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Rocket Gravity Dc4926

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Rocket Gravity Dc4926


1. The problem is to find the gravity of a rocket, which usually refers to the gravitational acceleration acting on it. 2. The formula to calculate gravitational acceleration $g$ at a distance $r$ from the center of a planet of mass $M$ is given by Newton's law of gravitation: $$g = \frac{GM}{r^2}$$ where $G$ is the universal gravitational constant ($6.674 \times 10^{-11} \text{m}^3\text{kg}^{-1}\text{s}^{-2}$). 3. Important rules: - $M$ is the mass of the planet or celestial body. - $r$ is the distance from the center of the planet to the rocket. - Gravity decreases with the square of the distance from the planet's center. 4. To find the gravity acting on the rocket, you need to know the mass of the planet and the rocket's distance from the planet's center. 5. Example: For a rocket near Earth's surface, $M$ is Earth's mass ($5.972 \times 10^{24} \text{kg}$) and $r$ is Earth's radius ($6.371 \times 10^6 \text{m}$), so $$g = \frac{6.674 \times 10^{-11} \times 5.972 \times 10^{24}}{(6.371 \times 10^6)^2} \approx 9.8 \text{m/s}^2$$ This is the standard gravity near Earth's surface. 6. If the rocket is farther from the planet, increase $r$ accordingly to find the reduced gravity.