# Launching east from a mountain on the equator at midnight during a new moon; ranking of each contribution?

This answer is intriguing and I'm curious if it's correct, and especially which effects are most important.

If you want to avoid gravity assists, the most fuel-efficient way out of the Solar System is to launch due East from from a launch site in the Ecuadorean Andes, sometime before local midnight on a July 4 when there's a new moon. This gives you the maximum possible benefit from the Earth's movement, leaving only about 12,000 m/s of delta-V needed in excess of Earth escape velocity.

Breaking that down:

1. launch due East
2. site in the Ecuadorean Andes
3. sometime before local midnight
4. on a July 4
5. when there's a new moon

How do these rank in terms of contribution towards lowering delta-V to escape velocity from the Solar system? Do numbers 4 and 5 have more to do with Earth's instantaneous velocity, or due to a reduction of the gravitational well?

• July 4 midnite on new moon: maximum fireworks visibility – Organic Marble Feb 28 '19 at 2:51
• July 4 is aphelion; earth velocity relative to the solar system is at a minimum. If the answer is correct (which I don’t doubt) the reduction in solar escape velocity due to distance is greater then the reduction in orbital velocity. That math doesn’t seem too hard. – prl Feb 28 '19 at 5:56
• Since the earth and moon orbit their common center of mass, at the new moon, the moon is traveling at its lowest solar-relative velocity of the month, so the earth is traveling at the fastest. – prl Feb 28 '19 at 6:00

Breaking that down:

1. launch due East
2. site in the Ecuadorean Andes
3. sometime before local midnight
4. on a July 4
5. when there's a new moon
1. Launch due east.
With the exception of launch sites that cannot launch due east lest a failed launch rain debris on some other country, this is the preferable direction. Launching to the east takes advantage of the eastward velocity provided by the Earth's rotation. At the equator, this added velocity amounts to about 465 meters per second of Δv. The benefit of launching due east vs launching due west at the equator is about 930 meters per second.

2. Site in the Ecuadorean Andes.
There are two factors here, an equatorial launch site and a high altitude launch site. A low latitude has a big payoff when launching to the east; the effect varies with the cosine of the latitude. Altitude doesn't buy as much. Think of it this way: the European Space Agency launches from the Guiana Space Centre, 5.2° north latitude at sea level. The US launches to the east from the Kennedy Space Center, 28.5° north latitude at sea level. SpaceX is developing a launch site at Boca Chica, Texas, 26 north latitude at sea level. Logistical concerns and not having a failed launch rain debris on people (particularly people in a different country) outweigh elevation gain by a wide margin. The benefit of launching from 6263.47 meters (the height of Chimborazo) versus from sea level is about 248 meters per second.

3. Sometime before local midnight.
What's more important is the direction in which the vehicle leaves the Earth's gravitational well. Assuming the vehicle doesn't dwell in low Earth orbit, launching sometime before local midnight has a huge advantage over launching sometime before local noon, about 60 kilometers per second.

4. On a July 4.
This is exactly backwards. July 4 is when the Earth is at aphelion. This is when the Earth is furthest from the Sun but it's also when the Earth's orbital velocity with respect to the Sun is smallest. The third of January would be a better choice. This benefit of a larger orbital orbital velocity with respect to the Sun outweighs the disadvantage of a larger escape velocity thanks to the Oberth effect. This is a small effect, about 290 meters per second for January 3 vs July 4.

5. When there's a new moon.
This takes advantage of the Earth's orbit about the Earth-Moon center of mass. This is a small effect, about 25 meters per second for launching when there's a new moon versus launching when there's a full moon.

The obvious winner is "sometime before local midnight" with its 60 kilometer per second (60000 meters per second) advantage over launching sometime before local noon. The other effects are small compared to this; none are over a kilometer per second. Launching due east from the equator comes in second. Launching at perihelion (January 3, not July 4) comes in third, and launching at altitude comes in fourth. Launching when there's a new moon is such a small effect that it's hardly worth mentioning.

• Great! Thanks! It was very confusing that you changed units for #3. I was surprised it was the smallest until I got to the last paragraph. – prl Feb 28 '19 at 17:21
• This is really great, thanks! But I'm having a had time understanding #3; Why is direction important? (doesn't a trajectory somewhat towards the Sun still escape after a perihelion?) Is 60 km/s a typo? – uhoh Feb 28 '19 at 19:51
• @uhoh - Launching shortly before local noon would result in the delta v being directed against the Earth's orbital velocity. To escape in that direction would involve canceling the Earth's orbital velocity (30 km/s) and adding another 42 km/s to achieve escape velocity, for a total of 72 km/s. Escaping in the direction of the Earth's orbital velocity vector requires only an additional 12 km/s on top of the 30 km/s that the vehicle gets for free. So, no, 60 km/s was not a typo. – David Hammen Feb 28 '19 at 20:09
• okay I'm half-way there, I'll review in the morning, thanks. – uhoh Feb 28 '19 at 20:12
• @uhoh, if you launch at solar noon, you've got two bad choices: you can launch west, which keeps the "Earth orbit" and "new moon" benefits, but costs you the Earth's rotation, or you can launch east, which keeps the rotation benefit, but costs you the "Earth's orbit" and "new moon" benefits. – Mark Feb 28 '19 at 20:46