Ceres, the largest asteroid known, has a mass of roughly 8.7 ×10^20 kg. If Ceres passes within

step 1 The largest asteroid known has a mass of 8 .7 times 10 to the 20 kilograms. We know the gravitat

Ceres, the largest asteroid known, has a mass of roughly 8.7...

Ceres, the largest asteroid known, has a mass of roughly $8.7 \times 10^{20} \mathrm{~kg}$. If Ceres passes within 14,000 $\mathrm{km}$ of a spaceship in which you are traveling, what force does it exert on a 95-kg astronaut in your ship?

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Key Concepts

Newton’s Law of Universal Gravitation

This principle calculates the gravitational force between two masses by using the formula F = G × (m? × m?) / r². It explains how the force increases with the masses and decreases with the square of the distance between them.

Gravitational Constant

The gravitational constant, denoted as G, is a key proportionality constant in Newton's law. It quantifies the strength of the gravitational force and is essential in relating mass and distance to the resulting force.

Importance of Mass in Gravitational Calculations

Mass is a fundamental component in determining gravitational forces. The gravitational pull between two objects is directly proportional to the product of their masses, meaning larger masses produce stronger gravitational effects.

Role of Distance and Units Conversion

Distance plays a critical role in gravitational calculations due to its inverse square relationship with force. Correct units conversion, such as converting kilometers to meters, is essential to ensure that the calculated force is accurate and adheres to the SI unit system.

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