Here's a situation to challenge you and your friends: A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape using a given amount of fuel, should it fire its engines at the apogee (the point at which it is farthest from Earth) or at the perigee (the point at which it is closest to Earth)? (Hint: Let the formula Fd = AKE guide your thinking. Suppose the thrust F is brief and of the same duration in either case. Then consider the distance d that the rocket would travel daring this brief burst at the apogee and at the perigee.)
Here's a situation to challenge you and your friends: A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape using a given amount of fuel, should it fire its engines at the apogee (the point at which it is farthest from Earth) or at the perigee (the point at which it is closest to Earth)? (Hint: Let the formula Fd = AKE guide your thinking. Suppose the thrust F is brief and of the same duration in either case. Then consider the distance d that the rocket would travel daring this brief burst at the apogee and at the perigee.)
Here's a situation to challenge you and your friends: A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape using a given amount of fuel, should it fire its engines at the apogee (the point at which it is farthest from Earth) or at the perigee (the point at which it is closest to Earth)? (Hint: Let the formula Fd = AKE guide your thinking. Suppose the thrust F is brief and of the same duration in either case. Then consider the distance d that the rocket would travel daring this brief burst at the apogee and at the perigee.)
Let’s imagine that you have an idea for an experiment to fly on NASA’s “Vomit Comet.” (What’s special about this plane? It flies in parabolic paths (aka freefall) which result in near weightlessness. This means that you can ignore the effects of gravity when plan your experiment.) You want to mimic the orbital motion of the planets but by using electrostatic force rather than gravitational. And, instead of a planet, you will be orbiting a droplet of water that is 0.5mm in radius and has an deficit of 1.5 x 106 electrons. The droplet is to orbit around a small (1cm radius) sphere. If you want the droplet to move with an orbital radius of 14cm and period of one minute, what should the charge be on the central sphere? BTW The density of water is 997 kg/m3.
The orbit of a 1.9 x 1010 kg comet around the Sun is elliptical, with an aphelion distance of 25.0 AU and perihelion distance of 0.870 AU. (Note: 1 AU = one astronomical unit = the average distance from the Sun to the Earth = 1.496 x 1011 m.)
(a) What is its orbital eccentricity?
(b) What is its period? (Enter your answer in yr.)
yr
(c) At aphelion what is the potential energy (in J) of the comet-Sun system?
Synchronous orbits occur when the natural (sidereal) rotation of a body coincides with the orbital period of an object orbiting around it. When this happens, the relative position of the two objects stays the same over time. On Earth, we this would translate to an orbital period of around 24 hours, and the satellite in geosynchronous orbit would appear at the same position in the sky every year, every day, and every hour. Look up the mass of Saturn. If Saturn rotates once every 10 hours and 42 minutes, what semi-major axis do you need to be in a Saturn-synchronous orbit?
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