According to keplar, the period of revolution of a planet ( T ) and its mean distance from the s

Name: Problem 800, Chapter 6: JEE Physics
Uploaded: 2022-04-10T14:17:37-08:00
Duration: 1 min 25 s
Channel: Yuva S
Description: According to keplar, the period of revolution of a planet ( T ) and its mean distance from the sun (r) are related by the equation (A) T^3 r^3= constant (B) T^2 r^-3= constant (C) Tr^3= constant (D) T^2 r= constant

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According to keplar, the period of revolution of a planet ( $\mathrm{T}$ ) and its mean distance from the sun (r) are related by the equation (A) $\mathrm{T}^{3} \mathrm{r}^{3}=$ constant (B) $\mathrm{T}^{2} \mathrm{r}^{-3}=$ constant (C) $\mathrm{Tr}^{3}=$ constant (D) $\mathrm{T}^{2} \mathrm{r}=$ constant

   According to keplar, the period of revolution of a planet ( $\mathrm{T}$ ) and its mean distance from the sun (r) are related by the equation
(A) $\mathrm{T}^{3} \mathrm{r}^{3}=$ constant
(B) $\mathrm{T}^{2} \mathrm{r}^{-3}=$ constant
(C) $\mathrm{Tr}^{3}=$ constant
(D) $\mathrm{T}^{2} \mathrm{r}=$ constant

JEE Physics

StemEZ 1st Edition

Chapter 6, Problem 800

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Solved by Expert Yuva S

04/10/2022

Step 1

Mathematically, this can be represented as: T² ∝ r³ To remove the proportionality, we introduce a constant k: T² = k * r³ Show more…

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According to keplar, the period of revolution of a planet ( $\mathrm{T}$ ) and its mean distance from the sun (r) are related by the equation (A) $\mathrm{T}^{3} \mathrm{r}^{3}=$ constant (B) $\mathrm{T}^{2} \mathrm{r}^{-3}=$ constant (C) $\mathrm{Tr}^{3}=$ constant (D) $\mathrm{T}^{2} \mathrm{r}=$ constant

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Key Concepts

Kepler’s Third Law

Kepler’s Third Law of planetary motion establishes that the square of a planet’s orbital period (T) is proportional to the cube of its orbit's semi-major axis (r). This law is fundamental in celestial mechanics as it links the time a planet takes to complete an orbit with its average distance from the sun, revealing an intrinsic relationship between time and spatial dimensions in orbits.

Mathematical Proportionality in Orbital Mechanics

This concept involves setting up a relationship where the square of the orbital period (T^2) divided by the cube of the orbit radius (r^3) remains constant for all planets orbiting the same body. This mathematical proportionality not only serves as a predictive tool for planetary motions but also underscores the harmony in the dynamical systems of celestial bodies.

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