Solving Direct Variation Problems For the following exercises, use Kepler's Law, which states that the square...
For the following exercises, use Kepler's Law, which states that the square of the time, T (measured in Earth years), required for a planet to orbit the Sun varies directly with the cube of the mean distance, a (measured in billions of miles), that the planet is from the Sun. a. Use Mars's time of 2 and mean distance of 0.142 billion miles, find the equation relating T and a. (Enter an equation in terms of T and a. Round...
Solving Direct Variation Problems For the following exercises, use Kepler's Law, which states that the square of the time, T (measured in Earth years), required for a planet to orbit the Sun varies directly with the cube of the mean distance, a (measured in billions of kilometers), that the planet is from the Sun. a. Use Uranus's time of 84 and mean distance of 2.871 billion kilometers, find the equation relating T and a. (Enter an equation in terms of...
please answer and show work for all parts of equation Kepler's Law, which states that the square of the time, T (measured in Earth years), required for a planet to orbit the Sun varies directly with the cube of the mean distance, d (measured in billions of kilometers), that the planet is from the Sun. 19 a. It takes Saturn approximately 30 Earth years to orbit the Sun with a mean distance of 1.4 billion kilometers. Use this information to...
1. Kepler's harmonic law of planetary motion (his 3rd law) states that the square of the orbital period is proportional to the cube of the characteristic distance of the planet from the sun. Test this by fitting a power law to the data below. Give your answer to 4 decimal places. Data file #period (days), distance (AU) # Data supporting Kepler's third law # distance is measured relative to the earth's mean distance, # which is about 9.26e7 miles and...
1 (10 pts). In 1601 the German astronomer Johannes Kepler became director of the Prague Observatory. Kepler had been helping Tycho Brache in collecting 13 years of observations on relative motion of the planet Mars. By 1609, Kepler had formulated his first two laws of planetary motion: i. Each planet moves on an ellipse with the sun at one focus. ii. For each planet, the line from the sun to the planet sweeps out equal areas is equal times. Kepler's...
4. Use Kepler's Second Law and the fact that L-fxp to determine at which points in an elliptical orbit around the Sun a planet has maximum and minimum speeds. (Section 13.5 will help.) 5. At the end of example 13.10, there's an "Evaluate" blurb about how inside the surface of the Earth the force of gravity varies proportionally to the distance from the center, and it makes reference to the next chapter. which is about oscillation. Model the motion of...
Multivariable Calculus help with the magnitude of angular momentum: My questions is exercise 4 but I have attached exercise 1 and other notes that I was provided 4 Exercise 4. In any mechanics problem where the mass m is constant, the position vector F sweeps out equal areas in equal times the magnitude of the angular momentum ILI is conserved (Note: be sure to prove "if and only if") (Note: don't try to use Exercise 2 in the proof of...