Many people mistakenly believe that the astronauts who orbit the Earth are "above gravity." Calculate g for space shuttle territory, 225 kilometers above the Earth's surface (dashed line in sketch). Earth's mass is 6 1024 kg, and its radius is 6.38 106 m (6380 km).
The value is g is inversely proportional to the square of the distance from the center of the earth.
The sea level g is therefpre reduced by a factor
[6380/(6380+225)]^2 = 0.933
That make it 9.15 m/s^2
Thank you so much for your help!!!
Hi I also have another question what would be the percentage of my answer of 9/8m/s^2? How do I calculate that to find my percentage?
To calculate the value of the acceleration due to gravity (g) at a specific height above the Earth's surface, we can use the formula:
g = (G * M) / (r + h)^2
Where:
- G is the gravitational constant (approximately 6.67 × 10^-11 N m^2 / kg^2)
- M is the mass of the Earth (6 × 10^24 kg)
- r is the radius of the Earth (6.38 × 10^6 m)
- h is the height above the Earth's surface
Given that the height (h) is 225 kilometers, we need to convert it to meters by multiplying by 1000:
h = 225 km * 1000 = 225,000 m
Now, we can substitute the values into the formula and calculate g:
g = (6.67 × 10^-11 N m^2 / kg^2 * 6 × 10^24 kg) / (6.38 × 10^6 m + 225,000 m)^2
First, calculate the sum in the denominator:
r + h = 6.38 × 10^6 m + 225,000 m = 6.605 × 10^6 m
Next, square the sum:
(r + h)^2 = (6.605 × 10^6 m)^2 = 4.356 × 10^13 m^2
Now, substitute the values into the formula:
g = (6.67 × 10^-11 N m^2 / kg^2 * 6 × 10^24 kg) / 4.356 × 10^13 m^2
Perform the multiplication of the numerator:
(6.67 × 10^-11 N m^2 / kg^2 * 6 × 10^24 kg) = 4.002 × 10^14 N m^2 / kg
Finally, divide the numerator by the denominator:
g = 4.002 × 10^14 N m^2 / kg / 4.356 × 10^13 m^2 ≈ 9.18 m/s^2
Therefore, the value of the acceleration due to gravity (g) at a height of 225 kilometers above the Earth's surface is approximately 9.18 m/s^2.