- #1
Gregor
- 39
- 0
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/s²from 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 ..... 19.6133at 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/s²from 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 ..... 19.6133at 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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