## Tuesday, July 22, 2008

### Makemake

Dwarf planet 2005 FY9 has been given the name Makemake, the Polynesian god of fertility. Last month the International Astronomical Union created a new class of subplanets called Plutoids. Makemake is the third Plutoid following Pluto and Eris. 2/3 the size of Pluto, it was discovered in 2005 by planet-hunter Michael Brown.

Kea said...

Nice picture. I will be visiting Mt John next week, which has the planet hunting MOA telescope.

11:17 AM
nige said...

Thanks for these photos. It is very interesting to think about what effects there would be of visiting small planets. I see from Wikipedia that Makemake has a mean radius of about 750 km and a surface gravity of about 0.5 m/s^2 or 5% of that on the Earth's surface. I always wonder what the effects of low gravity would really be like, useful or dangerous.

The height a person can jump (assuming that air resistance is trivial compared to gravitational deceleration for the jump) is:

s = (1/2)(u^2)/g

where u is initial upward velocity and g is acceleration due to gravity.

If someone jumps 0.5 m in a 9.8 m/s^2 gravity field on the Earth, their initial upward velocity is (2sg)^(1/2) = 3.13 m/s according to this formula, so on Makemake you might expect them to jump (1/2)*(3.13^2)/0.5 = 9.8 metres.

Which would quite scary when you start to fall back to the ground. However, because gravity is weaker, when you fall back gravity doesn't accelerate you as much as it does on the Earth, so you only hit the ground with the same speed that you jumped with (gravity returns to you the same kinetic velocity which you had at the beginning, just pointed in the downward direction). So you hit the ground at the same speed you would after jumping on the Earth, despite having gained greater altitude before falling back.

However, the time taken for the jump is enormous, and that would be surreal.

For falling distance s, the time taken to fall is: t = (2s/g)^(1/2) = (2[(1/2)(u^2)/g]/g)^(1/2) = u/g

The total time spent in the air during the jump will be double this fall time, because the time for gravity to decelerate you from initial jump velocity u to zero is the same as the fall time (the acceleration from zero velocity up to u).

So if you jump upwards at initial velocity u, the time you spend in the off the ground is 2u/g.

So for the previous example of a person jumping upward at u = 3.13 m/s on Makemake with g = 0.5 m/s^2, the time spent off the ground is 2u/g = 12.5 seconds.

That would be quite a surreal experience, because for the same speed of jump on the Earth, the entire jump lasts only 0.6 second.

On the Moon (1/6th Earth gravity) the entire jump would last 3.8 seconds and the height reached would be 0.5*6 = 3 metres. It would be fun jumping there, too.

I wonder what the effect of gravity is on the ability to walk? How much further can a person walk in a low gravity field than on the Earth, when comparing equal masses?

Presumably a person can walk a lot further in low gravity conditions, because the leg muscles are picking up the person's weight and moving it with each step. So with reduced gravity, walking will leave the person less tired and endurance will be increased. But by how much exactly?

Is the same true for wheeled vehicles? I know the Lunar Rovers used during the Apollo missions had a good range and speed for lightweight electric cars, but I wonder how much greater their range was on the Moon than when they were tested on the Earth? The reduced weight in a low gravity field would reduce friction on bearings, as well as between the wheel and the ground.

12:15 PM
L. Riofrio said...

Happy travels, Kea!

For nige: Wednesday I had privilege of talking to Rusty Schweickhart about that subject. (more about that soon) He noted how the gravity field of asteroids is so inconsequential that mooring to them would be difficult.

7:33 AM
CarlBrannen said...

Louise,

I've been busy with quarks and leptons recently, but I ran into a flat space cosmology paper by the geometric algebra people I'm fond of over at Cambridge. You might find it of interest.

11:02 AM
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