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Gravitational force is a fundamental concept in physics defined by Newton's Law of Universal Gravitation. Simply put, it describes the attractive force between two objects that have mass. The formula for gravitational force is: \[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \] where:

• \( F \) is the gravitational force.
• \( G \) is the gravitational constant \(6.674 \times 10^{-11} \text{Nm}^2/\text{kg}^2\).
• \( m_1 \) and \( m_2 \) are the masses of the two objects.
• \( r \) is the distance between the centers of the two objects.

This law tells us that the gravitational force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. This means as the distance increases, the force decreases rapidly. This is critical when calculating forces in space, like the gravitational pull on a spacecraft, which greatly varies with distance.

Understanding how to calculate mass is crucial when working with gravitational forces. In our exercise, the space station's weight on Earth is known, and from this, we need to find its mass. Weight is the force exerted by gravity on an object and can be calculated using: \[ F = m \cdot g \] where:

• \( F \) is the force, equivalent to weight when referring to gravity on Earth.
• \( m \) is the mass.
• \( g \) is the gravitational acceleration, about 9.81 m/s² on Earth.

To find the mass \( m \) of the space station based on its known weight of 10.0 MN, we rearrange the formula:\[ m = \frac{F}{g} \] Substituting the values (with \( F = 10.0 \times 10^6 \text{N} \)), we find: \[ m = \frac{10.0 \times 10^6}{9.81} \approx 1.02 \times 10^6 \text{kg} \] This calculation is essential for further gravitational force determinations at varying distances.

In gravitational calculations, the distance between two objects greatly influences the resulting force. In the original problem, the space station is relocated to a distance ten times Earth's radius from Earth's center. This requires using a known value for Earth's radius, \( R_{\text{Earth}} \approx 6.371 \times 10^6 \text{m} \), leading us to: \[ r = 10 \times R_{\text{Earth}} = 6.371 \times 10^7 \text{m} \] The gravitational formula depends on squaring this distance (\( r^2 \)), highlighting why gravitational forces diminish significantly as the distance increases. This distance change is integral to calculating the new gravitational pull experienced by the space station in space, showcasing how even slight increases in distance can significantly decrease gravitational attraction due to the inversely proportional square relationship. Understanding this concept helps to grasp the physics of orbits and space maneuvers.