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Tuesday, March 19, 2024

Commuting within the solar system

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How do we send a spacecraft to outer space? How does it get to another planet or planetary body? The most basic physics answer is that a spacecraft has to change its speed in order to get around.

In the space sciences, the change of speed needed for an object to get from one part of the universe to another is called delta-V. The delta in delta-V is a Greek letter that stands for “change of”. Meanwhile, the V stands for velocity, which is an object’s speed plus its direction of motion.

Right now, as you are sitting while reading this, you are moving at incredible speeds with respect to the center of the Earth. You are moving at even greater speeds with respect to the center of the Solar System inside the Sun. 

Speed, after all, is always relative. Nothing in the universe has an absolute speed. Speed is always measured with respect to a chosen reference frame.

Back to the topic of sending things to space. I mentioned the fact that you are moving at great speed with respect to the Earth’s center because that is important when thinking about sending spacecraft into orbit around the Earth. Right now, even if you are stationary with respect to the ground, you are moving at a whopping 1,700 kph with respect to the Earth’s center. However, to send a spacecraft into orbit, you must make it travel at speed even much faster than this.

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How fast? Now imagine throwing a ball horizontally. After some time it falls on the ground in front of you. To get there, it followed a certain path. Scientists call the shape of this path a parabola, and they would say that the ball had a parabolic trajectory.

Now imagine throwing the ball faster. You will notice that it falls farther from you. The faster you throw the ball, the farther it falls from you. The amazing thing is that, there is a throwing speed at which the ball falls to the ground in such a way that the Earth curves underneath it. At this speed, the ball will keep on falling while the Earth will keep on curving underneath it, so the ball will never hit the ground. It will keep on orbiting the Earth!

Of course this imaginary scenario is impossible because there will be many things in the way of the ball. There are trees, buildings, people, mountains, and most especially there will be air. Even without the other obstacles, the air resistance will eat away at the ball’s speed and will slow it down, making it fall to the ground even if it had enough speed.

But what if you hurl the ball high into space, where there are no obstacles, including air? Well then that ball becomes a satellite of the Earth! 

That is how we send satellites into orbit: we use rockets to hoist them up into space, and then we push them horizontally at high speeds so that they fall in such a way that they never hit the ground.

How fast should we hurl spacecraft horizontally so that they orbit the Earth? In the orbit of the International Space Station and the Philippines’ Diwata-1 microsatellite, the answer is 27,600 kph with respect to the ground!

Now remember that an object on the ground is actually moving at 1,700 kph with respect to the Earth’s center. The difference between this speed and the required speed of orbit, 27,600 kph, is the delta-V needed. That is a delta-V of 25,900 kph.

The orbit of the ISS and Diwata-1 is not that high by the standards of space. At a mere 400 kms. above the ground, this place is called the Low Earth Orbit or LEO.

To get from LEO to where the GPS satellites, the ones that help us navigate, are orbiting, an additional delta-V of around 14,000 kph. 

Meanwhile, to go from LEO to an orbit around the Moon, a delta-V of around 22,000 kph is needed. To land on the surface of the Moon, an additional 6,000 kph is needed.

Every kph of delta-V means kilograms of expensive fuel. This is why when you look at the paths of actual spacecraft moving across the Solar System, they are actually more roundabout. They pass by other planet for gravitational assistance that increases their delta-V without using much fuel. 

Right now, all this talk sounds a bit too abstract or distant. However, in the future, such a way of viewing the Solar System might be second nature to our descendants who will be shuttling back and forth across our neighbors in space.

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