Find the best tutors and institutes for Class 11 Tuition
Q8.24:
A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = $2 \times 10^{30}$ kg; mass of mars = $6.4 \times 10^{23}$ kg; radius of mars = 3395 km; radius of the orbit of mars = $2.28 \times 10^8$ km; G = $6.67 \times 10^{-11}$ N m$^2$ kg$^{–2}$.
Solution :
Given Variables & Initial Setup
To launch a spaceship out of the solar system, we must provide sufficient energy to overcome the gravitational potential energy exerted by both the Sun and Mars. The total energy required ($E$) is the negative of the total mechanical energy of the spaceship in its current position.
- Mass of spaceship ($m$) = $1000 \, \text{kg}$
- Mass of Sun ($M_S$) = $2 \times 10^{30} \, \text{kg}$
- Mass of Mars ($M_M$) = $6.4 \times 10^{23} \, \text{kg}$
- Radius of Mars ($R_M$) = $3395 \times 10^3 \, \text{m} = 3.395 \times 10^6 \, \text{m}$
- Radius of Mars' orbit ($r$) = $2.28 \times 10^8 \, \text{km} = 2.28 \times 10^{11} \, \text{m}$
- Gravitational constant ($G$) = $6.67 \times 10^{-11} \, \text{N m}^2 \text{kg}^{-2}$
Step 1: Calculating the Potential Energy at the Surface of Mars
The total energy ($E_{total}$) is the sum of the potential energy due to the Sun ($U_S$) and the potential energy due to Mars ($U_M$), plus the kinetic energy ($K$) of the spaceship due to Mars' orbital motion. [Per the Law of Conservation of Energy, $E_{launch} = -E_{total}$].
Potential energy due to Mars ($U_M$):
$U_M = -\frac{GM_Mm}{R_M}$ $U_M = -\frac{(6.67 \times 10^{-11})(6.4 \times 10^{23})(1000)}{3.395 \times 10^6}$ $U_M \approx -1.258 \times 10^{10} \, \text{J}$Step 2: Calculating Potential Energy due to the Sun
The spaceship is at the distance of Mars from the Sun.
$U_S = -\frac{GM_Sm}{r}$ $U_S = -\frac{(6.67 \times 10^{-11})(2 \times 10^{30})(1000)}{2.28 \times 10^{11}}$ $U_S \approx -5.851 \times 10^{11} \, \text{J}$Step 3: Accounting for Kinetic Energy of the Spaceship
The spaceship possesses kinetic energy due to the orbital velocity ($v_o$) of Mars. [Per the principle of orbital mechanics, $v_o = \sqrt{\frac{GM_S}{r}}$].
$K = \frac{1}{2}mv_o^2 = \frac{1}{2}m\left(\frac{GM_S}{r}\right)$ $K = \frac{(1000)(6.67 \times 10^{-11})(2 \times 10^{30})}{2 \times 2.28 \times 10^{11}}$ $K \approx 2.925 \times 10^{11} \, \text{J}$Step 4: Total Energy Required
The total mechanical energy $E_{total} = U_M + U_S + K$. The energy required to escape ($E_{expended}$) is $-E_{total}$.
$E_{total} = (-0.1258 \times 10^{11}) + (-5.851 \times 10^{11}) + (2.925 \times 10^{11})$ $E_{total} = -2.9268 \times 10^{11} \, \text{J}$Energy to be expended:
$E_{expended} = -(-2.9268 \times 10^{11} \, \text{J})$ $E_{expended} \approx 2.93 \times 10^{11} \, \text{J}$Visualization of Gravitational Well
Final Solution: The energy required to launch the spaceship out of the solar system is approximately $2.93 \times 10^{11} \, \text{J}$.
More Questions from Class 11 Physics Gravitation Additional Exercises
- Q8.22: As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 36,000 km from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite ? (Take the potential energy at infinity to be zero). Mass of the earth = $6.0 \times 10^{24}$ kg, radius = 6400 km.
- Q8.23: A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity ? (mass of the sun = $2 \times 10^{30}$ kg).
- Q8.25: A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s$^{–1}$. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it ? Mass of mars = $6.4 \times 10^{23}$ kg; radius of mars = 3395 km; G = $6.67 \times 10^{-11}$ N m$^2$ kg$^{–2}$.
CBSE Solutions for Class 11 Physics Gravitation
Chapters in CBSE - Class 11 Physics
Top Tutors who teach Gravitation
Top Tutor
Laxmi Vihar, Hisar
4 yrs of
Exp
3 students
267 hrs of classes completed
800
per hour
Online Classes
I've taught Mathematics of class 11th and 12th in an academy for 2 years. And now teaching on UrbanPro from last 4 years. I focus on letting the student reach the deepest level of concept and then do problems of reference books like RD Sharma and others. My main target is to make student learn how to approach a question so that he can do by himself should he face any new problem.
Saurabh sir is a good teacher, and is clearly very knowledgeable in Mathematics. He takes time to clarify each and every concept, and caters to any schedule requirements, etc. The classes are interactive and super helpful.
Top Tutor
Sector 33, Gurgaon
18 yrs of
Exp
11 students
739 hrs of classes completed
1000
per hour
Online Classes
Tutor's home
Expert Chemistry Mentor for IIT-JEE | NEET | CBSE – 18+ Years of Experience Hi, I’m Anuranjita. I am a Senior Chemistry Expert with over 18 years of experience at India's leading institutes like Aakash, FIITJEE, and TIME and hold an M.Tech. degree from Anna University, Chennai—one of the top 10 engineering universities in India. I have refined a highly structured, result-oriented teaching methodology designed to crack • IIT-JEE (Main & Advanced) • NEET • Score 100% in CBSE Board exams. (Class 11 & 12 – Chemistry) Over the years, I have trained thousands of students, many of whom have successfully secured admissions into AIIMS, IITs, NITs, and other top medical and engineering colleges across India. Here is what makes my classes uniquely effective: • Interactive and concept-driven teaching • Focus on building strong fundamentals • Personalized learning based on each student’s pace • Regular doubt-clearing sessions & Chapter-wise tests • Exam-oriented tips and problem-solving strategies • The "Exclusive 5" Batch Model (Personalized Attention) Unlike massive online batches with thousands of students where individual voices get lost, my classes are strictly limited to a maximum of 5 students. This ensures that every single student receives 1-on-1 level attention, and I can monitor each student's real-time progress, strengths, and weaknesses. • Rigorous Testing & PYQ Practice: Chapter-wise tests modeled strictly on the latest NTA patterns, alongside exhaustive solving of past years' questions (PYQs). Looking forward to helping you master chemistry! Best Regards Anuranjita
"Chemistry Mam has been very helpful for my daughter’s study. After struggling with the overload at standard coaching institutes, finding a teacher who simplifies complex topics made all the difference. Her passion and willingness to take unplanned classes show how much she truly cares about her students' success. Highly recommended!"
Sanganer, Jaipur
2 yrs of
Exp
Student's Home
Tutor's home
I have around two years of experience in teaching. By profession, I am a spoken English trainer. Since 2016, I have been in this field. I hold a B.Sc degree from MGS University of Bikaner. I love to help students who want to be fluent in English. I'm well-versed in Hindi, English and Punjabi.
Top Tutor
Bade Kajipur, Gorakhpur
20 yrs of
Exp
10 students
1218 hrs of classes completed
350
per hour
Online Classes
Student's Home
Tutor's home
This is 12 Month NEET Physics Syllabus Crash Course Starting From 1 April 2026 to 30 April 2027. Four Days in a Week. Every Live Class is of 1hour 30 minutes, including Precise Notes of each topic Practice Questions and Online Test With Video Solutions. Formula Sheet for every chapter. Course Fees of NEET 2026 Crash Course for Physics is 9000/- I prefer to teach physics specially class 11 and 12, I do focus on Competitive level Physics like N.E.E.T. and I.I.T.J.E.E. along with basic physics to make my students understand physics easier. My focus is on competitive exam for betterment of students. This is 12 Month NEET Physics Syllabus Crash Course Starting From 1 April 2026 to 30 April 2027. Four Days in a Week. I have been teahing Physics twenty years of teaching experience, I had done my schooling and college from Gorakhpur city Uttar Pradesh. I am Teaching since 2004 in Gorakhpur initially off-line, and teaching online since 2020 with zoom and Google Meet I do provide study material like Notes, Question Bank and D.P.P., No Additional charge is require to pay, it is included in class fees. Monthly Fees 4000/- for 3 days in a week and in a month 12 hours
Your positive attitude and enthusiasm for teaching have made a lasting impression on me. Thank you for being a teacher who truly cares about their students’ success and well-being.
Super Tutor
Patpar Ganj, Delhi
20 yrs of
Exp
10 students
966 hrs of classes completed
500
per hour
Online Classes
Student's Home
I am a teacher. I love teaching and want to share my knowledge with my students. I will take online classes. My approach combines clear concepts, regular practice, and student-friendly strategies to make learning effective and enjoyable.
