Wednesday, July 14, 2010
I noticed in a few of the articles on Rosetta's flyby of the 21 Lutetia asteroid that some were not sure whether this asteroid was the type where one misstep could send you careening into space, or whether it had sufficient gravity to hold people to the surface. The answer is of course that with a diameter of 100 km it has more than enough gravity to hold people to the surface, and indeed it would be impossible to escape without a velocity of some 300 kph. But while calculating the surface gravity and escape velocity of a body isn't very complicated it still isn't one that can be done in one's head in the same way area, circumference and all the rest can, so I thought it would be helpful to come up with a quick chart of the surface gravity, escape velocity and surface area of asteroids at different diameters.
The calculation assumes a sphere, and while smaller asteroids are almost never perfectly spherical it's the only way to make a rough calculation. It also assumes an average density of 4 grams per cm3, and so keep in mind that this can vary a bit as well. I have also added equivalent regions or countries to the surface area in order to give a good idea of how much there is to explore.
You can see that it doesn't take much to have an asteroid where the escape velocity is greater than any slight misstep, and a diameter of 5 km is sufficient here, while by the time you get to a diameter of 15 km those on the surface are very secure. The asteroid 243 Ida has an escape velocity that varies depending on how far away you are from the centre, but even at the furthest tip it's still 52 kph and this can reach as high as 100 kph closer to the centre, so that asteroid is safe for human explorers as well.
Back to the chart: it goes up to 300 km and then straight to 4 Vesta (the most massive asteroid but not the largest; 2 Pallas is slightly larger), as once you reach 200 - 300 km it's easier to just look directly at the information for each asteroid as there aren't many left. Ceres, of course, is larger still though it is no longer considered to be just an asteroid.
|Diameter||Surface gravity (% Earth)||Escape velocity||Surface area||Equivalent city/country|
|0.0006%||0.27 kph||31415 m2|
|500 m||0.0028%||1.3 kph||0.78 km2||Slightly more than|
|1 km||0.0057%||2.7 kph||3.14 km2||Slightly more|
|2 km||0.01%||5.4 kph||12.56 km2||Tokelau|
|3 km||0.017%||8 kph||28 km2||Macau|
|5 km||0.029%||13.5 kph||78 km2||Guernsey|
|10 km||0.057%||27 kph||314 km2||Malta|
|15 km||0.086%||40 kph||706 km2||Singapore|
|20 km||0.11%||54 kph||1256 km2||Hong Kong|
|25 km||0.14%||67 kph||1963 km2||Mauritius|
|30 km||0.17%||80 kph||2827 km2||Luxembourg|
|35 km||0.2%||94 kph||3848 km2||Cape Verde|
|40 km||0.23%||108 kph||5026 km2||Trinidad and Tobago|
|45 km||0.26%||121 kph||6361 km2||Palestinian Territories|
|50 km||0.29%||134 kph||7854 km2|
|60 km||0.34%||161 kph||11309 km2||Qatar|
|70 km||0.4%||188 kph||15393 km2||East Timor|
|80 km||0.46%||215 kph||20106 km2||Slovenia|
|90 km||0.51%||242 kph||25446 km2||Macedonia|
|100 km||0.57%||269 kph||31415 km2||Belgium|
|125 km||0.71%||336 kph||49087 km2||Slovakia|
|150 km||0.86%||404 kph||70685 km2||Ireland|
|175 km||1%||471 kph||96211 km2||South Korea|
|200 km||1.14%||538 kph||125 663 km2||North Korea|
|250 km||1.42%||672 kph||196 400km2||Segenal|
|300 km||1.7%||807 kph||282 740 km2||New Zealand|
|2.24%||1260 kph||840 000 km2||larger than Turkey|