What is the acceleration due to gravity at a distance of 1.2 Earth radii above Earth�s surface?
Use M_{Earth} = 5.972 x 10^{24} kilograms
and
r_{Earth} = 6370 km
a_{gravity} =______________{m}{s^2}
F = G Mm /R^2
F' = G M m /(1.2R)^2 = G M m /R^2 * 1/1.44
9.81 * 1/1.44 = 6.81 m/s^2
The rest is just to confuse the student by the way.
To find the acceleration due to gravity at a distance of 1.2 Earth radii above Earth's surface, you need to use the formula for gravitational acceleration:
a_gravity = (G * M_earth) / (r_distance^2)
where:
G = gravitational constant = 6.67430 x 10^-11 m^3 kg^-1 s^-2
M_earth = mass of the Earth = 5.972 x 10^24 kilograms
r_distance = distance from the center of the Earth = 1.2 * r_earth
First, let's calculate the radius of the Earth in meters:
r_earth = 6370 km * 1000 m/km = 6,370,000 meters
Next, let's calculate the distance from the center of the Earth at a distance of 1.2 Earth radii:
r_distance = 1.2 * r_earth = 1.2 * 6,370,000 meters
Now, substitute the values into the formula:
a_gravity = (6.67430 x 10^-11 m^3 kg^-1 s^-2 * 5.972 x 10^24 kg) / (1.2 * 6,370,000 meters)^2
Calculate the value:
a_gravity = (4.0034 x 10^14 m^3 kg^-1 s^-2) / (1.2^2 * 6,370,000 meters)^2
a_gravity ≈ 9.466 m/s^2
Therefore, the acceleration due to gravity at a distance of 1.2 Earth radii above Earth's surface is approximately 9.466 m/s^2.