The weight of a 75 kg body, 8km above earth surface is 550 Newton. Calculate the gravitational strength at that height
weight = m g
so
g = weight/m = 550/75 = 7.33 m/s^2
just for kicks, compute earth radius now
7.33 / 9.81 = Re^2/(Re+8000)^2
.8646 = Re/(Re + 8000)
.8646 Re + 6917 = Re
.1354 Re = 6917
Re = 51086 meters
I do not think so. Maybe you mean 80 km ?
To calculate the gravitational strength at a certain height above the Earth's surface, we need to use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 Nm^2/kg^2)
m1 and m2 are the masses of the two objects (in this case, the mass of the body and the mass of the Earth)
r is the distance between the centers of the two objects (in this case, the distance from the center of the Earth to the 8 km height above its surface).
We can rearrange the formula to solve for the gravitational strength at that height:
F = G * m1 * m2 / r^2
First, we need to calculate the mass of the Earth, which is approximately 5.972 × 10^24 kg.
Now we can substitute the values into the formula:
F = (6.67430 × 10^-11 Nm^2/kg^2) * (75 kg) * (5.972 × 10^24 kg) / (8000 m)^2
Calculating this will give us the gravitational strength at that height:
F = 43.98 N
Therefore, the gravitational strength at 8 km above Earth's surface is approximately 43.98 Newton.