Question
Medium
Solving time: 3 mins
Passage II A spaceship is in a circular orbit of radius around a star of mass . The spaceship's rocket engine can alter its velocity (instantaneously) by an . Amounts direction of firing is measured by angle between the ship's velocity and the vector from the tail to the nose of the ship. To conserve fuel in a sequence of fringes, it is desirable to minimise is known as the specific impulse. We want to use the ship's engine to cause it to crash into the star (assume the radius of the star to be negligible). In order to visit a planet in a circular orbit of radius , what is the minimum specific impulse required to reach the planet's orbit if the engine is again fired in a single rapid burst ?
Text solutionVerified
After the first burst, the ship escape from the circular orbit around the star and moves along a parabolic orbit. When the ship reaches the circular orbit of the planet, the engine is again fired in a single rapid burst. For the ship to move along the circular orbit of radius , its speed must be Let be the speed of the ship as it arrives at and before the burst. Conservation of angular momentum requires
or
Conservation of energy gives,
or
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Question Text | Passage II
A spaceship is in a circular orbit of radius around a star of mass . The spaceship's rocket engine can alter its velocity (instantaneously) by an . Amounts direction of firing is measured by angle between the ship's velocity and the vector from the tail to the nose of the ship. To conserve fuel in a sequence of fringes, it is desirable to minimise is known as the specific impulse. We want to use the ship's engine to cause it to crash into the star (assume the radius of the star to be negligible).
In order to visit a planet in a circular orbit of radius , what is the minimum specific impulse required to reach the planet's orbit if the engine is again fired in a single rapid burst ? |
Topic | Gravitation |
Subject | Physics |
Class | Class 11 |
Answer Type | Text solution:1 |
Upvotes | 57 |