The value of g at the Earth's surface is about 9.8 m/s2. What is the value of g at a distance from the Earth's center that is 9.5 times the Earth's radius?
9.8 m/s^2/(9.5)^2 = 0.109 m/s^2
To find the value of g at a distance from the Earth's center that is 9.5 times the Earth's radius, we can use the formula for gravitational acceleration.
The formula for gravitational acceleration is given by:
g = G * M / r²
Where:
- g is the gravitational acceleration
- G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)²)
- M is the mass of the Earth
- r is the distance from the Earth's center
We know that the value of g at the Earth's surface is about 9.8 m/s², which we will call g₁. The Earth's radius, denoted as R, and the distance from the Earth's center are related as:
r = 9.5 * R
To find the value of g at a distance 9.5 times the Earth's radius, we need to substitute the expression for r into the gravitational acceleration formula:
g = G * M / (9.5 * R)²
Now, to calculate g, we need to find the mass of the Earth, M. The mass of the Earth is approximately 5.972 × 10^24 kg.
Finally, we can substitute the values into the formula to find the value of g:
g = (6.67430 × 10^-11 N(m/kg)²) * (5.972 × 10^24 kg) / (9.5 * (radius of the Earth in meters))²
Calculating this expression will give you the value of g at a distance from the Earth's center that is 9.5 times the Earth's radius.