insight

## Energy to Orbit vs Launch into Deep Space

This is from Sanjoy Mahajan's The Art of Insight Problem 1.11 Estimate the energy in a 9-volt battery. Is it enough to launch the battery into orbit? I tried to answer this with the energy density required to launch into deep space. But this is different to going into orbit; how much energy is required to get into low Earth orbit? Low Earth Orbit A low orbit has to be above the height of the atmosphere (otherwise will require propuslion to overcome atmospheric friction), and so is typically above 300 km.

• Edward Ross
insight

## Energy Desnsity to Launch into Space

This is from Sanjoy Mahajan's The Art of Insight Problem 1.11 Estimate the energy in a 9-volt battery. Is it enough to launch the battery into orbit? I have already (mis)estimated the energy of a battery, but looked it up as 500 mAh. Energy density required to launch into space To launch into space you have to exchange energy to counteract the change in gravitational energy (at least, you'll need more for air resistance).

• Edward Ross
insight

## How Much Energy is there in a 9V Battery

This is from Sanjoy Mahajan's The Art of Insight Problem 1.11 Estimate the energy in a 9-volt battery. Is it enough to launch the battery into orbit? We're just going to estimate the first part. Battery Energy A volt is energy per unit charge $$V = \frac{E}{q}$$. To get towards an energy we need an amount of charge; the current in Ampere is the charge per unit time $$I = frac{q}{t}$$.

• Edward Ross
insight

## Population Density Australia

How dense is the population in Australia? I've looked at the Gridded Population of the World and you can see that the population is concentrated around the few capital cities on the coast. It's hard to visually average something so lumpy, but it's easy to estimate it. I know it's about 10 hours driving from Melbourne to Sydney, and about the same again to Brisbane. Brisbane is about halfway between Melbourne in the south and Cairns in the far north.

• Edward Ross
insight

• Edward Ross
insight

## Estimating Weight with Body Mass Index

When estimating things it's good to find approximate constants, typically ratios, that are easier to remember than things that vary. The Body Mass Index (BMI) is an example for measuring people. It's relatively easy to measure human height, as a human. For example I'm about 180cm tall; the top of my nose is about 170cm, the bottom of my chin is about 160cm and the bottom of my neck is about 150cm.

• Edward Ross
insight

## How much Money is in a Suitcase?

This is from Sanjoy Mahajan's The Art of Insight Problem 1.3 In the movies, and perhaps in reality, cocaine and elections are bought with a suitcase of $100 bills. Estimate the dollar value in such a suitcase. Size of$100 note Let's assume a banknote is about the same thickness as paper; Australian notes are probably a little bit thicker. A 500 page ream of paper is about 5cm tall, so each sheet is about 0.

• Edward Ross
insight

## How Much Does a Box of Books Weigh?

This is from Sanjoy Mahajan's The Art of Insight Problem 1.1 How heavy is a small moving-box filled with books? Guesstimating weight I've moved small boxes of books a few times, it's light enough for me to carry. It's much heavier than a couple of 2kg bag of onions, but probably more similar to a 20kg bag of pool salt. I'd guess it's in the range 10-20kg, so I'd guess around 15kg.

• Edward Ross