Answer :
To escape from Pluto, the spacecraft must reach a speed of at least 11.2 km/s, which is the escape velocity from Pluto.
The escape velocity is calculated using the following formula:
v_escape = √(2GM/r)
where G is the gravitational constant, M is the mass of Pluto, and r is the distance from the center of Pluto to the spacecraft.
In order to escape from Pluto, the spacecraft will need to perform a burn at its periapsis, which is the point in its orbit where it is closest to Pluto. This burn should be performed in the direction that will increase the spacecraft's speed and energy, which is the direction that is opposite to the velocity vector at periapsis.
To calculate the amount of delta-v (change in velocity) required to escape from Pluto, we can use the rocket equation:
delta-v = Ispgln(m_0/m_f)
where Isp is the specific impulse of the spacecraft's engine, g is the gravitational acceleration at the surface of Pluto, m_0 is the initial mass of the spacecraft (including propellant), and m_f is the final mass of the spacecraft (excluding propellant).
Plugging in the values from the problem statement, we get:
delta-v = 230s * 9.81 m/s^2 * ln(1300 kg / 1200 kg)
This gives us a delta-v of approximately 3.6 km/s.
Since the escape velocity from Pluto is 11.2 km/s and the required delta-v is 3.6 km/s, the spacecraft should be able to escape from Pluto with the given amount of propellant.
It's worth noting that this calculation assumes that the spacecraft is able to achieve a 100% efficient burn, which may not be possible in practice. There may also be other factors that could affect the spacecraft's ability to escape from Pluto, such as atmospheric drag or interference from other celestial bodies.
Learn more about Escape velocity at:
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