[Solved] Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is 4.22×108m. Show that the mass of Jupiter is about one-thousandth that of the sun. - Physics Part-I

Gravitational force = Centripetal ForceRp2GMpMJ=RpMpvp2...............(1)Also, vp= Tp2πRp...............(2)Substituting (2) in (1),MJ=GTP24π2RP3 =1.9×1027 kgMJ/MS=2×10301.9×1027≈10−3

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Io, one of the satellites of Jupiter has an orbital period of

Physics Part-I

Class 11

NCERT

Chapter 1: Physical World

16 questions

Chapter 2: Units and Measurements

51 questions

Chapter 3: Motion in Straight Line

50 questions

Chapter 4: Motion in a Plane

43 questions

Chapter 5: Laws of motion

52 questions

Chapter 6: Work, Energy and Power

41 questions

Chapter 7: System of Particles and Rotational Motion

45 questions

Chapter 8: Gravitation

33 questions

Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that of the earth ?

Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is

4.22 \times 1 0^{8} m

. Show that the mass of Jupiter is about one-thousandth that of the sun.

Let us assume that our galaxy consists of

2.5 \times 1 0^{11}

stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be

1 0^{5}

ly.

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Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is $4.22 \times 1 0^{8} m$ . Show that the mass of Jupiter is about one-thousandth that of the sun.

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Updated on: Nov 9, 2023

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Physics Part-I (NCERT)

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Samuel Discussed

Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is

4.22 \times 1 0^{8} m

. Show that the mass of Jupiter is about one-thousandth that of the sun.

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Gravitational force = Centripetal Force

\frac{G M _{p} M _{J}}{R _{p}^{2}} = \frac{M _{p} v _{p}^{2}}{R _{p}} ............... (1)

Also,

v_{p} = \frac{2 π R _{p}}{T _{p}} ............... (2)

Substituting (2) in (1),

M_{J} = \frac{4 π ^{2} R _{P}^{3}}{G T _{P}^{2}}

= 1.9 \times 1 0^{27} k g

M_{J} / M_{S} = \frac{1.9 \times 1 0 ^{27}}{2 \times 1 0 ^{30}} \approx 1 0^{- 3}

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Practice more questions from Physics Part-I (NCERT)

Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that of the earth ?

Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is

4.22 \times 1 0^{8} m

. Show that the mass of Jupiter is about one-thousandth that of the sun.

Let us assume that our galaxy consists of

2.5 \times 1 0^{11}

stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be

1 0^{5}

ly.

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Question Text	Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is $4.22 \times 1 0^{8} m$ . Show that the mass of Jupiter is about one-thousandth that of the sun.
Updated On	Nov 9, 2023
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 3
Upvotes	449
Avg. Video Duration	15 min

Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is $4.22 \times 1 0^{8} m$ . Show that the mass of Jupiter is about one-thousandth that of the sun.

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Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is 4.22×108m. Show that the mass of Jupiter is about one-thousandth that of the sun.

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Io, one of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is $4.22 \times 1 0^{8} m$ . Show that the mass of Jupiter is about one-thousandth that of the sun.