What is the acceleration due to gravity 100km above the surface of the Earth? (Average radius of Earth is, Re=6.4x10^3km)
To find the acceleration due to gravity 100 km above the surface of the Earth, we need to calculate the new distance from the center of the Earth.
1. Start by converting the given average radius of the Earth into meters:
Re = 6.4 × 10^3 km
Re = 6.4 × 10^3 × 10^3 m
Re = 6.4 × 10^6 m
2. The new distance from the center of the Earth will be the sum of the average radius of the Earth (Re) and the altitude above the surface (h):
R = Re + h
R = 6.4 × 10^6 m + 100 × 10^3 m
R = 6.4 × 10^6 m + 10^5 m
R = 6.4 × 10^6 m + 10^5 m
R = 6.5 × 10^6 m
3. Now we can calculate the acceleration due to gravity (g) at the new distance from the center of the Earth using the formula:
g = G * M / R^2
Where:
G = Universal gravitational constant = 6.67430 × 10^-11 m^3 kg^-1 s^-2
M = Mass of the Earth = 5.972 × 10^24 kg
g = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6.5 × 10^6 m)^2
4. Calculate the value for g using the given values:
g = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6.5 × 10^6 m)^2
After performing the calculations, we find that the acceleration due to gravity 100 km above the surface of the Earth is approximately 9.13 m/s^2.