The mysterious Planet X has a radius of 5.40 times 10^6 m and an acceleration du

Question

The mysterious Planet X has a radius of 5.40 times 10^6 m and an acceleration due to gravity of 11.0 m/s^2 at its surface. Calculate its mass and average density. Ten days after it was launched toward Mars in December 1998, the Mars Climate orbiter spacecraft (mass 629 kg) was 2.87 times 10^6 km from the earth and traveling at 1.20 times 10^4 km/h relative to the earth. At this time, what were the following. (a) the spacecraft's kinetic energy relative to the earth (b) the potential energy of the earth-spacecraft system

Explanation / Answer

5) Acceleration due to gravity is given by,

g = GM/r2

Mass of the planet, M = gr2/G = 11*(5.4*106)2/(6.67*10-11) = 48.1*1023 kg

Density = M/V = 48.1*1023/{(4/3)*3.14*(5.4*106)3}= 7296.2 kg/m3

6)a) spacecraft's kinetic energy relative to earth, KE = (1/2)mv2 = 0.5*629*(1.2*104/3.6)2 = 3.5*109 J

b) Potential energy of earth-mass system

taking mass of earth, M = 6*1024 kg

U = -GMm/r = - 6.67*10-11*6*1024*629/(2.87*106) = - 8.8*1010 J

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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