91Ó°ÊÓ

When we talk about an object's weight, we are referring to the force exerted on it by gravity. On Earth, this is calculated using the formula: \( W = mg \), where \( W \) is the weight, \( m \) is the object's mass, and \( g \) is the acceleration due to gravity. The acceleration due to gravity on Earth is approximately \( 9.81 \text{ m/s}^2 \).
On the Moon, the gravity is much weaker. It is about one-sixth of what we experience on Earth. Thus, to calculate an object's weight on the Moon, we use the same formula but with the Moon's gravity, \( g_{moon} \approx 1.625 \text{ m/s}^2 \):

• Start with the object's Earth weight, e.g., 100 N.
• Apply the Moon's gravity factor, \( \frac{1}{6} \).
• This gives a Moon weight of \( \frac{100}{6} \approx 16.67 \text{ N} \).

Understanding how to calculate weight on the Moon helps us comprehend the influence of gravitational differences in our solar system.

Gravity is what makes objects fall toward the ground. The acceleration due to gravity is a measure of how quickly an object will accelerate when it is in free fall, solely under the influence of gravity. On Earth, this value is \( 9.81 \text{ m/s}^2 \).
The Moon, being smaller and less massive than Earth, has a lower value for its gravitational acceleration. Specifically, \( g_{moon} \approx 1.625 \text{ m/s}^2 \), which accounts for the fact that things weigh less on the Moon.
Here’s how the process works:

• On Earth, acceleration due to gravity is \( g = 9.81 \text{ m/s}^2 \).
• On the Moon, because of its lower mass, \( g_{moon} = 1.625 \text{ m/s}^2 \).

This fundamental concept explains why astronauts bounce when they walk on the Moon, showcasing the practical difference in gravitational pulls.

Newton's law of universal gravitation provides the basis for understanding forces between masses. According to this principle, every point mass attracts every other point mass by a force pointing along the line intersecting both points. The formula is:

• \( F = \frac{G M m}{r^2} \)

where:

• \( F \) is the force between the masses,
• \( G \) is the gravitational constant, \( 6.674 \times 10^{-11} \text{ N}\cdot\text{m}^2/\text{kg}^2 \),
• \( M \) and \( m \) are the masses of the objects,
• and \( r \) is the distance between the centers of their masses.

Applying this law to our specific problem, we can compute the gravitational force an object experiences depending on its distance from Earth’s center. When the distance increases, the gravitational force decreases. As seen in the problem, an object must be at a distance of approximately \( 2.45 \) Earth radii to weigh the same as it does on the Moon. This exercise uses Newton's formula to demonstrate how gravity diminishes with increased distance.