Space Chase: You have been sent in a small space craft to rendezvous with a spac

Question

Space Chase: You have been sent in a small space craft to rendezvous with a space station in circular orbit of radius ro from the Earth's center. Due to a mishandling of units by a technician, you find yourself in the same orbit as the station but exactly halfway around the circle from it. You do not apply forward thrust in attempt to "chase" the station. Instead, you apply brief braking thrust against the direction of your motion, to put you into an elliptical orbit, the highest point of which is your present position, but the period of which is half that of your present orbit. Thus you will return to your present position when the space station has come halfway around its circle to meet you. Is the minimum radius from the Earth's center - the low point - of your new elliptical orbit greater than the radius of the Earth, or have you botched your last physics problem?

Explanation / Answer

Kepler's 3rd law says that T^2 is prop to a^3, where a is the semi-major axis of an elliptical orbit. For a circular orbit, this is just the radius. In your case then we are given that Te = (1/2) Tc (Te is for elliptical orbit, Tc is for circular) and Te^2 = (1/4) Tc^2 So... a^3 = (1/4) r^3 where a is for the elliptical orbit and r is the circular take cube root a = 0.62996 * r =

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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