Satellites and Weightlessness

Name: Satellites and Weightlessness
Author: StemPy Lab

A satellite does not fall to the Earth, because it falls round it. In this course we find the speed and the period of a satellite, we study its energy and what happens when it is lifted or slowed by the air, we find where a geostationary satellite must be and why a polar satellite sees the whole Earth, and we explain why an astronaut feels weightless.

3 lessons, about 1 h 10 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Orbital speed and period of a satellite
A satellite in a circular orbit is held by gravity, which supplies the centripetal force: $\dfrac{GMm}{r^2} = \dfrac{mv^2}{r}$ . So $v = \sqrt{\dfrac{GM}{r}}$ , the same for any satellite mass, and the period is $T = 2\pi\sqrt{\dfrac{r^3}{GM}}$ . Close to the Earth, $v \approx 7.9\ \text{km/s}$ and $T \approx 85$ minutes; higher orbits are slower and longer.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 20 min
Energy of an orbiting satellite
A satellite in a circular orbit of radius $r$ has kinetic energy $K = \dfrac{GMm}{2r}$ and potential energy $U = -\dfrac{GMm}{r} = -2K$ , so its total energy is $E = -\dfrac{GMm}{2r} = -K$ . The negative total means it is bound. A higher orbit has more (less negative) total energy but less kinetic energy, and the energy needed to move it is the change in $E$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Geostationary and polar satellites, and weightlessness
A geostationary satellite orbits over the equator, eastward, once per day, so it stays above one place; this needs $r \approx 42\,300\ \text{km}$ , a height of about $36\,000\ \text{km}$ . Polar satellites pass over the poles in low orbits and see the whole Earth as it turns beneath them. Astronauts in orbit feel weightless because they and their craft fall freely together, not because gravity is absent.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Satellites and Weightlessness: Practice Paper

20 questions · 40 min

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Satellites and Weightlessness

Course outline (3 lessons)

Orbital speed and period of a satellite

Energy of an orbiting satellite

Geostationary and polar satellites, and weightlessness

Test Your Learning

Your teacher

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