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a Space Mission by D-Orbit   I

How do satellites get and stay in orbit?

May 8, 2017

Gravity on Earth is a fact of life. Our feet are stubbornly stuck on the ground, and when we jump, no matter how high, we inevitably fall back. When we throw an object up towards the sky, sooner or later it falls back to the ground, like Newton’s proverbial apple.

 

If we were to climb to the top of Mount Everest, 8.5km above the sea level, we would discover that even at that height gravity’s pull is still quite strong, so we wouldn’t be able to jump any higher than we can do at sea level.

 

While you may not have been on the top of the tallest mountains, you have probably gone even higher than that while flying on a commercial airliner. Yet, even when flying above 10km, our buttocks are stuck to our airplane seat like a sack of potatoes.

 

How high must you fly to go beyond the reach of gravity?

 

Gravity in space

 

A common misconception about space is that there is no gravity there. It’s true that astronauts inside the International Space Station (ISS) are free to float weightless, but the reason they are apparently free from Newton’s laws has nothing to do with their distance from the surface of our planet. If you were able to climb a vertical ladder up to 450km, the average altitude of the ISS, stand on top of a platform and jump, there would be no happy flying for you. Even at that altitude the force of gravity would have the upper hand, so you’ll be enjoying a hell of a view, but not for long.

 

How comes?

 

Going to space is not a matter of reaching a certain altitude: it is about achieving orbit, which is a matter of velocity. Sure, you have to fly high to go beyond Earth’s atmosphere, but if you want to stay there you must acquire a specific tangential velocity.

 

To understand how this mechanism work, we’ll use the “Netwon Cannonball,” a thought experiment conceived by Isaac Netwon in the year 1687. 

 

Newton’s Cannonball

 

When we fire a cannonball horizontally (in ballistic terms, with 0 elevation), its trajectory follows a ballistic arc that depends on three main variables: the power of the cannon, the altitude from which we fire it, and the resistance of the air.

 

 

The trajectory of a cannonball depends on the firing power of the cannon, and on the altitude of the firing point.

 

If we fire our cannon from the top on a hypothetical 450km high mountain, an altitude where the atmosphere is extremely rarified, the cannonball will not be slowed down by atmospheric drag, so it will be able to travel much further away before reaching the ground. However, if our cannon is powerful enough, the cannonball’s trajectory will follow Earth’s curvature and perform a complete circle around the Earth without ever touching the ground (Spoiler alert: duck, if you don’t’ want to be hit on your head from behind).

 

A conceptual overview of Newton’s Cannonball experiment.

Credits: Andrew Bennett

 

A rocket applies the same principle to launch a spacecraft. After a vertical lift-off, the rocket performs a pitchover maneuver, gradually adding a horizontal component to the trajectory of its payload. When the tangential velocity is above a certain threshold, the payload achieves a stable orbit. Like a cannonball, the satellite moves both forward and downwards, but as the tangential component matches the gravitational pull, the satellite keeps falling around Earth in a circular motion that, thanks to the rarified atmosphere, does not require any additional thrust.

 

A spectacular night rocket launch. The rocket follows a parabolic trajectory designed to bring the payload beyond Earth’s atmosphere and impart on it a tangential velocity that will allow it to achieve orbit.

Credits: NASA.

 

And what about free-floating astronauts? Astronauts inside the ISS are in a state of weightlessness because they are in a perpetual free-fall around the Earth. Here on Earth you can experience an instant of weightlessness by riding an elevator downward or, if you have the stomach for it, by bungee jumping or skydiving. Weightlessness in space is less scary than a bungee jump because in this case your frame of reference, the entire spacecraft, is falling with you.

 

Astronauts live their lives inside the ISS in a condition of weightlessness.

Credits: Heraldblog

 

This is also the reason why satellites tend to remain in orbit well beyond the nominal duration of their mission. It takes the energy of a propulsive decommissioning maneuver to bring a satellite down, and most spacecraft are not equipped to perform one in an efficient and cost-effective way.

 

This is why we have developed D-Sat, a mission that will test a technology that will increase the reliability and the cost-effectiveness of this kind of maneuvers, creating the conditions for a new generation of self-decommissioning spacecraft that won’t leave additional debris in Earth’s orbit.

 

Do you want to know more? Check out our project page, and learn more about the KickStarter campaign we are about to launch. 

 

 

 

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