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Newton's Law of Universal Gravitation is a fundamental principle in physics that describes the attractive force between two masses. This law states that every mass attracts every other mass in the universe, and the force between the two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This is expressed mathematically as:

• \[ F = G \frac{m_1 m_2}{r^2} \]

Here, \( F \) is the gravitational force, \( m_1 \) and \( m_2 \) are the masses of the two objects, \( r \) is the distance between the centers of the masses, and \( G \) is the gravitational constant. This law is crucial for understanding how objects attract each other in space, such as planets, stars, and in our exercise, asteroids. By applying this formula, we can calculate the gravitational pull between any two celestial bodies.

The gravitational constant, represented by \( G \), is a key value in the formula for calculating gravitational force. It measures the strength of gravity in the universal framework and is a fixed number in the equation.

• The standard value of \( G \) is \( 6.674 \times 10^{-11} \, \text{N} \, \text{m}^2/\text{kg}^2 \).

This constant ensures that the units in the formula align correctly, providing a resulting force in newtons (N). Understanding \( G \) is important because it allows us to calculate the gravitational interactions not just on Earth but throughout the cosmos. It's a very small number, indicating that gravity is a weak force compared to other fundamental forces like electromagnetism, yet it plays a significant role in the universe due to the large masses involved in celestial bodies.

In our exercise, the gravitational attraction is calculated between two spherical asteroids. The assumption of spherical shape simplifies calculations, as it allows us to assume that the entire mass of the asteroid can be considered to be concentrated at its center of mass. This simplification is crucial in applying Newton's Law of Universal Gravitation straightforwardly.

• The shape simplifies mathematical modeling, making calculations feasible with basic geometry concepts.

When dealing with real celestial objects, they are often approximated as spheres to use this law effectively. This approach works particularly well for large distances, such as the separation between our asteroids, where smaller irregularities of shape become negligible. Understanding this concept helps to model interactions in space without requiring complex geometry to account for the actual shape of the bodies involved.

Performing a step-by-step calculation helps in understanding how gravitational force is determined. This structured approach allows us to carefully follow each part of the computation:

• First, identify the given masses and distance.
• Next, apply the formula \[ F = G \frac{m_1 m_2}{r^2} \], substituting these values.

In our problem with the asteroids, we calculated:

• The product of their masses \( m_1 m_2 = 800 \times 10^{20} \, \text{kg}^2 \).
• The square of the distance \( r^2 = 100 \times 10^{12} \, \text{m}^2 \).

Then, we plugged these into the formula and simplified:

• \[ F = 6.674 \times 10^{-11} \frac{800 \times 10^{20}}{100 \times 10^{12}} = 5.3392 \times 10^{-2} \, \text{N} \]

This methodical process clarifies how individual components contribute, ensuring the final result is accurate. The clarity of following a structured method enhances comprehension, vital for accurately applying similar calculations in future tasks.