blueflannel27 wrote:
What is the angular momentum of the solar system around the Milky Way Galaxy? (use standard SI units)

angular momentum is angular velo times moment of inertia. angular velo is v/r. v is 2pir/time. divide by r is 2pi/time. time is 2.5E8 yr or 7.5E15 sec. 2pi/7.5E15 is around 8E-16. Moment of inertia is mr^2. R is 2E17 km or 2E20 m^2 is 4E40. Mass should be appriximentaly the mass of the sun. Times 2E30 is 8E70*8E-16 is 6.4E55 or 56.

I believe my solution is correct (although I could be wrong)

How many joules are released every minuite due to lightning striking the earth?

South Woods MS, Syosset HS '21 Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Events!: Astro , Code , Fossils

2019-2020 Season
Cornell/LISO/Duke/MIT/Regionals/Brown/SOUP
Astro: 2/4/2/10/2/2/3
Code: 9/1/2/1/1/1/1
Fossils: 16/13/6/9/2/3/8

blueflannel27 wrote:
What is the angular momentum of the solar system around the Milky Way Galaxy? (use standard SI units)

angular momentum is angular velo times moment of inertia. angular velo is v/r. v is 2pir/time. divide by r is 2pi/time. time is 2.5E8 yr or 7.5E15 sec. 2pi/7.5E15 is around 8E-16. Moment of inertia is mr^2. R is 2E17 km or 2E20 m^2 is 4E40. Mass should be appriximentaly the mass of the sun. Times 2E30 is 8E70*8E-16 is 6.4E55 or 56.

I believe my solution is correct (although I could be wrong)

How many joules are released every minuite due to lightning striking the earth?

[math]10^{3}[/math] lightning strikes happen every minute and each lightning strike carries [math]10^{9}[/math] Joules. Answer: 12

A bolt of lightning appears to contain about 5 billion Joules ([url=http://www.physics.org/facts/toast-power.asp]source[/url]). Lightning strikes Earth about 100 times a second ([url=https://learn.weatherstem.com/modules/learn/lessons/36/02.html]source[/url]), which is 6000 times a minute. Answer: 13

How long (in years) does it take a galaxy in a galaxy cluster to orbit the cluster's center of mass once, assuming that the cluster has an average density 100 times that of the universe's?

edit: added units

University of Texas at Austin '22
Seven Lakes High School '18
Beckendorff Junior High '14

Adi1008 wrote:
How long (in years) does it take a galaxy in a galaxy cluster to orbit the cluster's center of mass once, assuming that the cluster has an average density 100 times that of the universe's?

edit: added units

so first we have to estimate the distance from a galaxy to the center. Distance to andro is 2E22 m so lets say the average distance is E24. The volume would be 4/3pi(E24^3) or about 4E72 m^3. iirc density is 4 protons per m^3 so 1.6E73 protons 1.6E46 kg. 100 times is 1.6E48. distance^3/mass=time^2. E72/1.6E48 is about 6E23. sqrt, 8E11 years so 12??????

so (assuming the milky way represents an average galaxy), the distance is 4.8E23 according to wikipedia. Volume is 1.5E71. Density is -26 so mass =1.5E45. d^3 is 1.1E71/1.5E45 is 7.37E25. sqrt is 8.6E12 or 13. Correct me if I screwed up anything

If the volume of every person alive was instead filled with butter how many kcal does this contain?

South Woods MS, Syosset HS '21 Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Events!: Astro , Code , Fossils

2019-2020 Season
Cornell/LISO/Duke/MIT/Regionals/Brown/SOUP
Astro: 2/4/2/10/2/2/3
Code: 9/1/2/1/1/1/1
Fossils: 16/13/6/9/2/3/8

Adi1008 wrote:
How long (in years) does it take a galaxy in a galaxy cluster to orbit the cluster's center of mass once, assuming that the cluster has an average density 100 times that of the universe's?

edit: added units

so first we have to estimate the distance from a galaxy to the center. Distance to andro is 2E22 m so lets say the average distance is E24. The volume would be 4/3pi(E24^3) or about 4E72 m^3. iirc density is 4 protons per m^3 so 1.6E73 protons 1.6E46 kg. 100 times is 1.6E48. distance^3/mass=time^2. E72/1.6E48 is about 6E23. sqrt, 8E11 years so 12??????

so (assuming the milky way represents an average galaxy), the distance is 4.8E23 according to wikipedia. Volume is 1.5E71. Density is -26 so mass =1.5E45. d^3 is 1.1E71/1.5E45 is 7.37E25. sqrt is 8.6E12 or 13. Correct me if I screwed up anything

If the volume of every person alive was instead filled with butter how many kcal does this contain?

uhh assume that butter is a perfect fat so it yields around 9 kcal/g and then like it's probably close to the density of water so 9 kcal/mL. We will also make the assumption that everyone alive is an adult human, which has a volume of 66.4L. Sooo use some dimensional analysis and get 6e5 kcal / person. Multiply this by 7e9 people (lets just round down because we are overestimating a lot of stuff), and then you get like 4e15 kcal, so 15.

turns out, 14 grams of butter is 100 kcalories, yielding 7.14 kcal / g. density of butter is 0.911 g/mL, so 7.14 kcal/g * 0.911g/mL = 6.5 kcal / mL (oops). The volume of an adult human is indeed 66.4L, yielding 4e5 kcal / person. Now the tricky part is like avoiding the assumption that all people are adults. So it turns out around 75% of people are over 18 so the sigfig shouldn't change too drastically. 4e5*8e9 = 3e15, or 15

Assuming perfect efficiency, how many McDonald’s Hamburgers would need to be combusted per second to equate the total amount of energy in the Universe? (hint: this question is troll)