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}
9.81/1.44
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To find the acceleration due to gravity at a distance of 1.2 Earth radii above Earth's surface, we can utilize the formula:
a_gravity = (G * M_Earth) / (r_distance^2)
Where:
G = gravitational constant (approximately 6.67430 x 10^-11 N(m/kg)^2)
M_Earth = mass of Earth (approximately 5.972 x 10^24 kilograms)
r_distance = distance from the center of Earth (1.2 times the Earth's radius)
First, we need to find the distance from the center of Earth:
r_distance = 1.2 * r_Earth
where
r_Earth = radius of Earth (6370 km = 6370000 meters)
r_distance = 1.2 * 6370000 meters
r_distance = 7644000 meters
Now we can substitute the values into the formula:
a_gravity = (6.67430 x 10^-11 N(m/kg)^2 * 5.972 x 10^24 kilograms) / (7644000 meters)^2
Calculating this, we have:
a_gravity ≈ 9.69 m/s^2
Therefore, the acceleration due to gravity at a distance of 1.2 Earth radii above Earth's surface is approximately 9.69 m/s^2.
To calculate the acceleration due to gravity at a certain distance above Earth's surface, we can use Newton's Law of Universal Gravitation, which states that the force of gravity between two objects is proportional to their masses and inversely proportional to the square of the distance between their centers.
The formula to calculate the acceleration due to gravity at a distance "h" above Earth's surface is:
a_gravity = (G * M_earth) / (r_earth + h)^2
Where:
G is the gravitational constant (approximately 6.67430 x 10^-11 Nm^2/kg^2)
M_earth is the mass of the Earth
r_earth is the radius of the Earth
h is the distance above Earth's surface
Given:
M_earth = 5.972 x 10^24 kg
r_earth = 6370 km (which is equivalent to 6370,000 meters)
h = 1.2 Earth radii (1.2 * r_earth)
Let's calculate the acceleration due to gravity:
1. Convert the units:
r_earth = 6370,000 meters
h = 1.2 * 6370,000 meters
2. Substitute the values into the formula:
a_gravity = (6.67430 x 10^-11 Nm^2/kg^2 * 5.972 x 10^24 kg) / (6370,000 m + 1.2 * 6370,000 m)^2
3. Simplify the equation:
a_gravity = (6.67430 x 10^-11 Nm^2/kg^2 * 5.972 x 10^24 kg) / (1.2^2 * 6370,000 m)^2
4. Calculate the denominator:
Denominator = (1.2 * 6370,000 m)^2 = (7,644,000 m)^2 = 58,572,336,000,000 m^2
5. Substitute the denominator into the equation:
a_gravity = (6.67430 x 10^-11 Nm^2/kg^2 * 5.972 x 10^24 kg) / 58,572,336,000,000 m^2
6. Calculate the numerator:
Numerator = 6.67430 x 10^-11 Nm^2/kg^2 * 5.972 x 10^24 kg = 3.987 x 10^14 Nm^2
7. Substitute the numerator and denominator into the equation:
a_gravity = (3.987 x 10^14 Nm^2) / 58,572,336,000,000 m^2
8. Calculate the final answer:
a_gravity ≈ 6.8 m/s^2
Therefore, the acceleration due to gravity at a distance of 1.2 Earth radii above Earth's surface is approximately 6.8 m/s^2.