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klcarrasquillo klcarrasquillo
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5 years ago
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?
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5 years ago
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.

\(6=\frac{4.018\times 10^{14}}{d^2}\)

\(d=\sqrt{\frac{4.018\times 10^{14}}{6}}=your\ answer\)
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