91Ó°ÊÓ

• Mass of astronaut is m=75 kg
• Distance from Earth to Hubble space telescope is r’=600 km

The expression for the gravitational force is given by,

$F=G\frac{m_1{m}_2}{r^2}$

Here, and are the masses of particles, r is the distance between the particles, G is the gravitational constant.

The standard values we have:

The mass of Earth is$m_e=5.972×{10}^{24}\text{ k²µ}$.

The radius of earth is$r_e=6.37×{10}^6\text{″¾}$.

The gravitation constant is $G=6.67×{10}^{−11}\text{ N}â‹\dots {\text{m}}^{\text{2}}â‹\dots {\text{kg}}^{−\text{2}}$.

The Earth’s gravity force on the astronaut can be expressed as,

$F_g=G\frac{m{m}_e}{r^2}$ …… (I)

The distance between Earth and astronaut can be expressed as

$\begin{array}{c}r=r_e+r\text{'}\\ =r_e+600×{10}^3\text{″¾}\\ =\left(6.37×{10}^6\text{″¾}\right)+\left(600×{10}^3\text{″¾}\right)\\ =6.97×{10}^6\text{″¾}\end{array}$

Substitute$6.67×{10}^{−11}\text{ N}â‹\dots {\text{m}}^{\text{2}}â‹\dots {\text{kg}}^{−\text{2}}$for G ,$6.97×{10}^6\text{″¾}$for r ,$5.972×{10}^{24}\text{ k²µ}$for m_e , and 75kg for m in equation (I).

$\begin{array}{c}{F}_g=G\frac{m{m}_e}{r^2}\\ =\left(6.67×{10}^{−11}\text{ N}â‹\dots {\text{m}}^{\text{2}}â‹\dots {\text{kg}}^{−\text{2}}\right)\frac{\left(75\text{ k²µ}\right)\left(\text{5.97}×{\text{10}}^{\text{24}}\text{ k²µ}\right)}{{\left(6.97×{10}^6\text{″¾}\right)}^2}\\ =614.7\text{ N}\end{array}$

Thus, the Earth’s gravity force on astronaut is 614.7 N.

The weight at Earth’s surface can be expressed as,

W = mg

Here, g is the acceleration due to gravity, and m is the mass of the body.

Thus, the weight of astronaut at Earth’s surface can be calculated as,

$\begin{array}{c}W=mg\\ =75\text{ k²µ}×9.8\text{″¾}/{\text{s}}^{\text{2}}\left(\frac{1\text{ N}}{\text{kg}â‹\dots \text{m}/s^2}\right)\\ =735\text{ N}\end{array}$

On comparing both values, the weight is higher at Earth’s surface.

Since the space shuttle moves in a closed orbit and the required centripetal force is provided by gravitation, the net force that acts on the astronaut inside the super shuttle is zero. Consequently, the astronaut will appear to be weightless.