Scientists want to place a 2700.0 kg satellite in orbit around Mars. They plan t

Question

Scientists want to place a 2700.0 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2562.0 m/s in a perfectly circular orbit. Here is some information that may help solve this problem:

Given:

mmars = 6.4191 x 1023 kg
rmars = 3.397 x 106 m
G = 6.67428 x 10-11 N-m2/kg2

Question: 1. What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

Explanation / Answer

In a circular orbit the centripetal force mv^2/r is equal to the force of gravity GmM/r^2. The radius to use is 2.7 x 3.397 x 10^6 m. Therefore v=sqrt (GM/r) = sqrt (6.67428 x 10^-11 x 6.4191 x 10^23 / (2.7 x 3.397 x 10^6 ) = sqrt(4.6711 x 10^6) = 2161 m/s > How much time does it take the satellite to complete one revolution? Period = circumference/velocity = 2 pi x 2.7 x 3.397 x 10^6 / 2161 = 2.667 x 10^4 sec =7.4 hour > What should the radius of the orbit be (measured from the center of Mars), if we want the satellite to take 8 times longer to complete one full revolution of its orbit? Kepler's third law tells you that distance cubed is proportional to period squared => distance is proportional to period^(2/3) = 4 So the orbit radius should be four times as much.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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