NASA plans to send a human mission to Mars. Using Kepler\'s laws of planetary mo

Question

NASA plans to send a human mission to Mars. Using Kepler's laws of planetary motion and Newton's law of universal gravitation, we can can examine the basic parameters of such a mission. a) The simplest way to get from Earth to another planet is via the Hohmann transfer, turn the spacecraft's roughly circular orbit around the sun into an elliptical one with aphelion at the target planet and perihelion at Earth. This transfer requires the least amount of fuel, but takes a great deal of time. Use the date below to determine the semi-major and semi-minor axes of the elliptical transfer orbit, the time it takes the spacecraft to reach mars, and the eccentricity of the orbit. Radius of Mars = 1.52 A.U. -Radius of earth= 1.00 A.U. - Period of Mars = 1.88 years. - Period of earth = 1.00 Years.

Explanation / Answer

The speed is

v1 = (2pi * r1/T1)

and v2 = (2pi * r2/T2)

where r1 = 1.52 A.U,T1 = 1.88 years,r2 = 1.00 A.U and T2 = 1.00 years

let S be the semi-major axes

we know that

v1^2 - v2^2 = 2gS

or S = (v1^2 - v2^2/2g)

where g = 9.8 m/s^2

let S1 be the semi-minor axes

we know that

v1^2 - v2^2 = 2gS1

where v2 = 0

or S1 = (v1^2/2g)

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

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