5/3/2021 0 Comments Rigging Math Problems
You can prove this for the moon and the ISS given the following data for R and T: Moon: R 385000 km, T 27.32 days. ISS: R 6776 km, T 92.68 minutes. You could also consider geostationary satellites which hover above a fixed point in the Earth, so T 24 hours and to achieve this R 42160 km.As part of this tutoring, I have been looking for good graphics that illustrate basic science concepts.
One common high-school physics problem involves computing the tension in ropes tied to an anchor by a pulley. Figure 1 is a graphic that nicely illustrates the tension between two ropes connected to an anchor point by a carabiner. The derivation assumes that there is no friction associated with the carabiner, which is not true. This idealization would be better if the carabiner was replaced with a pulley. It also computes the angle of the gray rope in Figure 1, which is not shown in that diagram. You can circumvent this discontinuity using one of three techniques. The classic approach for an engineer and the one I typically use. It would have to break known, testable, repeatable laws of projectile motion. If you drop an object and propel an object from a given height the time needed for both objects to reach the ground is equal. This is because gravity acceleration is unaffected by horizontal motion or speed. Since the orbiting iss is 240 miles up it is still subjected to 89 of earth gravity. Therefore we can figure out that it would hit the earth in roughly 4.9 minutes if dropped from that high. Since we know that horizontal speed doesnt affect vertical acceleration due to gravity then its safe to assume there is not a football field sized craft magically speeding around the earth. If you wish to beat the quote to death, here is a NASA forum discussion on this very topic some agree with Heinlein, some dont. ![]() Thus the Moon is falling towards the Earth and the planets are falling towards the Sun but luckily their concurrent horizontal velocity component prevents collisions. Isaac Newton carried out a similar thought experiment to yours, when you imagined the ISS being suddenly deprived of its horizontal velocity and hence falling to Earth. He did the same thing and worked out that the Earth and Moon together would fall to the Sun in 66 days and 19 hours, Venus in 40 days and Jupiter in two years and one month. Are orbits achievable at any altitude As long as they go fast enough. We can abstract either of the components but the actual motion is composite of both. It is analogous to Marks statics calculation in which he resolves a diagonal force into vertical and horizontal components. The actual force is then the sum of vectors H and V, but H without V or V without H is meaningless. For a given altitude, any object will orbit the Earth if the horizontal velocity is sufficient to maintain it, as measured by its orbital period. ![]() ISS: R 6776 km, T 92.68 minutes. You could also consider geostationary satellites which hover above a fixed point in the Earth, so T 24 hours and to achieve this R 42160 km.
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