Final answer:
The tangential impulse required for a rocket to escape a planet's gravity is the product of the rocket's mass and the change in velocity from its initial orbital speed to the escape velocity, calculated as the square root of (2 times the gravitational constant times the planet's mass divided by the separation).
Step-by-step explanation:
The student asked what tangential impulse must be given to a rocket in circular orbit so that it just escapes to infinity. In physics, to find the escape velocity, we use the conservation of energy principle where the total energy of the system is zero at the point of escape. For a rocket of mass m orbiting at a separation R from the center of a planet of mass M, the escape velocity vesc from this orbit can be calculated using the formula derived from gravitational potential energy and kinetic energy: vesc = √(2GM/R). The impulse needed would be the change in momentum, which is m(vesc - vi) where vi is the initial orbital velocity of the rocket. The mass m cancels out, indicating the escape velocity is independent of the mass of the escaping object. A practical understanding of this would involve applying thrust to change the rocket's initial orbital velocity to the escape velocity. This thrust is facilitated by expelling mass, such as fuel, in the opposite direction of desired travel.