Compared with the strength of Earth's gravity at its surface, how much weaker is gravity at a distance of 10 Earth radii from Earth's center? At 20 Earth radii?
The strength of gravity is inversely proportional to the square of the distance from the center of the Earth. In other words, as you move farther away from the Earth's center, gravity becomes weaker.
To calculate the difference in gravity at various distances from Earth's center, we can use the formula:
Gravity at distance r = (1/r^2) * Gravity at Earth's surface
At a distance of 10 Earth radii from Earth's center, the gravity can be calculated as:
Gravity at 10 Earth radii = (1/10^2) * Gravity at Earth's surface
The strength of gravity at 10 Earth radii is 1/100th (or 0.01) times the strength of gravity at Earth's surface.
Similarly, at a distance of 20 Earth radii from Earth's center, the gravity can be calculated as:
Gravity at 20 Earth radii = (1/20^2) * Gravity at Earth's surface
The strength of gravity at 20 Earth radii is 1/400th (or 0.0025) times the strength of gravity at Earth's surface.
To determine how much weaker gravity is at a distance from Earth's center, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Let's start with the strength of gravity at Earth's surface. On the surface of the Earth, the force of gravity keeps objects grounded, and we can express this as the acceleration due to gravity, denoted as "g," which is approximately 9.8 meters per second squared (m/s^2).
To find the strength of gravity at a distance of 10 Earth radii from Earth's center, we need to consider the change in distance but assume that the mass of Earth remains constant. Let's denote the distance at the surface of the Earth as "d1" and the distance 10 Earth radii away as "d2." The ratio of the strengths of gravity can be given by:
(g2 / g1) = (d1 / d2)^2
Substituting the values, we have:
(g2 / 9.8) = (1 / 10)^2
Simplifying the equation further, we find:
g2 = 9.8 / 100
So, the strength of gravity at a distance of 10 Earth radii from the Earth's center is approximately 0.098 m/s^2, which is about 1/100th of the strength at the Earth's surface.
Now, let's calculate the strength of gravity at a distance of 20 Earth radii. Using the same formula as above, we can rewrite the equation as:
(g3 / 9.8) = (1 / 20)^2
Simplifying the equation, we find:
g3 = 9.8 / 400
The strength of gravity at a distance of 20 Earth radii from the Earth's center is approximately 0.0245 m/s^2, which is about 1/400th of the strength at the Earth's surface.
Therefore, at a distance of 10 Earth radii, the gravity is approximately 1/100th as strong as on the Earth's surface, while at a distance of 20 Earth radii, the gravity is about 1/400th as strong.