Zero, a hypothetical planet, has a mass of 5.1 times 10^23 kg, a radius of 3.2 t

Question

Zero, a hypothetical planet, has a mass of 5.1 times 10^23 kg, a radius of 3.2 times 10^6 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 times 10^7 J, what will be its kinetic energy when it is 4.0 times 10^6 m from the center of zero? (b) If the probe is to achieve a maximum distance of 8.0 times 10^6 m from the center of zero, with what initial kinetic energy must it be launched from the surface Zero?

Explanation / Answer

(a)

initial energy is,

Ei = Ki + Ui

Ei = Ki - GMm / ri

Ei = 5.0 * 10^7 - [6.67*10^(-11) * 5.1*10^23 * 10 / 3.2*10^6]

Ei = -5.63*10^7 J

Final energy is,

Ef = Kf - GMm / rf^2

Ef = Kf - [6.67*10^(-11) * 5.1*10^23 * 10 / 4*10^6]

Ef = Kf - 8.50*10^7 J

from energy conservation,

Ei = Ef

-5.63*10^7 = Kf - 8.50*10^7 J

Kf = 2.87*10^7 J

(b)

Ei = Ki + Ui = Ki -  [6.67*10^(-11) * 5.1*10^23 * 10 / 3.2*10^6]

Ei = Ki - 10.63*10^7 J

Ef = 0 -  [6.67*10^(-11) * 5.1*10^23 * 10 / 8*10^6]

Ef = -4.25*10^7 J

From energy conservation,

Ki - 10.63*10^7 =  -4.25*10^7

Ki = 6.38*10^7 J

Related Questions

Navigate

• Browse (All)
• Browse Z
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.