Section 13.5 Gravitational Potential EnergyA space station

Chapter 13, Problem 15E

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QUESTION:

Problem 15E

Section 13.5 Gravitational Potential Energy

A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?

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QUESTION:

Problem 15E

Section 13.5 Gravitational Potential Energy

A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?

ANSWER:

We have to find the minimum speed does the probe need to escape the solar system

The minimum speed of the probe can be found using the law of conservation of energy.

\(K_{2}+U_{2}=K_{1}+U_{1}\)

2 represents the energy of the probe at a faraway distance. 1 represents the energy of the probe at a distance equal to the orbital radius of Earth around the Sun.

\(\frac{1}{2} m_{p} v_{2}^{2}-\frac{G M_{s} m_{p}}{r_{2}}=\frac{1}{2} m_{p} v_{1}^{2}-\frac{G M_{s} m_{p}}{R_{s-p}}\)

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