Question 11 Mark
If the height of the orbit of a satellite increases, its velocity must also increase.
Answer
View full question & answer→False.
Explanation:
Centripetal force on the satellite $\frac{m v_c^2}{R+h}=$ gravitational force exerted by the earth on the satellite $\frac{G M m}{(R+h)^2}$
where,
m : mass of the satellite
$u_c$ : critical velocity of the satellite
$h$ : height of the satellite from the surface of the earth
$M$ : mass of the earth
$R$ : radius of the earth
$G$: gravitational constant
$\therefore v_c^2=\frac{G M}{R+h}$
$\therefore v_c=\sqrt{\frac{G M}{R+h}}$
Thus, if the value of $h$ changes, the value of $v_c$ also changes. It means a satellite needs to be given a specific velocity (in the tangential direction) to keep it revolving in a specific orbit.
As per the formula $v_c=\sqrt{\frac{G M}{R+h}}$, if the value of $h$ increases, the value of $U_c$ decreases. Hence, if the height of the satellite from the surface of the earth increases, its velocity decreases.
Explanation:
Centripetal force on the satellite $\frac{m v_c^2}{R+h}=$ gravitational force exerted by the earth on the satellite $\frac{G M m}{(R+h)^2}$
where,
m : mass of the satellite
$u_c$ : critical velocity of the satellite
$h$ : height of the satellite from the surface of the earth
$M$ : mass of the earth
$R$ : radius of the earth
$G$: gravitational constant
$\therefore v_c^2=\frac{G M}{R+h}$
$\therefore v_c=\sqrt{\frac{G M}{R+h}}$
Thus, if the value of $h$ changes, the value of $v_c$ also changes. It means a satellite needs to be given a specific velocity (in the tangential direction) to keep it revolving in a specific orbit.
As per the formula $v_c=\sqrt{\frac{G M}{R+h}}$, if the value of $h$ increases, the value of $U_c$ decreases. Hence, if the height of the satellite from the surface of the earth increases, its velocity decreases.
