What is the distance from the earth's center to a point where your weight would be 1/25 of what you weigh at the surface?
By the way, the equation is:
Fg = GM/r^2
Where G = Gravitational Constant (6.67 * 10^-11)
M = Earth's mass
r = Earth's radius
The givens are:
Earth's mass = 5.98 * 10^24 kg
Earth's radius = 6.38 * 10^6 m
the distance from the center of the earth would be 5r, so from Earth, then 4r.
To determine the distance from the Earth's center where your weight would be 1/25th of what you weigh at the surface, we need to take into account the concept of the gravitational field strength. The weight of an object can be calculated using the equation:
Weight = Mass × Gravitational Field Strength
The gravitational field strength on the surface of the Earth is denoted by "g" and is approximately 9.8 m/s². So, at the Earth's surface, your weight is equal to your mass multiplied by 9.8 m/s².
To find the distance from the Earth's center where your weight would be 1/25th of what you weigh at the surface, we can set up a proportion. Let's assume that "d" is the distance from the Earth's center. Therefore, at this distance, the gravitational field strength becomes 1/25th of the surface value (9.8 m/s²).
Now, the proportion can be set up as follows:
Weight / Mass = Gravitational Field Strength at surface / Gravitational Field Strength at distance "d"
Since we know that Weight / Mass is equal to the surface gravitational field strength (9.8 m/s²) and that the gravitational field strength at the distance "d" is 1/25th of the surface value, the proportion can be written as:
9.8 m/s² / 1 = (1/25) × 9.8 m/s² / (d/R)²
Here, "R" represents the radius of the Earth. We square the fraction (1/25) because the gravitational field strength follows an inverse square law with distance from the center of the Earth.
Simplifying the equation further gives us:
9.8 m/s² = 9.8 m/s² / (25 × (d/R)²)
Next, we can cancel out the common factors:
1 = 1 / (25 × (d/R)²)
Now, rearrange the equation to find the value of (d/R)²:
(d/R)² = 1 / 25
Finally, taking the square root on both sides gives:
d/R = sqrt(1 / 25)
Now, we can substitute the value of d/R back into the equation:
d/R = 1/5
Re-arranging this equation gives:
d = R/5
Since we know the approximate radius of the Earth is 6,371 kilometers (or 6,371,000 meters), we can calculate the value of d:
d = 6,371,000 meters / 5
Hence, the distance from the Earth's center where your weight would be 1/25th of what you weigh at the surface is approximately 1,274,200 meters or 1,274 kilometers.