How far above the surface of Earth would you weigh 63.6 percent of your surface weight?
If the new radius is R, and the earth's radius is r,
.636 * Mmg/r^2 = = Mmg/R^2
.636/r^2 = 1/R^2
R = r/.797 = 1.25r
plug in your favorite value for r, and figure the difference
To determine the distance above the surface of the Earth where you would weigh 63.6 percent of your surface weight, you need to understand the concept of gravitational force and how it changes with distance.
The weight of an object is the force with which it is attracted to the Earth due to gravity. As you move away from the surface of the Earth, the gravitational force weakens because it follows an inverse square law. This means that the force decreases with the square of the distance.
To find the distance where your weight is 63.6 percent of your surface weight, you can set up an equation comparing the gravitational forces at both locations.
Let's call the surface weight W₀ and the weight at the desired distance W. According to the question, we want to find the distance where W is 63.6 percent (or 0.636) of W₀.
The equation would be:
W = (0.636) * W₀
Since weight is directly proportional to the gravitational force, we can rewrite the equation using the formula for gravitational force:
F = (G * m₁ * m₂) / r²
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10⁻¹¹ N m²/kg²),
m₁ and m₂ are the masses of the two objects (in this case, your mass and Earth's mass),
and r is the distance between the centers of the two objects.
Equating the two weights and gravitational forces, we have:
(G * m₁ * m₂) / r² = (0.636) * (G * m₁ * m₂) / R²
Where R is the radius of the Earth (approximately 6,371 kilometers or 3,959 miles).
Simplifying the equation, we find:
1 / r² = (0.636) / R²
To solve for r, we can take the reciprocal of both sides and then find the square root:
r = √(R² / (0.636))
Plugging in the value for R and evaluating the expression, we can find the distance above the surface of the Earth where you would weigh 63.6 percent of your surface weight.