Calculate the effective value of g, the acceleration of gravity (in meters/second^2), at 8600 km above the earth's surface.
Since the force is inversely proportional to the square of the distance,
it will be g * (R/(R+8600))^2
where R is the earth's radius.
To calculate the effective value of g, the acceleration of gravity at a certain height above the Earth's surface, we need to use the formula for gravitational acceleration:
g = G * (M / r^2)
Where:
- g is the acceleration due to gravity
- G is the gravitational constant (approximately 6.67430 x 10^-11 N(m/kg)^2)
- M is the mass of the Earth (approximately 5.972 x 10^24 kg)
- r is the distance between the center of the Earth and the object's location
In this case, we need to find the value of g at a height of 8600 km above the Earth's surface. To do this, we need to calculate the distance from the center of the Earth to the specified height:
r = R + h
Where:
- R is the radius of the Earth (approximately 6.371 x 10^6 meters)
- h is the height above the Earth's surface
So, plugging in the values:
r = 6.371 x 10^6 + 8.6 x 10^6
Now we can use the formula for g:
g = G * (M / r^2)
To calculate the value of g, you need to input these values into the formula and perform the necessary calculations.