 0.1103248125

1.569064 ................... 0.16 ............... 0.12552512

1.6671305 ................. 0.17 ............... 0.1417060925

1.765197.................... 0.18 ............... 0.15886773

1.8632635 ................. 0.19 ............... 0.1770100325

1.96133 .................... 0.20 ............... 0.196133

exact values from rest to 2 seconds - in 0.1 s intervals

__Velocity m/s.........Time (s)..........Distance (m)__0 .............................0 ..................... 0

0.980665 .................. 0.1 .................. 0.04903325

1.96133 .................... 0.2 .................. 0.196133

2.941995 .................. 0.3 .................. 0.44129925

3.92266 .................... 0.4 .................. 0.784532

4.903325 .................. 0.5 .................. 1.22583125

5.88399 .................... 0.6 .................. 1.765197

6.864655 .................. 0.7 .................. 2.40262925

7.84532 .................... 0.8 .................. 3.138128

8.825985 .................. 0.9 .................. 3.97169325

9.80665 ................... 1 ..................... 4.903325

10.787315 ................ 1.1 .................. 5.93302325

11.76798 .................. 1.2 .................. 7.060788

12.748645 ................ 1.3 .................. 8.28661925

13.72931 .................. 1.4 .................. 9.610517

14.709975 ................ 1.5 .................. 11.03248125

15.69064 .................. 1.6 .................. 12.552512

16.671305 ................ 1.7 .................. 14.17060925

17.65197 .................. 1.8 .................. 15.886773

18.632635 ................ 1.9 .................. 17.70100325

19.6133 ................... 2 ..................... 19.6133

at 1 g

an object will (from rest) fall 1 m in 0.452 s ---- reaching a velocity of 4.4326058 m/s

an object will (from rest) reach a velocity of 1 m/s in 0.10197162129779282425700927431896 s

and will (during this interval) travel a distance of 0.050985810648896412128504637158521 m

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