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TL;DR

- Interkosmos and the first Asian in Space
- I solved global warming with orbital mechanics!

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This week in space history

I'm always down for a little representation out and about the cosmos! On July 23, 1980, Pham Tuan became the first Asian in space, launching on Soyuz 37 to the Salyut 6 space station.

Commander Viktor Gorbatko and Flight Engineer Pham Tuan of Soyuz 37 |

Tuan was chosen as part of the Soviet Interkosmos Program, a fascinating initiative started in the late 1970s to send cosmonauts from across the Eastern bloc and other pro-Soviet nations into space. While the missions were politically motivated to show off the technological superiority of Communism, Interkosmos nonetheless achieved many firsts in space diversity - the first Latin American / black person in space, the first Indian, even the first Japanese and British astronauts in the 90s at the twilight of the Cold War!

"I was always in control" | Photo credit: Justin Mott, 2011 |

Pham Tuan's life story is really worth telling - for the Vietnamese Communist party, he was the perfect man to be the first Asian in space, a war hero who rose from a poor village to repel the American invaders during the Vietnam War. As a MiG-21 fighter pilot, he's the only person to have ever downed an American B-52 Stratofortress in aerial combat (though the USAF still disputes this claim), and even today as a retired Lieutenant General, he's still a national hero to his people. But at 72 years old, he's enjoying the quiet life in Hanoi, playing tennis and taking care of his numerous birds and plants. Learn more about him - great article here!

Me at Reunification Palace in Ho Chi Minh City (May 2018) | The poster says, "The friendship of the Soviet Union and Vietnam is forever" |

#### Today I learned

As an investment banker who dreams of going to space, I often poke fun at my lack of formal science and math background on Astronomical Returns. But today, I get to show off a little! My brother-in-law was complaining about the scorching summer heat, and he asked me, "Hans, how much force would it take to slightly raise Earth's orbit and cool us all down?" Turns out, I actually know how to calculate it!

2 billion billion of these bad boys solves global warming! |

Here's my answer - if you fire the propulsive equivalent of 2 billion BILLION Saturn V first stages for 60 seconds, you can raise Earth's orbit by 5%!! Let me know if you agree or disagree with my math below!!

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Isaac Newton defined the vis-viva equation (learn more here), which provides us the instantaneous velocity of an object in an elliptical orbit around a central body

$V = \sqrt{GM(\frac{2}{r} - \frac{1}{a})}$

$V =$ instantaneous velocity

$G =$ Newton's gravitational constant

$M =$ mass of the central body

$r = $ radial distance between the central body and the satellite

$a =$ semi-major axis

We'll assume Earth's orbit around the Sun is circular (which is basically true), that way we can simplify this equation to just $V = \sqrt{\frac{GM}{r}}$ because $a = r$ at all times

Here are some constants we're going to need:

Gravitational constant: $G = 6.674 \cdot 10^{-11} \thinspace m^3\cdot kg^{-1}\cdot s^{-2}$

Mass of the Sun: $M_{Sun} = 1.989 \cdot 10^{30} \thinspace kg$

Earth's orbital radius: $r = 1.496 \cdot 10^{11} \thinspace m$

***Going forward, I'll just use G and M to keep the formulas concise*

So let's calculate Earth's current orbital velocity:

$V = \sqrt{\frac{GM}{1.496 \cdot 10^{11}}}= 29,788 \thinspace m/s$

Our goal is to raise Earth's orbit 5%, so the new orbital radius is given by:

$r_{new} = (1.496 \cdot 10^{11}) * 1.05 = 1.571 \cdot 10^{11}\thinspace m$

Using the vis-viva equation again, we can determine what the new orbital velocity would be a the higher orbit

$V_{new} = \sqrt{\frac{GM}{1.571 \cdot 10^{11}}}= 29,070 \thinspace m/s$

To get Earth from the current lower orbit to the new higher orbit, we're going to use what's called a Hohmann Transfer Orbit (learn more here), which simply uses two engine burns at the opposite ends of an intermediate elliptical orbit to reach a higher circular orbit

Starting at the blue orbit, properly sized burns at V1 and V2 will get you to the orange orbit |

Since we already know $r$ and $r_{new}$, we can calculate $a$, the semi-major axis of the Hohmann Transfer Orbit (gray)

$a = \frac{(1.496 \thinspace \cdot \thinspace 10^{11}) + (1.571 \thinspace \cdot \thinspace 10^{11})}{2} = 1.533 \cdot 10^{11} \thinspace m$

Now that we have the semi-major axis, we can use the vis-viva equation to calculate the necessary velocities at perihelion (closest approach) and aphelion (furthest approach)

$v_{perihelion} = \sqrt{GM(\frac{2}{1.496 \thinspace \cdot \thinspace 10^{11}} - \frac{1}{1.533 \thinspace \cdot \thinspace 10^{11}})} = 30,149 \thinspace m/s$

$v_{aphelion} = \sqrt{GM(\frac{2}{1.571 \thinspace \cdot \thinspace 10^{11}} - \frac{1}{1.533 \thinspace \cdot \thinspace 10^{11}})} = 28,714 \thinspace m/s$

Now we have everything we need to calculate the change in Earth's velocity we must produce to raise its orbit

$\Delta v_1 = 30,149 - 29,788 = 361 \thinspace m/s$

$\Delta v_2 = 29,070 - 28,714 = 357 \thinspace m/s$

$\Delta v_{total} = 361 + 357 = 718 \thinspace m/s$

So now we know how much delta-v we need to produce in Earth's orbit. Given the Earth's mass, we can finally calculate the thrust needed to move the Earth.

Mass of the Earth: $M_{Earth} = 5.972 \cdot 10^{24} \thinspace kg$

Mass of the Earth: $M_{Earth} = 5.972 \cdot 10^{24} \thinspace kg$

$Force = mass \cdot acceleration = M_{Earth} \cdot \frac{\Delta v}{\Delta T} = 5.972 \cdot 10^{24} \cdot \frac{718}{60} = 7.144 \cdot 10^{25} N$

For context, the first stage of the Saturn V produced $3.510 \cdot 10^{7}N$

Do the math:

$7.144 \cdot 10^{25} / 3.510 \cdot 10^{7} = 2.035 \cdot 10^{18}$ Saturn V's needed!!

And there you have it - who says investment bankers can't do science?! Space is for everyone!

**"Give me a lever long enough and a fulcrum on which to place it, and I shall move the world"**

*- Archimedes*

Looking good at Ho Chi Minh City! Wish I could visit. And hope more Asians go to space!

ReplyDeleteHaha I think that's the first picture of myself I've ever put in a blog post

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