(a)
The escape speed of a spacecraft from Europa (Jupiter’s moon), which revolves around an orbit of radius
(a)

Answer to Problem 13Q
Solution:
Explanation of Solution
Given data:
A spacecraft landed on Jupiter’s moon, which revolves around Jupiter in an orbit of radius
Formula used:
The relation for the escape velocity is as:
Here,
Explanation:
Mass of Europa is
Recall the above formula.
Substitute
Conclusion:
Therefore, the escape velocity to leave Europa is
(b)
The escape speed from Jupiter at the distance of Europa’s orbit, if a spacecraft landed on Jupiter. Given that the orbit of Europa has a radius of
(b)

Answer to Problem 13Q
Solution:
Explanation of Solution
Given data:
A spacecraft landed on Jupiter’s moon, which moves around Jupiter in an orbit of radius
Formula used:
The relation for the escape velocity is as:
Here,
Explanation:
The mass of Jupiter is
Recall the above formula.
Substitute
Conclusion:
Therefore, the escape speed from Jupiter at the distance of Europa’s orbit is
(c)
The explanation that the space craft must leave Europa with a speed greater than the speed, which is calculated in part (a) or part (b), in order to begin its homeward journey if the spacecraft landed on Jupiter’s moon, which revolves around Jupiter in an orbit of radius
(c)

Answer to Problem 13Q
Solution:
The large escape velocity is required, to cross Jupiter, as compared to Europa’s escape velocity.
Explanation of Solution
Introduction:
Escape velocity: The lowest velocity which is required by the body to escape the gravitational attraction of a particular planet is known as its escape velocity.
Explanation:
The escape velocity for Europa is
From the above calculations, it can be observed that the escape velocity for Europa is less than the escape velocity for Jupiter. If a spacecraft achieves a velocity which is equal to the escape velocity of Europa, then the spacecraft cannot cross the Jovian system. There is requirement of larger velocity than the escape velocity of Europa, to escape the Jovian system for the spacecraft.
Conclusion:
Therefore, for the spacecraft to escape from the Jovian system, an escape velocity larger than that of Europa is required.
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