Project Management: A Trip To The Moon

Scene: meeting room, some people dialling in remotely. The plan is to launch a manned rocket to the moon, and the project manager (PM) is kicking off the project.

PM "Right, team, let's plan this space journey to the moon. What kind of fuel will we use in our rocket?"

Designer 'Before I answer that, we want to discuss the colour of the nose cone. The design is to paint it blue.'

PM "Okay, blue is fine. Have you had any thoughts about the engine?"

Designer 'No, but we actually think a red nosecone might be better.'

PM "Noted. Let's move on from that, and come back to it nearer the launch time."

Marketing: We thought blue. Now, how we will we choose the pilots? PM "I was thinking that we would have a rigorous selection process."

Marketing: "We can do that. But we'd like to address the name of the spaceship. Our subsidiary want to call it the USSS Pegasus. We want to refer to it as the US Pegasus - the 'SS' was a suggestion from our previous owner. As this is a combined program, we're going to go with the US Pegasus."
PM "Noted. The US Pegasus. Now, about the pilots..."
Designer "And the name of the ship must be in blue text."
PM [making notes] "...blue text..."
Designer "To match the nose cone." PM "Now, circling back to the question of the pilots."
Stakeholder: "Oh, you can't say that. Circling back suggests that the ship isn't going to land on the moon." PM "Sure. So let's go on to the pilots?"
Stakeholder; "Yes, we can sort that out." PM "Thanks. Now - timelines. Do you have a target date for landing on the moon?" Stakeholder; "Yes, we want to land on 28 July, 2020. When do you need to launch?"
PM "How long will the flight take?" Stakeholder "That depends on the fuel." PM "Doesn't it depend on the engine?" Marketing "Possibly. But it's important that we land on 28 July." Stakeholder "Yes. 28 July. We've set that date with our president. It's his birthday"
PM "So who can give me the launch date?"
Stakeholder "Well, we expected you to provide that." PM "Okay, let's assume it takes four days to reach the moon. Can you have everything built and fuelled by then?" Stakeholder "And we'll want to check everything works." PM "Like a test launch?" Marketing "Oh no, we can't have a test launch. We can't have our competitors knowing what we're doing."
PM "No test launch?" Marketing "No." PM "And the pilots?" Stakeholder "I'm working on it." PM "And the fuel?" Stakeholder "I'll find somebody. Somebody somewhere must know something about it."
Marketing "And we'll need hourly readouts on speed. Preferably minute by minute. And oxygen levels; distance from the earth; internal and external temperatures. All those things." PM "Are you interested in the size of the engine?"
Stakeholder "We've been planning this for six months already. We know it'll need an engine." Engineer; "Sorry I'm late, I've just joined." PM "Thanks for joining. We're just discussing the rocket engine. Do you know what size it will be?" Engineer: "Big." PM "Big enough?" Engineer: "Yes. 1000 cubic units. Big enough." PM: "Great. Thanks. Let's move on." Stakeholder: "Wait, let's just check on that detail. Are you sure?"

Engineer; "Yes. I've done the calculations. It's big enough." Stakeholder: "To get to the moon?" Engineer: "Yes." Stakeholder: "And back?" Engineer: "Yes." Designer: "Even if we have blue text instead of red?"
Engineer: "Yes."
Marketing; "What about if we have red text."
Engineer; "The colour of the text isn't going to affect the engine performance." Stakeholder "Are you sure?"
Engineer: "We're not burning the paint as fuel. We're not painting the engine. We're good." PM: "Thank you. Now; how much fuel do you need?"
Engineer: "That depends. How quickly do you want to get there?" PM: "We need to land on the moon on 28 July 2020. I've estimated a four-day flight time." Engineer; "I'd make it five days, to be on the safe side, and I would calculate 6000 units of class-one fuel, approximately." PM: "Okay, that sounds reasonable. Will the number of pilots affect the fuel calculation?" Engineer: "Yes, but it won't significantly change the 6000 units estimate. When you know the number and mass of the pilots, we can calculate the fuel tank size we'll need."
Stakeholder; "But we won't know that until launch." PM: "Until launch?" Stakeholder: "Yes. We don't know how many people we want to send to the moon until the day of the launch." PM: "And the colour of the text? And the nose cone? And the actual text."
Stakeholder: "Will all depend on people we send."
PM: "No test launch?" Marketing; "No. We need this to be secret so that our competitors don't know what we're doing." PM: "So we're launching an undetermined number of people, in an untested rocket of unknown name and size, to the moon, with an approximate flight time and fuel load, at some point in the future."
Marketing: "But it must land on 28 July." PM: "2020, yes. Ok, We've run out of time for today, but let's catch up tomorrow with progress. Between now and then, let's work to decide some of the smaller details like the fuel and the engine, and tomorrow we can cover the main areas, such as the size of the rocket and where it's going. Thank you, everybody. Goodbye for now."

Moon's Orbital Radius Increasing

In an unexpected and unprecented move, the European Space Agency announced this morning that their data shows that the Moon has started to increase its mean orbital radius at a rate considerably higher than previously believed.  It's been known for some time that the distance from the Earth to the Moon is increasing, but the rate of increase is worrying.  In other words, the Moon is moving further away from the Earth faster than we thought, and in a few year's time will leave the Earth's orbit completely.  

This finding comes after a series of measurements of the Earth-Moon distance (carried out using a more accurate process than this one), using a laser beam pointed at a network of mirrors which Neil Armstrong placed on the Moon's surface over 40 years ago, during the Apollo 11 mission.  By measuring how long it takes for a beam of light to travel to the Moon and back, ESA scientists have been able to determine that the distance from the Earth to the moon has, over the last three years, increased by an average of 140 metres per year.  

However, more alarming is the fact that the rate of increase is also going up - the Moon is, on average, moving further away at a faster rate with time.  The increase over the last six months is about 1.4% more than the average increase over the previous six months.
 

Exact forecasts vary, but ESA scientists are all agreed that within 14 years the Moon's orbit will have extended so far that it will leave the Earth's gravitational field completely, and head off into space.  The team of scientists have proposed various reasons for the Moon's recent moves, and the most common suggestions are related to the recent tectonic activity on Earth - the tsunami of 2004, the volcano in Iceland during 2009-10, and possibly the recent earthquakes near New Zealand, an in particular Japan, which has left to a shortening of the length of the Earth's day.  The recent earthquakes have coincided with the moon coming towards a particularly close approach (perigee) and the theory proposes that this has caused the moon to increase its speed while making this close approach, which will lead to it reaching a larger distance at its furthest point 14 days later.

Other scientists have yet to confirm the team's findings, which have sparked considerable controversy in astronomical circles.  Teams in the southern hemisphere have carried out measurements into the exact time for the moon's orbit and have not noticed a significant change in this - either an increase or a decrease, and therefore have concluded that the moon's orbital radius has not changed.  Other teams are preparing to carry out their own measurements using Armstrong's mirrors, and will be sharing their results later next week.

Other astronomy related articles you may find interesting:

Calculating the height of geostationary satellites
Calculating the angle of elevation of geostationary satellites
The Earth-Moon distance is increasing (published 1 April 2011)
What are constellations?

Calculating (and explaining) escape velocity

Astronomy 1: Stars, Planets and Moons

Following last night's visit to Keele Observatory, I thought it might be helpful to cover some of the basics of astronomy, and then move onto some more detailed topics.  Everybody's got to start somewhere, so I figure it's best to start with home, and move on from there.

The Earth spins on its own axis, taking one day to complete one revolution (one full turn).  This gives us day and night.

The Earth orbits (goes around) the Sun, going around the Sun in one year.  One year is 365.25 days.

Stars:  Stars are huge (very, very big) balls of gas that are carrying out nuclear reactions.  It might be easier to think of a star as an enormous nuclear reactor, constantly going out of control.  The Sun is a star.

Planets:  Planets are smaller balls of rock or gas that go around stars.  There are nine planets that go around our star, the Sun.  The nine planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto (going in order from nearest to the Sun to furthest away).  

Moons:  Moons are smaller than planets, and go around planets in their own orbits.  Our Moon goes around the Earth in just under 28 days; some planets (such as Mercury and Venus) have no moons, while other planets (such as Jupiter and Saturn) have over 10 moons each.

One of the basic principles of astronomy is that smaller (lighter) objects go around larger (heavier) objects, and that's all due to gravity.  Galileo, who was one of the first people to make serious use of a telescope, saw Jupiter and four of its moons going around it, and started to wonder if the Earth goes around the Sun.  It wasn't a popular theory at the time, but a serious step forwards in our understanding of astronomy.

Our star, and its nine planets, are all part of a bigger group of stars (about 10 billion stars, roughly) that are all held together by gravity, in a group called a galaxy.  Our galaxy is called the Milky Way.  It's called the Milky Way because, if and when you can see the faint stars in our galaxy in the sky, they look like a milky cloud stretching across the sky.  Almost all of the stars that we can see in the night sky are in our galaxy.  Our nearest neighbouring galaxy is called Andromeda, and in the right conditions, it can be seen without a telescope or binoculars.

Why don't the planets crash into each other?
Because they're all going around the Sun at different distances.  Mercury is closest to the Sun, and completes one orbit in 88 Earth days, while Pluto, which is furthest away from the Sun, takes 220 times longer than the Earth to go around the Sun.

What is a light year?
A light year is a measurement of distance, and it's equal to the total distance that a ray of light would travel in a year.  The speed of light is 300,000,000 metres per second, or 186,000 miles per second, and there are 31 million seconds in a year (60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, 365.25 days in a year).  This means that in 31 million seconds, light would travel 9,467,280,000,000,000 metres, or 9,467,280,000,000 kilometres, and this distance is called a light year.  The distances in space are so far, that we need a meaningful measurement that we can use to compare distances between objects.  

The Sun's nearest neighbour is called Proxima Centauri ("proxima" meaning "close") and that's 4.22 light years away.  This means that light shining from Proxima Centauri takes just over four years to reach us, and that means that we're seeing what it looks like four years ago.  This, it is true, is a very strange situation, and that's because we're used to looking at objects that are much closer, where we can assume that we're seeing things as they are now (because the speed of light is very, very fast, and it takes fractions of a second for the light to travel from the object to our eyes).

I should make it clear that a light year (despite its name) is not a measurement of time, it's a measurement of distance!

In my next post, I'll try and move onto some more specific details, and answer a few questions that I've heard or been asked about astronomy.
Other astronomy related articles you may find interesting:
Calculating the height of geostationary satellites
Calculating the angle of elevation of geostationary satellites
The Earth-Moon distance is increasing (published 1 April 2011)
What are constellations?
Calculating (and explaining) escape velocity

Calculating the Earth-Moon distance

This post follows up my previous post on geostationary satellites.  Long before we were launching satellites (even non-geostationary ones), our natural satellite, the Moon, was orbiting the Earth.  As the moon goes around the earth, its phase (shape) changes, and in fact, the word "month" derives from "moonth", the time taken for the moon to go from new to full to new again.  This time is the time taken for one complete orbit around the Earth - the different phases of the moon are a result of us seeing a different amount of the lit half of the moon (I once based a very neat science lesson on this principle - in fact I used it in my interview lesson  and subsequently got the job).

One of my photographs of the moon, taken through a telescope.
The darkening at the bottom of the image is the edge of the
telescope's field of view

We can use physics, and our knowledge of the mass of the Earth, the value of pi and the time the Moon takes to complete one orbit, to work out how far it is from the Moon to the Earth.

Back to the two key equations that we'll need, which are the force on a body moving in a circular path:

where

And Newton's Law of Gravity

Equating the two, and rearranging to find r, gives us

This is the same equation used for geostationary satellites, and describes the basic relationship between the distance between two bodies (a planet and a moon, for example, or a star and a planet).  This gives it great power as it can be used in many different situations.

Turning to the current situation, then:

Calculation of the Earth-Moon distance:

G is the universal gravitational constant, 6.67300 × 10^-11 m³ kg^-1 s^-2

M is the mass of  the Earth, 5.9742 × 10²⁴ kg

T is the time to complete one orbit, which for the Moon is 27.32166 days, which is 2,360,591 seconds.

Plugging the numbers into the formula above gives the distance as 383,201 km

However, this is not the distance to the Moon from the Earth's surface.  Newton's law of gravity gives the distance between the centres of gravity of the two bodies.  I'm ignoring the radius of the Moon (which is perhaps an oversight on my part, you decide) but we must subtract the radius of the Earth from this value, to give the orbital height.  Radius of Earth = 6378.1 km, so the distance to the Moon is calculated as  = 376,823 km, or, if you prefer, (at 1.61 km to the mile), 234,147 miles.

Previously, I've learned that the Moon is about a quarter of a million miles away, so I'm glad the method I've used shows a figure which is 'about right' without any checking.  Looking at other sources, it looks like my figures are close enough, considering the assumptions I've made.  One key assumption I've made is to suggest that the moon travels in a circular orbit, and it doesn't.  It has an elliptical orbit, which means the distance from Earth to Moon changes during the orbit - so I've calculated an average distance.  Still, my figure is pretty close, and not a million miles away (and next time somebody reliably informs you that their opinion is not a million miles away, you can tell them that not even the Moon is that far away).

Other astronomy related articles you may find interesting:

Calculating the height of geostationary satellites
Calculating the angle of elevation of geostationary satellites
The Earth-Moon distance is increasing (published 1 April 2011)
What are constellations?

Calculating (and explaining) escape velocity
Measuring g using a pendulum