What is the value of g for space-shuttle territory , about 200km above the Earth's surface. Data: Earth's mass is 6x10^24kg, and radius is 6380 km
To find the value of acceleration due to gravity (g) at a certain height above the Earth's surface, we can use the formula:
g = (G * M) / (R^2)
Where:
- g is the acceleration due to gravity,
- G is the gravitational constant (approximately 6.67 x 10^-11 N*m^2/kg^2),
- M is the mass of the Earth,
- R is the distance between the object and the center of the Earth.
In this case, we need to calculate the value of g for a height of 200 km above the Earth's surface.
1. Convert Earth's radius to meters:
Earth's radius = 6380 km = 6380 x 1000 meters = 6,380,000 meters
2. Calculate the distance from the center of the Earth to the space-shuttle territory:
Distance = Earth's radius + height above the Earth's surface
Distance = 6,380,000 meters + 200,000 meters = 6,580,000 meters
3. Plug the values into the formula:
g = (G * M) / (R^2)
= (6.67 x 10^-11 N*m^2/kg^2 * 6 x 10^24 kg) / (6,580,000 meters)^2
4. Calculate the square of the distance:
(6,580,000 meters)^2 = 4.326 x 10^13 square meters
5. Plug the values into the formula and calculate:
g = (6.67 x 10^-11 N*m^2/kg^2 * 6 x 10^24 kg) / (4.326 x 10^13 square meters)
Using a scientific calculator or software to perform the calculations, we get:
g ≈ 8.68 m/s^2
Therefore, the approximate value of acceleration due to gravity at a height of 200 km above the Earth's surface is 8.68 m/s^2.