Question

Find weight of 45 kg at height 800 km from earth's surface?​

Answer 1

The weight is 348.4 N

Step-by-step explanation:

Effect of the Altitude on the Acceleration of Gravity

The effect of gravity decreases with altitude because greater altitudes mean greater distances from the Earth's center.

The practical formula to calculate the gravity as a function of the altitude h is:

`{\displaystyle g_(h)=g_(0)\left({\frac {R_{\mathrm {e} }}{R_{\mathrm {e} }+h}}\right)^(2)}`

Where go is the conventional gravitational acceleration =
`9.80665\ m/s^2`

R is the Earth's mean radius at the equator = 6,378 Km

h is the altitude.

At a height of h=800 Km, the acceleration of gravity is:

`{\displaystyle g_(h)=9.80665 m/s^2\left(\frac {6,378 Km }{6,378 Km+800Km}}\right)^(2)}`

Calculating:

`g_h=7.74\ m/s^2`

The weight is the product of the acceleration of gravity by the mass of the object, thus:

`W=45\ Kg\cdot 7.74\ m/s^2=348.4\ N`

The weight is 348.4 N