Compared with the strength of Earth's gravity at its surface, how much weaker is gravity at a distance of 11 Earth radii from Earth's center?
it is in proportion to 1/11 squared, or 1/121.
Odd question to me.
Frank Steelman
Office: Phone or Course Chat
Office Hours: By appointment - as needed by the student.
Phone: 609-204-0359
To calculate the strength of gravity at a distance of 11 Earth radii from Earth's center, we can use the inverse-square law of gravitational attraction.
The gravitational force between two objects is inversely proportional to the square of the distance between their centers of mass. The formula for the gravitational force is:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the universal gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between their centers of mass.
Considering the Earth's surface gravity as g (approximately 9.8 m/s^2) and the distance from Earth's center to the distance of 11 Earth radii as R (6371 km * 11), we can calculate the gravitational force at the given distance.
g = (G * M) / R^2
Where:
M is the mass of Earth.
Now, we can calculate the strength of gravity at a distance of 11 Earth radii.
g' = (G * M) / (11R)^2
To find how much weaker gravity is at this distance compared to the surface of the Earth, we can calculate the ratio of the two gravitational forces.
Ratio = g' / g
Let's plug in the values and calculate the result step-by-step.
To calculate the strength of gravity at a distance of 11 Earth radii from Earth's center, we need to use the universal law of gravitation. The formula for the strength of gravity is given by:
𝐹 = (𝐺 * 𝑚₁ * 𝑚₂) / 𝑟²
Where:
- 𝐹 represents the force of gravity
- 𝐺 is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
- 𝑚₁ and 𝑚₂ are the masses of the two objects (in this case, the mass of Earth and the mass of the object experiencing gravity)
- 𝑟 is the distance between the centers of the objects
To find out how much weaker gravity is at a distance of 11 Earth radii from Earth's center compared to the surface, we can use the above formula. First, we'll calculate the strength of gravity at the surface of Earth, and then at a distance of 11 Earth radii.
1. Calculating gravity at the surface of Earth:
- 𝑚₁ = mass of Earth (approximately 5.972 × 10^24 kg)
- 𝑚₂ = mass of the object (this can be canceled out when comparing the two scenarios)
- 𝑟 = radius of Earth (approximately 6,371 km or 6,371,000 meters)
Substituting the values into the formula:
𝐹 surface = (𝐺 * 𝑚₁) / 𝑟²
2. Calculating gravity at a distance of 11 Earth radii:
- 𝑟 = 11 * radius of Earth = 11 * 6,371,000 meters
Substituting the values into the formula:
𝐹 11 radii away = (𝐺 * 𝑚₁) / (11 * 𝑟)²
After calculating both forces, we can find the ratio by dividing the force at 11 radii away by the force at the surface:
𝐹 11 radii away / 𝐹 surface = ((𝐺 * 𝑚₁) / (11 * 𝑟)²) / ((𝐺 * 𝑚₁) / 𝑟²)
Simplifying the ratio, we get:
𝐹 11 radii away / 𝐹 surface = 1 / (11²)
So, gravity at a distance of 11 Earth radii from Earth's center is approximately 1/121, or about 0.00826, times weaker than gravity at the surface.