Does acceleration due to gravity, $g$, which is calculated by Newton's equation, decrease with altitude? Forgive the silly question.
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1$\begingroup$ Yes, it does, but it does it only slowly. The acceleration of gravity will be a quarter of its value on the ground at an altitude of one Earth diameter. Even at 10000m, as high as passenger jets go, it has only decreased by a fraction of a percent. $\endgroup$– CuriousOneMay 26, 2015 at 3:23
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$\begingroup$ I am afraid your question is a little vague. I believe you are asking if the acceleration decreases with an increase in altitude, then the answer is yes. If you however mean that the acceleration decreases with a decrease in altitude, study more. $\endgroup$– HorusMay 26, 2015 at 8:31
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$\begingroup$ @Horus Please be nice. $\endgroup$– rob ♦May 26, 2015 at 12:50
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1$\begingroup$ @rob I agree I may have been too harsh. I apologize. $\endgroup$– HorusMay 30, 2015 at 13:22
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2 Answers
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The gravitational force on a small mass $m$ some distance $R$ from the center of a large spherical mass $M$ is given by $$ |F| = \frac{GMm}{R^2}. $$ If your distance from the center is some altitude $r$ above the radius of the Earth's surface $R_\oplus$, the force is $$ |F| = \frac{GMm}{(R_\oplus + r)^2} = \frac{GMm}{R_\oplus^2} \left( 1 + \frac{r}{R_\oplus} \right)^{-2} \approx \frac{GMm}{R_\oplus^2} \left( 1 - \frac12 \frac{r}{R_\oplus} \right) $$ So for $r\ll R_\oplus$, you can say that the gravitational force gets weaker linearly with altitude. Low-earth orbit has $r/R_\oplus \lesssim 25\%$, so for higher "low" orbits this approximation starts to fail (you could take the next term in the binomial expansion if you wanted). The atmosphere has $r/R_\oplus \lesssim 1\%$, so all gravitational accelerations in the atmosphere are the same to about three significant figures.
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Yes, because gravity decreases with the square of distance. The amount that it decreases is very small, however. Interestingly enough, you can measurably weigh more inn one city than in another, due to differing densities and altitudes.
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$\begingroup$ Well, yes, but why does gravity decrease closer to the core of the Earth(or does it?) $\endgroup$ May 26, 2015 at 5:58
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$\begingroup$ @AditiChandra Do you mean if we dug a hole? $\endgroup$– Jimmy360May 26, 2015 at 6:00
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