What is the value of the gravitational acceleration at a height of 2000 km above the surface of the Earth?
To find the value of the gravitational acceleration at a height of 2000 km above the surface of the Earth, we can use the formula for gravitational acceleration:
g = G * (M / r^2),
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 (approximately 5.972 × 10^24 kg),
and r is the distance between the center of the Earth and the object.
In this case, we need to calculate the value of the gravitational acceleration at a height of 2000 km, which means we need to find the distance, r. The distance r would be the sum of the radius of the Earth (r_earth) and the height above the surface (h). The radius of the Earth is approximately 6371 km.
r = r_earth + h
= 6371 km + 2000 km,
Now we can calculate the value of the gravitational acceleration:
g = G * (M / r^2)
= 6.67430 × 10^-11 (m/kg)^2 * (5.972 × 10^24 kg) / (r^2),
where r is the calculated distance in meters.
By substituting the values, we can solve for g.