Which one of the following statements is corr | vedclass

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(D) $1$. For a satellite of mass $m$ at a distance $r$ from the center of the Earth,the total energy $E = -\frac{GMm}{2r}$. The energy required to esc

Vedclass · Accepted Answer

The orbital speed of the $SYNCOMS$ (Synchronous communications satellite) is $3.07 	imes 10^3 \ m \ s^{-1}$.

Vedclass · Answer

(D) $1$. For a satellite of mass $m$ at a distance $r$ from the center of the Earth,the total energy $E = -\frac{GMm}{2r}$. The energy required to escape is $E_{escape} = -E = \frac{GMm}{2r}$.$2$. For a stationary object at the same height $r$,the potential energy is $U = -\frac{GMm}{r}$. The energy required to escape is $E'_{escape} = -U = \frac{GMm}{r}$.$3$. Since $\frac{GMm}{r} > \frac{GMm}{2r}$,option $A$ is incorrect.$4$. Total energy $E = K + U$. For a satellite,$K = -\frac{1}{2}U$. Thus,$E = -\frac{1}{2}U + U = \frac{1}{2}U$. Option $B$ is incorrect.$5$. Sputnik $I$ was launched in $1957$,not $1950$. Option $C$ is incorrect.$6$. The orbital speed of a geostationary satellite is $v = \sqrt{\frac{GM}{r}}$. For $r \approx 42200 \ km$,$v \approx 3.07 	imes 10^3 \ m \ s^{-1}$. Option $D$ is correct.

Which one of the following statements is correct?

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