An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface.  The radius of the earth is R, while its mass is M.  The gravitational pull FG on the astronaut is :

  • Option 1)

    Zero since astronaut feels weightless

     

  • Option 2)

    0< F_{G}< \frac{GMm}{R^{2}}

  • Option 3)

    \frac{GMm}{\left ( R+h \right )^{2}}< F_{G}< \frac{GMm}{R^{2}}

  • Option 4)

    F_{G}= \frac{GMm}{\left ( R+h \right )^{2}}

 

Answers (1)

As we learnt in

Orbital velocity of satellite -

V=\sqrt{\frac{GM}{r}}

r=R+h

r\rightarrow Position of satellite from the centre of earth

V\rightarrow Orbital velocity

- wherein

The velocity required to put the satellite into its orbit around the earth.

 

 and

Newton's Law of Gravitation -

F\; \alpha\; \frac{m_{1}m_{2}}{r^{2}}

F\; = \frac{G\, m_{1}\, m_{2}}{r^{2}}

F\rightarrow Force    

G\rightarrow Gravitalional constant

m_1,m_2\rightarrow  Masses

r\rightarrow  Distance between masses

- wherein

Force is along the line joining the two masses

 

 Gravitational Pull on ths astronaut is F=0


Option 1)

Zero since astronaut feels weightless

 

Incorrect

Option 2)

0< F_{G}< \frac{GMm}{R^{2}}

Incorrect

Option 3)

\frac{GMm}{\left ( R+h \right )^{2}}< F_{G}< \frac{GMm}{R^{2}}

Incorrect

Option 4)

F_{G}= \frac{GMm}{\left ( R+h \right )^{2}}

Correct

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