(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

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

(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: $v = \sqrt{\frac{GM}{2R}} = \sqrt{\frac{3v_0^2}{2}} = \sqrt{\frac{3}{2}} v_0$.

Class 11 Physics Gravitation Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

Difficult

Spaceman Fred's spaceship (which has negligible mass) is in an elliptical orbit about Planet Bob. The minimum distance between the spaceship and the planet is $R$; the maximum distance between the spaceship and the planet is $2R$. At the point of maximum distance,Spaceman Fred is traveling at speed $v_0$. He then fires his thrusters so that he enters a circular orbit of radius $2R$. What is his new speed?

A
$\sqrt{3/2} \, v_0$
B
$\sqrt{5} \, v_0$
C
$\sqrt{3/56} \, v_0$
D
$\sqrt{2} \, v_0$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Gravitation

Subtopic

Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

The rotation period of an earth satellite close to the surface of the earth is $83$ minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be .......... $\min$

Medium

View Solution

$A$ satellite of mass $M$ is in a circular orbit of radius $R$ about the center of the Earth. $A$ meteorite of the same mass $M$,falling towards the Earth,collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same,just before the collision. The subsequent motion of the combined body will be:

MediumJEE MAIN 2019

View Solution

If the orbital speed of a body revolving in a circular path near the surface of the earth is $8 \ km s^{-1}$,then the orbital speed of a body revolving around the earth in a circular orbit at a height of $19,200 \ km$ from the surface of the earth is (Radius of the earth $R = 6400 \ km$). (in $km s^{-1}$)

MediumTS EAMCET 2025

View Solution

Assuming that the earth is revolving around the sun in a circular orbit of radius $R$,the angular momentum is directly proportional to $R^{n}$. The value of $n$ is

MediumMHT CET 2024

View Solution

Two satellites revolve around a planet in coplanar circular orbits in an anticlockwise direction. Their periods of revolution are $1\, h$ and $8\, h$ respectively. The radius of the orbit of the nearer satellite is $2 \times 10^{3}\, km$. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{\pi}{x}\, rad\, h^{-1}$ where $x$ is ..... .

DifficultJEE MAIN 2021

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

The rotation period of an earth satellite close to the surface of the earth is $83$ minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be .......... $\min$

Assuming that the earth is revolving around the sun in a circular orbit of radius $R$,the angular momentum is directly proportional to $R^{n}$. The value of $n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module