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Physics / Physics: Principles with Applications 6 / Chapter 5 / Problem 38P

Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli

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You are explaining why astronauts feel weightless while orbiting in the space shuttle

Chapter 5, Problem 38P

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QUESTION:

Problem 38P

You are explaining why astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.

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QUESTION:

Problem 38P

You are explaining why astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.

ANSWER:

Solution 38P

Step 1 of 2

We have to find the acceleration due to gravity experienced by astronauts orbiting the Earth in a space shuttle at a height of 250 km from the Earth’s surface.

The acceleration due to gravity at a height of 250 km from the Earth’s surface is given by the expression,

$g=\frac{G\ {M}_{Earth}}{{r}^{2}}$

where,

$G=$ Universal gravitational constant

= $6.67\times{}1{0}^{-11}$ N $\cdot{}$ m2/kg2

${M}_{Earth}=$ Mass of the Earth = $5.97\times{}1{0}^{24}$ kg

$r={R}_{Earth}+250$ km

${R}_{Earth}=$ Radius of the Earth

= $6.38\times{}1{0}^{6}$ m

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