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Question #43517
The Question
A geostationary satellite is in a circular orbit of radius around a planet. The planet and the satellite both have an angular velocity . A maintenance rocket initially docked with the satellite detaches and instantaneously acquires a radial velocity relative to the satellite, directed away from the planet's center. Immediately after detachment, what is the radius of curvature of the rocket's trajectory as observed in a reference frame rotating with angular velocity (the frame in which the satellite is at rest)?
Options
- A.
- B.
- C.
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Variable_Constraint
Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.
Concepts Behind This Question
Geostationary Satellite Constraints|Frame of Reference|Pseudo Force Directionality
Why This Question Is Tricky
Common Mistakes
This question tests the student's ability to correctly apply pseudo-forces in a rotating non-inertial reference frame.
A common trap is ignoring the Coriolis force or missing its factor of 2 (Option B), leading to incorrect trajectory analysis.
Students often mistakenly assume that because the satellite is 'stationary' in this frame, only standard kinematics or centrifugal forces apply (Option C).
Furthermore, attempting to solve this in the inertial frame without properly extracting the perpendicular component of acceleration leads to Option D.
The core concept is recognizing that any relative velocity in a rotating frame induces a perpendicular Coriolis acceleration that dictates the initial curvature of the path.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Gravitation - Class 11 Part 1 |
| Concept | Geostationary Satellite Constraints |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |