
When a satellite in a circular orbit around the earth enters the atmospheric region, it encounters small air resistance to its motion. Then:
(This question have multiple correct option)
A) Its kinetic energy increases
B) Its kinetic energy decreases
C) Its angular momentum about the earth decreases.
D) Its period of revolution about the earth increases.
Answer
126.3k+ views
Hint: When there is air drag force acting on a satellite it decreases its mechanical energy and due to this change in mechanical energy there is also a change radius of orbit in which the satellite is moving. Due to change in radius of orbit there is a change in kinetic energy, potential energy and angular momentum of earth.
Complete step by step solution:
When a satellite in a circular orbit around the earth enters the atmospheric region, it experiences a drag force on it due to encounter of small air resistance to its motion, this drag force is always opposite in direction of motion so, there is a negative work done of that drag force, which causes decrease of mechanical energy and this energy is converted in heat energy.
We know that, $K.E.=\dfrac{GMm}{r}$, $P.E.=\dfrac{-GMm}{r}$,
Where, $K.E.$ is kinetic energy, $G$is universal gravitation constant, $M$ is the mass of the earth, $m$ is the mass of satellite, $r$ is the radius of orbit, $P.E.$ is potential energy of satellite.
When its mechanical energy decreases then satellites go into a spiral path with decreasing radius of orbit. We can see that its kinetic energy and potential energy is inversely proportional to the radius of orbit. So, its kinetic energy increases with decrease in radius of orbit, but its potential energy decreases because of negative sign in its formula.
Also, for angular momentum $L$, $L=\sqrt{GMr}$
$\Rightarrow L\propto \sqrt{r}$
So, decrease in radius of orbit is also the cause of decrease in angular momentum of the satellite.
Hence, option (A) and option (C) is correct.
Note: We have to remember that potential energy is negative and in decrease it also decreases. Also its time of revolution also depends on the radius of orbit. i.e. $T\propto {{r}^{\dfrac{3}{2}}}$, So the decrease in radius of orbit decreases in angular momentum.
Complete step by step solution:
When a satellite in a circular orbit around the earth enters the atmospheric region, it experiences a drag force on it due to encounter of small air resistance to its motion, this drag force is always opposite in direction of motion so, there is a negative work done of that drag force, which causes decrease of mechanical energy and this energy is converted in heat energy.
We know that, $K.E.=\dfrac{GMm}{r}$, $P.E.=\dfrac{-GMm}{r}$,
Where, $K.E.$ is kinetic energy, $G$is universal gravitation constant, $M$ is the mass of the earth, $m$ is the mass of satellite, $r$ is the radius of orbit, $P.E.$ is potential energy of satellite.
When its mechanical energy decreases then satellites go into a spiral path with decreasing radius of orbit. We can see that its kinetic energy and potential energy is inversely proportional to the radius of orbit. So, its kinetic energy increases with decrease in radius of orbit, but its potential energy decreases because of negative sign in its formula.
Also, for angular momentum $L$, $L=\sqrt{GMr}$
$\Rightarrow L\propto \sqrt{r}$
So, decrease in radius of orbit is also the cause of decrease in angular momentum of the satellite.
Hence, option (A) and option (C) is correct.
Note: We have to remember that potential energy is negative and in decrease it also decreases. Also its time of revolution also depends on the radius of orbit. i.e. $T\propto {{r}^{\dfrac{3}{2}}}$, So the decrease in radius of orbit decreases in angular momentum.
Recently Updated Pages
JEE Main 2023 (April 8th Shift 2) Physics Question Paper with Answer Key

JEE Main 2023 (January 30th Shift 2) Maths Question Paper with Answer Key

JEE Main 2022 (July 25th Shift 2) Physics Question Paper with Answer Key

Classification of Elements and Periodicity in Properties Chapter For JEE Main Chemistry

JEE Main 2023 (January 25th Shift 1) Maths Question Paper with Answer Key

JEE Main 2023 (January 24th Shift 2) Chemistry Question Paper with Answer Key

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility & More

JEE Main Login 2045: Step-by-Step Instructions and Details

Class 11 JEE Main Physics Mock Test 2025

JEE Main Exam Marking Scheme: Detailed Breakdown of Marks and Negative Marking

JEE Main 2023 January 24 Shift 2 Question Paper with Answer Keys & Solutions

JEE Mains 2025 Correction Window Date (Out) – Check Procedure and Fees Here!

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Fluids

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line
