Orbital Velocity Class 11 Physics | JEE Main 2027

Gravitation: Orbital Velocity – Complete Concepts, Formulas and JEE Main Questions | Class 11 Physics

Orbital Velocity Class 11 Physics aur JEE Main ke liye Gravitation chapter ka ek important concept hai. Is topic mein hum samjhenge ki satellite planet ke around kaise ghoomti hai, orbital velocity ka formula kaise derive hota hai aur satellite ki height badhne par uski speed par kya effect padta hai.

Agar aap JEE Main 2027 ki preparation kar rahe ho, toh orbital velocity ke saath escape velocity aur satellite ke time period ke formulas bhi yaad hone chahiye. Is article mein concepts ko simple Hinglish, formula derivations aur solved numerical examples ke saath explain kiya gaya hai.

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1. Orbital Velocity Kya Hoti Hai?

Orbital velocity woh tangential speed hai jisse satellite kisi planet ke around circular orbit mein move kar sakti hai.

Satellite ko orbit mein rakhne ke liye gravitational force centripetal force provide karti hai. Satellite continuously planet ki taraf accelerate karti hai, lekin uski tangential velocity ki wajah se woh planet par seedha girne ke bajay orbit mein move karti rehti hai.

Basic Concept

Gravitational Force = Centripetal Force

Orbital velocity ka derivation isi principle par based hai. Hum assume karte hain ki satellite circular orbit mein move kar rahi hai aur planet ka mass satellite ke mass se bahut zyada hai.

Important: Formula \(v = \sqrt{GM/r}\) circular orbit ke liye hai. Yahan r planet ke centre se satellite ki orbital distance hai, sirf satellite ki height nahi.

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2. Orbital Velocity Ka Formula and Derivation

Orbital velocity ka formula derive karne ke liye gravitational force aur centripetal force ko equal karte hain.

Step 1: Gravitational Force

Newton's law of gravitation ke according:

F = GMm/r²

Where:

• G: Universal gravitational constant.
• M: Planet ka mass.
• m: Satellite ka mass.
• r: Planet ke centre se satellite ki distance.

Step 2: Centripetal Force

Circular motion mein required centripetal force hoti hai:

F = mv²/r

Yahan v satellite ki orbital velocity hai.

Step 3: Dono Forces Equal Karo

GMm/r² = mv²/r

Satellite ka mass m dono sides se cancel ho jayega.

GM/r² = v²/r

Equation ko simplify karne par:

v² = GM/r

Square root lene par final formula milta hai:

v = √(GM/r)

Orbital Velocity Formula Mein Variables

Symbol	Meaning	SI Unit
v	Orbital velocity	m/s
G	Universal gravitational constant	N m²/kg²
M	Planet ka mass	kg
r	Planet ke centre se orbital distance	m

JEE Trick: Orbital velocity ke formula mein satellite ka mass m nahi aata. Isliye same circular orbit mein satellite ki orbital velocity uske mass par depend nahi karti.

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3. Earth Ke Near Orbital Velocity

Jab satellite Earth ki surface ke bahut paas circular orbit mein move karti hai, toh satellite ki orbital radius approximately Earth ke radius ke equal hoti hai.

r ≈ R

General formula:

v = √(GM/r)

Earth ke near, r ≈ R rakhne par:

v = √(GM/R)

Alternative Formula Using g

Earth ki surface par gravitational acceleration ka relation hai:

g = GM/R²

Isliye:

GM = gR²

Is value ko orbital velocity ke formula mein substitute karne par:

v = √(gR²/R)

v = √(gR)

Earth Ke Liye Calculation

• g ≈ 9.8 m/s²
• R ≈ 6.4 × 10⁶ m

v = √(9.8 × 6.4 × 10⁶)

v ≈ 7.9 × 10³ m/s

Orbital velocity ≈ 7.9 km/s

Iska matlab Earth ki surface ke paas ideal circular orbit mein satellite ki speed approximately 7.9 km/s hoti hai.

Exam Tip: Surface ke near orbital velocity ka approximate value 7.9 km/s yaad rakho. Numerical questions mein units ko carefully convert karna.

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4. Height Badalne Par Orbital Velocity Par Kya Effect Hota Hai?

Orbital velocity ka formula hai:

v = √(GM/r)

Same planet ke liye G aur M constant rehte hain. Isliye orbital velocity orbital radius ke square root ke inversely proportional hoti hai.

v ∝ 1/√r

• Orbital radius badhega, toh orbital velocity decrease hogi.
• Orbital radius decrease hoga, toh orbital velocity increase hogi.

Case 1: Orbital Radius Double Ho Jaye

Initial orbital velocity:

v₁ = √(GM/r₁)

New radius:

r₂ = 2r₁

Velocity ratio:

v₂/v₁ = √(r₁/r₂)

v₂/v₁ = √(1/2) = 1/√2

v₂ = v₁/√2

Radius double hone par orbital velocity initial value ki 1/√2 times ho jayegi.

Case 2: Orbital Radius Four Times Ho Jaye

r₂ = 4r₁

v₂/v₁ = √(r₁/4r₁)

v₂ = v₁/2

Radius four times karne par orbital velocity half ho jati hai.

Shortcut: Radius n times ho, toh new orbital velocity old velocity ki 1/√n times hoti hai.

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5. Orbital Velocity vs Escape Velocity

Orbital velocity aur escape velocity Gravitation chapter ke important formulas hain. Dono ka purpose different hai.

Orbital Velocity

vₒ = √(GM/r)

Yeh circular orbit mein satellite ko maintain karne ke liye required speed hai.

Escape Velocity

vₑ = √(2GM/r)

Escape velocity woh minimum initial speed hai jo ideal conditions mein object ko planet ke gravitational field se escape karne ke liye chahiye, jab final speed infinitely far away zero approach karti hai.

Relation Between Orbital and Escape Velocity

Escape velocity ka formula:

vₑ = √(2GM/r)

Orbital velocity ka formula:

vₒ = √(GM/r)

Dono equations compare karne par:

vₑ = √2 × vₒ

Ya:

vₒ = vₑ/√2

Yeh relation same distance r se calculate ki gayi orbital velocity aur escape velocity ke liye valid hai.

Earth Ke Near Comparison

Quantity	Approximate Value
Orbital velocity	7.9 km/s
Escape velocity	11.2 km/s

JEE Trick: Same radius par escape velocity, orbital velocity se √2 times hoti hai. Dono formulas mein radius same hona chahiye.

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6. Satellite Ka Time Period

Time period woh time hai jo satellite ko apni orbit ka ek complete revolution karne mein lagta hai.

Circular orbit ka circumference:

2πr

Distance = Speed × Time use karne par:

T = 2πr/v

Orbital velocity ka formula substitute karo:

T = 2πr / √(GM/r)

Simplify karne par:

T = 2π√(r³/GM)

Important Relation

T² = 4π²r³/GM

Same planet ke around circular orbits ke liye G aur M constant hain, isliye:

T² ∝ r³

Iska matlab orbital radius badhne par satellite ka time period badhta hai. Is relation ko Kepler's third law ke saath connect kiya ja sakta hai.

JEE Shortcut: Agar radius k times ho jaye, toh time period k^3/2 times ho jayega.

Example: Orbital radius 4 times ho, toh time period 4^3/2 = 8 times ho jayega.

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7. Solved JEE Main Question: Orbital Velocity

Question: Ek satellite Earth ke around circular orbit mein 7.9 km/s ki speed se move kar rahi hai. Agar uski orbital radius 4 times kar di jaye, toh new orbital velocity kya hogi?

Given

• Initial orbital velocity, v₁ = 7.9 km/s
• New orbital radius, r₂ = 4r₁

Step 1: Formula Apply Karo

v₂/v₁ = √(r₁/r₂)

Step 2: Values Substitute Karo

v₂/v₁ = √(r₁/4r₁)

v₂/v₁ = 1/2

Step 3: New Velocity Calculate Karo

v₂ = 7.9 × 1/2

v₂ = 3.95 km/s

Final Answer

New orbital velocity = 3.95 km/s

Quick Method: Radius four times hui hai, isliye orbital velocity half ho jayegi. Directly 7.9/2 = 3.95 km/s.

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8. Common Mistakes and Important Exam Tricks

1. Orbital radius: r = R + h. Planet ke centre se distance use karo, sirf height h nahi.
2. Formula: Circular orbit ke liye v = √(GM/r) use karo.
3. Mass cancellation: Satellite ka mass orbital velocity ke formula se cancel ho jata hai.
4. Radius aur speed: Orbital radius increase hone par orbital velocity decrease hoti hai.
5. Four-times rule: Radius four times hone par orbital velocity half hoti hai.
6. Escape velocity: Same radius par vₑ = √2 vₒ.
7. Time period: T = 2π√(r³/GM).
8. Kepler's third law: Same central planet ke liye T² ∝ r³.
9. Units: Calculations mein radius ko metres mein convert karo aur velocity ka final unit check karo.

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9. Orbital Velocity Formula Sheet

Concept	Formula
Orbital velocity	v = √(GM/r)
Orbital radius	r = R + h
Orbital velocity near Earth's surface	v = √(gR)
Escape velocity	vₑ = √(2GM/r)
Escape and orbital velocity relation	vₑ = √2 vₒ
Time period	T = 2πr/v
Time period using planet mass	T = 2π√(r³/GM)
Kepler's third law	T² ∝ r³
Orbital velocity and radius	v ∝ 1/√r

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10. One-Minute Revision

• Orbital velocity satellite ko circular orbit mein rakhne wali tangential speed hai.
• Gravitational force satellite ke liye centripetal force provide karti hai.
• Orbital velocity: v = √(GM/r).
• Orbital radius: r = R + h.
• Earth ke near orbital velocity approximately 7.9 km/s hai.
• Radius increase hone par orbital velocity decrease hoti hai.
• Radius four times hone par velocity half ho jati hai.
• Escape velocity: vₑ = √(2GM/r).
• Same radius par vₑ = √2 vₒ.
• Time period: T = 2π√(r³/GM).
• Kepler's third law: T² ∝ r³.

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11. Practice Questions for JEE Main

Question 1

Earth ke near circular orbit mein satellite ki orbital velocity approximately kitni hoti hai?

Answer: Approximately 7.9 km/s.

Question 2

Agar orbital radius 9 times ho jaye, toh new orbital velocity initial velocity ki kitni times hogi?

Solution: v₂/v₁ = √(r₁/r₂) = √(1/9) = 1/3.

Answer: Initial velocity ki one-third.

Question 3

Same orbital radius par escape velocity aur orbital velocity ka ratio kya hai?

Answer: vₑ/vₒ = √2.

Question 4

Agar satellite ki orbital radius 4 times ho jaye, toh time period kitna ho jayega?

Solution: T₂/T₁ = (r₂/r₁)^3/2 = 4^3/2 = 8.

Answer: Initial time period ka 8 times.

Question 5

Satellite ki height h aur planet ka radius R diya ho, toh orbital velocity ke formula mein r ki value kya hogi?

Answer: r = R + h.

Question 6

Kya same circular orbit mein different masses ke satellites ki orbital velocity different hoti hai?

Answer: Ideal conditions mein nahi. v = √(GM/r) formula mein satellite ka mass appear nahi karta.

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12. Download Orbital Velocity Notes PDF

Agar aap apne Orbital Velocity notes ko PDF ke form mein blog par show karna chahte ho, toh neeche diye gaye iframe mein apne PDF ka direct viewing URL add kar do.

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13. Frequently Asked Questions (FAQs)

Q1. What is orbital velocity?

Orbital velocity woh tangential speed hai jo satellite ko planet ke around circular orbit mein move karne ke liye required hoti hai.

Q2. What is the formula for orbital velocity?

Circular orbit ke liye formula v = √(GM/r) hai, jahan M planet ka mass aur r orbital radius hai.

Q3. What is the orbital velocity near Earth's surface?

Earth ke near ideal circular orbit ke liye orbital velocity approximately 7.9 km/s hai.

Q4. Why does orbital velocity decrease with height?

Height badhne par orbital radius increase hoti hai. Since v ∝ 1/√r, orbital velocity decrease ho jati hai.

Q5. What is the relation between orbital velocity and escape velocity?

Same distance from the planet ke liye escape velocity, orbital velocity ki √2 times hoti hai: vₑ = √2 vₒ.

Q6. What is the formula for the time period of a satellite?

Circular orbit mein satellite ka time period T = 2π√(r³/GM) hota hai.

Q7. Is orbital velocity included in JEE Main Gravitation?

Aapke provided notes ke according, JEE Main 2026 Gravitation syllabus mein orbital velocity, satellite motion aur time period included hain. Apne target examination ke liye latest official syllabus bhi check karein.

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Final Thoughts

Orbital Velocity chapter ko prepare karne ka sabse effective tareeka hai ki formula ko ratne ke bajay gravitational force aur centripetal force ko equal karke uska derivation samjho. Isse aap formula ki logic aur numerical questions dono ko easily handle kar paoge.

JEE Main preparation ke liye v = √(GM/r), v = √(gR), vₑ = √2vₒ aur T = 2π√(r³/GM) ko revise karo. Saath hi radius badalne wale questions ki practice karo, kyunki inmein square-root aur power relationships ka direct application hota hai.