if I weigh 141.2lbs at sea level what will I weigh 29,000ft above sea level
If I weigh 141.2lbs at sea level what will I weigh 29,000ft above sea level ?
29000 ft = 8839.2 m
Only Free-air correction:
Accounts for the 1/r^2 decrease in gravity with the distance from the center of the Earth:
$$g_1=\boxed{g_{(\text{ see level })}=\dfrac{GM_E}{R_E^2}}$$
and in 8839.2 m
$$g_2=\boxed{g_{(\ 29000\ ft \text{ above sea level})}=\dfrac{GM_E}{( R_E +8.8392\ km )^2}}$$
$$F_2 = F_1\cdot \dfrac{g_2}{g_1}\cdot \dfrac{\not{m}}{\not{m}}$$
$$\small{\text{
$
F_2 = F_1\cdot \dfrac{R_E^2} {( R_E +8.8392\ km )^2}
=F_1\cdot \dfrac{6371^2} {( 6371 +8.8392\ km )^2}=F_1\cdot 0.99723094065
$
}}$$
So we have 141.2lbs * 0.99723094065 = 140.809008820 lbs
If I weigh 141.2lbs at sea level what will I weigh 29,000ft above sea level ?
29000 ft = 8839.2 m
Only Free-air correction:
Accounts for the 1/r^2 decrease in gravity with the distance from the center of the Earth:
$$g_1=\boxed{g_{(\text{ see level })}=\dfrac{GM_E}{R_E^2}}$$
and in 8839.2 m
$$g_2=\boxed{g_{(\ 29000\ ft \text{ above sea level})}=\dfrac{GM_E}{( R_E +8.8392\ km )^2}}$$
$$F_2 = F_1\cdot \dfrac{g_2}{g_1}\cdot \dfrac{\not{m}}{\not{m}}$$
$$\small{\text{
$
F_2 = F_1\cdot \dfrac{R_E^2} {( R_E +8.8392\ km )^2}
=F_1\cdot \dfrac{6371^2} {( 6371 +8.8392\ km )^2}=F_1\cdot 0.99723094065
$
}}$$
So we have 141.2lbs * 0.99723094065 = 140.809008820 lbs