Question

In a balloon adventure, you reach 10 km in height. Find the percentage variation in the weight of the balloon-crew system with respect to sea level.

Answer 1

Answer:

0.31%

Explanation:

The acceleration due to gravity at sea level is:

g = GM / R²

where G is the gravitational constant, M is the mass of Earth, and R is the radius of the Earth.

The acceleration due to gravity a height h above sea level is:

g' = GM / (R+h)²

The percent variation is:

(g − g') / g

= 1 − g'/g

= 1 − [GM / (R+h)²] / [GM / R²]

= 1 − R² / (R+h)²

= 1 − (R / (R+h))²

The average radius of the Earth is 6370 km.  The height of the balloon is 10 km.

1 − (6370 / (6370 + 10))²

0.0031

0.31%