681: Gravity Wells

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Gravity Wells
This doesn't take into account the energy imparted by orbital motion (or gravity assists or the Oberth effect), all of which can make it easier to reach outer planets.
Title text: This doesn't take into account the energy imparted by orbital motion (or gravity assists or the Oberth effect), all of which can make it easier to reach outer planets.

The xkcd page links to a much larger version.

Explanation

The comic shows the solar system gravity field of each planet and some of their satellites.

Transcript

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Discussion

Why is Earth's well's depth listed as 5478km but as 6379km in the inset? Compare with Mars which has 1286 in both places. 87.174.225.131 07:21, 12 April 2013 (UTC)

Best guess is either a goof, or that the lower number is just for Earth itself, while the greater number is for the Earth/Moon system as a whole. Proportionally speaking, we have the largest moon in the solar system, so maybe it wouldn't nicely fit in the Earth well as easily as Mars's and Jupiter's moons do.--Druid816 (talk) 08:28, 12 April 2013 (UTC)
It may be the height needed to go from one gravity well to another. You don't have to get all the way up to escape speed for that.
Randall wasn't kidding about the Sun being "very very far down"; its well is 100 times deeper than Jupiter's!
Wwoods (talk) 19:47, 12 April 2013 (UTC)
OTOH, from the table above i'm thinking that the 5.4 might be the Venus figure, and it was wrongly placed besides Earth...
Secondly, what i found interesting was that the Earth's 6.4 looks so much like its radius! I wonder if it's merely a coincidence, or there's a connection between the two... -- 141.101.99.233 21:25, 30 October 2013 (UTC)
The table is great, it must be included in the article; layout and time is just my problem right now. PRO TIP: Do not care about the x-axis.--Dgbrt (talk) 22:18, 30 October 2013 (UTC)
The fact that the density of the Earth is 5478 kilograms per cubic kilometer makes me pretty sure it is a typo. Fewmet (talk) 03:04, 4 July 2014 (UTC)
Hehe, you might be right. That's the best explanation. It would be a strange coincidence otherwise. But your units are wrong: a cubic kilometer of water, ice-cream or Natalie Portmans would be already something like a billion kilograms. Or a trillion, if you are American. Oh, you might be American. In this case: happy 4th of July! -188.114.102.35 12:39, 4 July 2014 (UTC)
Thanks for catching that (and for the July 4 wishes). It should be kilograms per cubic meter. Looking into that, though, leaves me less sure that is the origin of the problem. I thought I had multiple sources for Earth having a density of 5478 kg/m3, but can find only one (and not a very compelling one at that). I have sounder sources for 5513 kg/m3. 5514 kg/m3, 5515 kg/m3, 5520 kg/m3 and 5540 kg/m3. It may be trivial in that all round to 5500 kg/m3.
It was corrected on the poster version. Earth's well in the main graphic is marked as 6379km, just like the inset.108.162.216.86 00:19, 21 August 2014 (UTC)
I solved for the wells on Earth, Moon and Mars using the equation Randall gave and masses and equatorial radii from NASA, getting 6371 km, 287 km and 1286 km, respectively. Fewmet (talk) 23:07, 5 July 2014 (UTC)

The Oberth Effect mentioned in the title text is well-explained here (assuming you are not intimidated by the algebra in squaring a binomial). The gist of it is that using a bit of fuel in a rocket thrust will increase the rocket’s kinetic energy . The higher the kinetic energy at the time of the thrust, the greater the increase in kinetic energy. It works because the energy of the fuel goes into increasing the kinetic energy of the ship and the kinetic energy of the spent fuel. The faster you go, the greater the portion of the energy the ship gets.

The “gravity assist” is also known as the slingshot effect. The Wikipedia explanation is good, especially with its diagram. In it a spaceship (or other body) accelerates toward a planet (or moon, star, etc.) in the same direction that body was going. The ship picks up a little of the body’s momentum and so goes faster, although only according to an external reference frame. An observer at rest with respect to that other body would actually see the ship approach and depart with the same speed.

The title text reference to orbital speed is unclear to me. I suppose it just means that the given gravity wells assume you are at rest on the surface of the planet. Then being in orbit (and necessarily having an orbital speed) would mean you are part way out of the well already. Fewmet (talk) 02:57, 4 July 2014 (UTC)


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