This final lesson will help you bridge the connection between circular motion and gravitation.
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Consider a neutron star with a mass equal to the sun, a radius of \(10\,\text{km}\), and a rotation period of \(1.0\,\text{s}\). What is the radius of a geosynchronous orbit about the neutron star? The mass of the sun can be found in the formula sheet above.
A communications satellite orbits the Earth at an altitude of \(35{,}000 \, \text{km}\) above the Earth’s surface. Take the mass of Earth to be \(6 \times 10^{24} \, \text{kg}\) and the radius of Earth to be \(6.4 \times 10^6 \, \text{m}\). What is the satellite’s velocity?
In \(2014\), the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we can approximate it as a \(50\,\text{km}\) diameter circular orbit with a period of \(11\) days.
Part (a)2 pts
What was the satellite’s orbital speed around the comet? (Both the comet and the satellite are orbiting the sun at a much higher speed.)
Part (b)3 pts
What is the mass of the comet?
Part (c)3 pts
The lander was pushed from the satellite, toward the comet, at a speed of \(70\,\text{cm/s}\), and it then fell—taking about \(7\) hours—to the surface. What was its landing speed? The comet’s shape is irregular, but on average it has a diameter of \(3.6\,\text{km}\). Assume the lander experienced constant acceleration from the time it left the satellite.
A \(2.2 \times 10^{21} \, \text{kg}\) moon orbits a distant planet in a circular orbit of radius \(1.5 \times 10^8 \, \text{m}\). It experiences a \(1.1 \times 10^{19} \, \text{N}\) gravitational pull from the planet. What is the moon's orbital period in Earth days?
Unit 3 Recap
Take a second to read the Unit 3 Speed Recap. This goes over everything you learned (in 5 minutes). Moreover, be sure to get in tons of practice in using UBQ. These questions are hand selected for you to master the concepts you learned!
Unit 4 Preview
Congrats! You finished Unit 3.
It’s time to move on to Unit 4 Energy. This unit marks the halfway point and is one of the easier to understand topics!
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This article was written by Jason
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