The earth orbits the sun in elliptical orbit, so that in January Earth is 3% closer to Sun than in July?

Question

We have a rocket parked in low height orbit around the Earth, which lies in the ecliptic plane, and want to launch the rocket outside the solar system without further help from other planets.

What is the best time of the year to initiate the launch fuel-wise?

Total mechanical energy is the same everywhere, but impact of additional velocity Δv provided by motor trust has greater effect on kinetic energy at higher speeds near perihelion.

Answer 1

January. At that point, perihelion, Earth is traveling with its maximum orbital velocity. Just be sure to ignite the engine while the rocket's traveling in the SAME DIRECTION as Earth!

Answer 2

Wow, I'd say start the burn about 9:30 pm on July 4th, over the Hawaii, that way you'd save on fireworks.

As for the rocket -- doesn't matter what time of years, so long as your launching in the direction of Earth's orbit around the sun. That's because the gravity field of the sun is conservative. Earth's orbit maintains a balance between Kinetic and Potential Energy such that the energy need to escape the sun's gravitational field is always the same. Ref: http://en.wikipedia.org/wiki/Conservation_of_energy#Mechanics

Answer 3

I'm torn between several answers; I'll put them all out here.

Yes, in a perihelic launch, the revolutionary speed of the Earth around the sun (and therefore any n-body orbiting Earth) is at its highest. One could use this extra speed to launch further (essentially using the Earth as a gravity boost). However, does the rocket carry enough fuel to make up for the loss of 3 million miles difference between apehelion and perihelion, as well as the higher delta-v needed to leave Earth orbit?

The gravity differential between ape- and perihelion isn't all that great on an object the mass of a rocket, so that's not a valid reason for a perihelic launch. However, there are several benefits. First, a gain of 3 million miles due to the elliptical nature of the orbit. Also, because the orbital speed of the Earth around the sun (again, including any n bodies around Earth), a slower delta-v is needed to leave Earth orbit on an extra-solar trajectory, meaning less fuel consumed.

All things considered (and without my "Principles of Astrodynamics" in front of me to double-check my answer), I would launch at the time of equihelion, when the Earth is at the midpoint of the minor axis of orbit. This would be the same as assuming the Earth had a circular orbit around the Sun, and the delta-v required to launch would be averaged out between ape- and perihelion.

Answer 4

there isn't any actual merchandise on the 2d focal factor of orbital ellipses of the planets (and asteroids, comets, and so on.). it extremely is in simple terms the character of ways issues formed that they weren't in proper circles; the sunlight's gravity nonetheless regulates all the strikes of the planets even at its off-middle area.

Answer 5

I'd guess you'd want to minimize the Sun's gravity on the rocket, so you'd want to launch at apehelion. This would reduce fuel consumption slightly.