Spaceman Fred's spaceship (which has negligib | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For a circular orbit of radius $r = 2R$,the orbital speed $v$ is given by $v = \sqrt{\frac{GM}{2R}}$.For the elliptical orbit,the semi-major axis

Vedclass · Accepted Answer

$\sqrt{3/2} \, v_0$

Vedclass · Answer

(A) For a circular orbit of radius $r = 2R$,the orbital speed $v$ is given by $v = \sqrt{\frac{GM}{2R}}$.For the elliptical orbit,the semi-major axis $a$ is the average of the periapsis and apoapsis distances: $a = \frac{R + 2R}{2} = \frac{3R}{2}$.Using the conservation of energy for the elliptical orbit at the apoapsis (distance $2R$): $\frac{1}{2}mv_0^2 - \frac{GMm}{2R} = -\frac{GMm}{2a} = -\frac{GMm}{3R}$.Rearranging the energy equation: $\frac{1}{2}v_0^2 = \frac{GM}{2R} - \frac{GM}{3R} = \frac{GM}{6R}$.Thus,$\frac{GM}{R} = 3v_0^2$.Substituting this into the expression for the circular orbit speed: $v = \sqrt{\frac{GM}{2R}} = \sqrt{\frac{3v_0^2}{2}} = \sqrt{\frac{3}{2}} v_0$.

Similar Questions

Why can the entire surface of the Earth be viewed with the help of a polar satellite?

What is the effect on the time period of a satellite orbiting around the Earth if its height decreases?

Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively,measured from the centre of mass of the system. The magnitude of the gravitational force that $m_1$ exerts on $m_2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module