**Rest, Rain, Dome Hiking, and Escape Velocity**

We understandably slept in a bit the next morning. I wrote a bit and watched the end of the movie that I missed the night before. I organized the gear and packed the car, while chatting with Will and Trev. We hoped to return and stay with them again next year and they seemed very open to that. Great guys.

We decided to head for the shorter, easier, cooler climbs of the high country and headed to the Meadows. We drove east and up into the high Sierra and found rain, plenty of it. We had hoped to climb On the Lamb, but that was clearly out. I pulled off at Olmsted Point and did a little hiking around on the slabs. I found a splitter hand crack that is apparently a known boulder problem. It looked great, though a bit of a high ball. I declined to attempt it in my approach shoes, in the wind, without a partner or a pad.

We drove on and when I spied this cool mini dome, on a whim, I pulled over. I’d driven by this dome many times and each time thought how nice it would be to hike up to the top and take a nap. Or read a book. Or just look out over the beauty of the Meadows. Alas, I was always headed to do something else. Something more…meaningful? But now was the time. Derek joined me and we hiked to the top, finding the friction remarkable good despite being wet. We’d use this realization two days hence. On top, we could see countless other domes, though some had their tops obscured by clouds. The next small dome to the northwest looked fun and we headed over to climb that one as well. While hiking over to it, we derived the mass of the earth. Seriously.

This is the type of stuff we frequently discuss. I love math and science and have been trying to instill that in my boys since they were young. We started with an assumption that the Earth was just a giant ball of iron (turns out to be just 35% iron, 28% oxygen, 17% magnesium, 14% silicon, and some other stuff). I wanted to know the specific gravity of iron (relative weight to water), but Derek didn’t know that phrase. Instead he knew the molar mass of iron and thought it was three times heavier than water (turns out it is 7.2 times the weight of water. Molar mass is not the same as weight and density...), which we knew to weigh one kilogram per liter. I knew the earth was about 8000 miles in diameter, which is a radius of 6500 kilometers. Using the formula for the volume of a sphere (4/3*pi*r

^{3}), we made a rough estimate of the volume. The cube of 6 is 216, so we used 250 and then a thousand cubed is a billion. We approximated 4/3*pi to be 4 and got a trillion cubic kilometers for the volume of the Earth. A cubic kilometer is a billion cubic meters (1000 cubed again). A cubic meter contains a thousand liters, so a cubic meter of water weighs 1000 kilograms. Multiplying this all together we get a trillion times a billion times a thousand, which is a trillion trillion or 10^{23}kilograms. But that’s for water, so we need to triple that. I’ll look up the real value when I get home, but this is probably within an order of magnitude. (I looked this up and the weight of the Earth is 6 x 10^{24}kilograms, so we were off by a factor of 20). I guess rounding and the wrong assumption of the density of the Earth account for this difference, but it was a fun exercise.
Back at the car, we decided to hike up Lembert Dome as well. Another one of my goals for the year is to climb 52 unique summits. I wasn’t going to count the two small, nameless domes we climbed, but since Lembert has a name, it counts. Once again, we were able to friction up remarkably steep, wet granite. We hiked up along the Northwest face and gazed down at the steep routes there and then on up to the true summit, where I’d never been before. We had fun exploring the more eastern slopes on the descent and Derek did some high-ball bouldering up a lieback crack...

And then we hiked the road back to the car.

Derek doing some badass bouldering! |

And then we hiked the road back to the car.

We ate a the TPR (Tioga Pass Resort) that night. This place has three tables - two 2-person tables and one 4-person table, and a counter with eight seats. It has a lot of character, but the food is mediocre and quite expensive. We crashed at the same campground we stayed at on Sunday night and would spend the next three nights there.

The summit of Lembert Dome |

The next morning I got up pretty early, but the sky was socked in again. It wasn't’ raining and wouldn’t actually rain much the entire day, but the sky was covered by fast moving, threatening clouds and Derek wasn’t motivated to do much of anything that day. We spent the entire day in camp, reading, writing, marmot-gazing, computing, and doing Derek’s calculus summer packet (already!). Derek helped me remember my calculus and we did a number of problems together. I worked on a talk I want to give on calculating the escape velocity of the earth by using physics equations that model gravity. You know - your typical climber rest-day activities.

The marmots got really active when most people left the campground. This one ran under a boulder when we tried to get close. |

Towards the end of the day, Derek announced, “We should climb My Favorite Things” tomorrow. I was more than a bit surprised, but I didn't question him! We packed out gear and hoped for better weather.

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