The "gravitational slingshot" is a process by which a small object with mass m such as a space probe can make a close approach to a planet with mass M, swing by due to the planet's gravity, and leave the interaction moving faster than it was before. Derive an expression for the object's final velocity v (x and y components) in terms of its initial speed vO, the angle of approach 0, the planet's orbital speed u, the masses, and any physical constants necessary. Please assume Mm to simplify your answer. other У ө

Question

Obtain the required relation please

The "gravitational slingshot" is a process by
which a small object with mass m such as a
space probe can make a close approach to a
planet with mass M, swing by due to the
planet's gravity, and leave the interaction
moving faster than it was before. Derive an
expression for the object's final velocity v (x
and y components) in terms of its initial speed
vO, the angle of approach 0, the planet's
orbital speed u, the masses, and any
physical constants necessary. Please assume
Mm to simplify your answer.
other
У
ө
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Transcribed Image Text

The "gravitational slingshot" is a process by which a small object with mass m such as a space probe can make a close approach to a planet with mass M, swing by due to the planet's gravity, and leave the interaction moving faster than it was before. Derive an expression for the object's final velocity v (x and y components) in terms of its initial speed vO, the angle of approach 0, the planet's orbital speed u, the masses, and any physical constants necessary. Please assume Mm to simplify your answer. other У ө

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