The nearest large galaxy to our Galaxy is about 2 ×10^6 ly...

The nearest large galaxy to our Galaxy is about $2 \times 10^{6} \mathrm{ly}$ away. If both galaxies have a mass of $3 \times 10^{41} \mathrm{~kg}$, with what gravitational force does each galaxy attract the other?

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Key Concepts

Newton's Law of Universal Gravitation

This principle states that any two masses in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them. It provides the fundamental framework for understanding how objects interact gravitationally, both on a small scale and in large-scale astronomical contexts.

Gravitational Constant

The gravitational constant, denoted by G, is a fundamental physical constant that appears in Newton's law of gravitation. It quantifies the strength of the gravitational force and ensures that the units in the law are consistent, allowing for accurate calculations of gravitational forces across a range of mass scales.

Unit Conversion in Astronomical Calculations

In astrophysical problems, distances are often given in units such as light years rather than meters. Converting these distances into a consistent set of units is critical for correctly applying formulas like Newton's law of gravitation, ensuring that the calculations reflect the true scale of cosmic distances.

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