Orbital Velocity

Tested in 4 real MPSC questions across 3 years (2015–2023). See it in context on the interactive Concept Graph →

Years it was asked

2023 2020 2015

What you need to know first

Gravitational Potential EnergyOrbital mechanics

Real questions that test this

खालीलपैकी कोणते विधान बरोबर आहे ? Which of the following statement is correct ?

a)ग्रहांचा वेग सूर्यापासून जास्तीत जास्त अंतर असताना सर्वात कमी आणि सूर्यापासून कमीत कमी अंतर असताना सर्वात जास्त असतो. / The speed of Planet is faster when they are nearer to the sun and slower when they are farther away from the sun.&check; Correct

b)ग्रहांचा वेग सूर्यापासून जास्तीत जास्त अंतर असताना सर्वात जास्त आणि सूर्यापासून कमीत कमी अंतर असताना सर्वात कमी असतो. / The speed of Planet is faster when they are farther from the sun and slower when they are nearer to the sun.

c)ग्रहांचा वेग सूर्यापासून जास्तीत जास्त व कमीत कमी अंतर असताना सारखाच असतो. / The speed of Planet is same when they are nearer to the sun or farther away from the sun.

d)ग्रहांचा वेग सूर्यापासून जास्तीत जास्त व कमीत कमी अंतर असताना सर्वात जास्त असतो. / The speed of Planet is faster when they are nearer to the sun or farther away from the sun.

According to Kepler's second law (Law of Areas), a planet moves faster when it is closer to the sun (perihelion) and slower when it is farther away (aphelion).

पृथ्वीच्या केंद्रापासून R इतक्या अंतरावर m इतक्या वस्तुमानाचा एका अग्निबाणाला गतिमान होण्यासाठी लागणारी ऊर्जा E = GmM_e (1/R_e - 1/R) इतकी आहे. तर ह्या अग्निबाणाला पृथ्वीच्या गुरुत्वाकर्षण क्षेत्रापासून पूर्णतः निसटण्यासाठी कमीत कमी किती वेग दिला पाहिजे ? The amount of energy needed to move a rocket having mass m from the surface of the Earth to a distance R from the Earth's center is E = GmM_e (1/R_e - 1/R). What is the minimum velocity, the rocket must have in order to completely escape the Earth's gravitational field ?

a)(2Gm/R_e)^(1/2)

b)(2GME_e/R_e)^(1/2)&check; Correct

c)(2gh)^(1/2)

d)(2mGRe)^(1/2)

The escape velocity from the Earth's gravitational field is derived by setting the total mechanical energy to zero, yielding v = sqrt(2GMe / Re).

पृथ्वीभोवती वर्तुळाकार कक्षेत फिरणाऱ्या उपग्रहा $E_k$ इतकी गतिज ऊर्जा आहे. पृथ्वीच्या क्षेत्रातून बाहेर निसरण्यासाठी किमान केवढी ऊर्जा दिली पाहिजे? A satellite having circular orbit around the earth has a kinetic energy $E_k$. What is the minimum amount of energy to be added so that it escapes from the earth ?

1)E_k/4

2)E_k/2

3)E_k&check; Correct

4)2E_k

Total energy of a satellite in a circular orbit is negative and equals -Ek. To escape to infinity, total energy must become zero, requiring an additional energy equal to its kinetic energy Ek.

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