A satellites are placed in a circular orbit that is 1.62 × 108 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?
To find the magnitude of the acceleration due to gravity at a certain distance from the Earth's surface, you can 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 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Earth (approximately 5.972 × 10^24 kg)
- r is the distance from the center of the Earth to the satellite (in this case, 1.62 × 10^8 m + the radius of the Earth)
First, calculate the distance from the center of the Earth to the satellite:
Distance from the Earth's surface to the satellite = 1.62 × 10^8 m
Radius of the Earth = approximately 6.371 × 10^6 m (average radius)
So, the distance from the center of the Earth to the satellite (r) = (1.62 × 10^8 m + 6.371 × 10^6 m)
Next, plug in the values into the formula for gravitational acceleration:
g = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg) / (r^2)
Calculate r^2:
r^2 = [(1.62 × 10^8 m + 6.371 × 10^6 m)]^2
Now, substitute the value of r^2 and calculate g:
g = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg) / [(1.62 × 10^8 m + 6.371 × 10^6 m)]^2
Evaluating the equation will give you the magnitude of the acceleration due to gravity at this distance.