An astronaut in space is in orbit $250$ $250$ $k m$ $km$ above the surface of Earth. What is the gravitational acceleration on the astronaut at this altitude?

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An astronaut in space is in orbit $250$ $250$ $k m$ $km$ above the surface of Earth. What is the gravitational acceleration on the astronaut at this altitude?

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Answer 1 · 2016-06-07T18:27:22

The acceleration due to gravity is given by $a = \frac{G M}{r^{2}}$ $a=(GM)/r^2$ where G is the gravitational constant and M is the mass of Earth. The value at this altitude is $9.08$ $9.08$ $m s^{- 2}$ $ms^-2$ .

Explanation:

Constants:

$G = 6.67408 \times 10^{- 11}$ $G=6.67408xx10^-11$ $m^{3} k g^{- 1} s^{- 2}$ $m^3 kg^-1 s^-2$
$M = 5.972 \times 10^{24}$ $M=5.972xx10^24$ $k g$ $kg$

The radius of Earth is $r = 6.371 \times 10^{6}$ $r=6.371xx10^6$ $m$ $m$

In this case, we need to add another $2.5 \times 10^{5}$ $2.5xx10^5$ $m$ $m$ (250 km) to the radius, to give $r = 6.621 \times 10^{6}$ $r=6.621xx10^6$ $m$ $m$

So:

$a = \frac{G M}{r^{2}} = \frac{6.67 \times 10^{- 11} \times 5.97 \times 10^{24}}{{(6.621 \times 10^{6})}^{2}} = 9.08$ $a=(GM)/r^2=(6.67xx10^-11xx5.97xx10^24)/(6.621xx10^6)^2=9.08$ $m s^{- 2}$ $ms^-2$

This makes sense, since the acceleration due to gravity is $9.81$ $9.81$ $m s^{- 2}$ $ms^-2$ . The radius has been increased by only about 4%, but the acceleration due to gravity is inversely proportional to the square of the radius.

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An astronaut in space is in orbit $250$ $250$ $k m$ $km$ above the surface of Earth. What is the gravitational acceleration on the astronaut at this altitude?

1 Answer

Explanation:

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Science

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An astronaut in space is in orbit 250250 kmkm above the surface of Earth. What is the gravitational acceleration on the astronaut at this altitude?

1 Answer

Explanation:

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An astronaut in space is in orbit $250$ $250$ $k m$ $km$ above the surface of Earth. What is the gravitational acceleration on the astronaut at this altitude?