Before You Begin

Question #43178

Difficulty: 8/10 | 🟢 Free

The Question

A perfectly absorbing spherical dust particle of mass $m$ and radius $R$ is in an unperturbed elliptical orbit around a star of mass $M$ . The orbit has a semi-major axis $a$ and eccentricity $e$ . A uniform, parallel photon beam of constant intensity $I$ from a distant quasar illuminates the system. The beam propagates in the plane of the orbit and is perpendicular to the major axis of the ellipse. Assuming the radiation force on the particle is a very small perturbation compared to the gravitational force from the star, and that the star does not shadow the particle, find the magnitude of the change in the particle's orbital angular momentum $|\Delta L|$ over one complete revolution.

(Given: $c$ is the speed of light in vacuum, $G$ is the universal gravitational constant)

Options

A.
$\frac{\pi^2 I R^2 e a^2}{c} \sqrt{\frac{a}{G M}}$
B.
$\frac{2 \pi^2 I R^2 e a^2}{c} \sqrt{\frac{a}{G M}}$
C.
$\frac{3 \pi^2 I R^2 e a^2}{c} \sqrt{\frac{a}{G M}}$
D.
$\frac{4 \pi^2 I R^2 e a^2}{c} \sqrt{\frac{a}{G M}}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Radiation Pressure|Kepler’s Second Law (Areal Velocity)|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous application of Keplerian orbital mechanics coupled with non-conservative torques.

A common trap (leading to Option A) is calculating the torque about the geometric center of the ellipse ( $x_c = a\cos E$ ) rather than the focus where the star resides, which yields an incorrect coefficient of 1.

Another trap (leading to Option B) is assuming a uniform rate of change for the eccentric anomaly ( $dt \propto dE$ ), ignoring the $(1 - e\cos E)$ factor dictated by Kepler's Second Law, which yields a coefficient of 2.

Students must correctly identify the reference frame (focus) and properly integrate over time using the eccentric anomaly to capture the asymmetric time spent near the apocenter versus the pericenter.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Waves - Class 12
Concept	Radiation Pressure
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free