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Title: The acceleration due to gravity is inversely proportional to the square Post by: klcarrasquillo on Jul 12, 2018 The acceleration due to gravity is inversely proportional to the square of the distance from the centre of Earth. The acceleration due to gravity for a satellite orbiting 7000 km above the centre of Earth is 8.2 m/s^2.
a) write a formula for this relationship. b) at what height will the acceleration due to gravity be 6 m/s^2? Title: Re: The acceleration due to gravity is inversely proportional to the square Post by: bio_man on Jul 12, 2018 Start with:
\(y=\frac{k}{x}\) \(a=\frac{k}{d^2}\) Make sure a and d are the same units. Convert 7000 km to meters. 7,000 km becomes 7 000 000 m \(8.2=\frac{k}{7000000^2}\) Solve for k: \(8.2\left(7000000^2\right)=k\) \(k=4.018\times 10^{14}\) \(\therefore a=\frac{4.018\times 10^{14}}{d^2}\) That answers part (a). For part b, substitute 6 m/s^2 into a, and solve for d. \(6=\frac{4.018\times 10^{14}}{d^2}\) \(d=\sqrt{\frac{4.018\times 10^{14}}{6}}=your\ answer\) |