The first proposal for how an artificial satellite would work is attributed to I

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The first proposal for how an artificial satellite would work is attributed to Isaac Newton. He reasoned that due to Earth's curvature, one could create an artificial satellite by launching an object horizontally at just the right speed. The object would follow projectile motion and fall toward the Earth's center. Due to the surface of the Earth being curved, the surface would "move away" from a horizontal trajectory. If the object's rate of falling toward the Earth's surface matched the rate at which the surface is curving away from a straight trajectory, the object would be in a constant state of falling but never coming any closer to the surface of the Earth. A rough illustration of the effect is shown below. For example, near the surface of the Earth, one can find that the object has to fall vertically about 5 meters for every 8000 meters of horizontal motion in order to maintain a circular orbit around the Earth.

http://imgur.com/qsSNNvu

This model works well even for satellites that are far from, but maintain a circular orbit around, the planet they are orbiting. Assume a satellite is circling around Planet X at a radius of 14.1

The first proposal for how an artificial satellite would work is attributed to Isaac Newton. He reasoned that due to Earth's curvature, one could create an artificial satellite by launching an object horizontally at just the right speed. The object would follow projectile motion and fall toward the Earth's center. Due to the surface of the Earth being curved, the surface would "move away" from a horizontal trajectory. If the object's rate of falling toward the Earth's surface matched the rate at which the surface is curving away from a straight trajectory, the object would be in a constant state of falling but never coming any closer to the surface of the Earth. A rough illustration of the effect is shown below. For example, near the surface of the Earth, one can find that the object has to fall vertically about 5 meters for every 8000 meters of horizontal motion in order to maintain a circular orbit around the Earth. This model works well even for satellites that are far from, but maintain a circular orbit around, the planet they are orbiting. Assume a satellite is circling around Planet X at a radius of 14.1 times 103 km from the center of the planet. For every 7.5 kilometers, how many meters does it have to fall towards Planet X in order to maintain a circular trajectory? The satellite has to fall meters for every 7.5 kilometers to maintain a circular trajectory.

Explanation / Answer

1. draw 2 lines from the center of the planet. 1 to the begining of 7.5 km and the second to the end of 7.5 km part.

2. now you have triangle with 90 degrees angle

3. you have sides as follows:

- 7.5 km

- 14.1e3 km

- 14.1e3 + x km, when x is the distance of falling that we need to calculate

4. use a^2+b^2=c^2

5. 7.5^2+`4.1e3^2 = (14.1e3+x)^2

6. --> x=0.00199 km --> x=1.99 m

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