Show that equations 1, 2 and 3 lead to Kepler’s Third Law of planetary motion. How are the orbital radius and period related? How do you obtain a linear plot from this relationship? Which quantities would be in the x-axis? y-axis?

Show that equations 1, 2 and 3 lead to Kepler’s Third Law of planetary motion. How are the orbital radius and period related? How do you obtain a linear plot from this relationship? Which quantities would be in the x-axis? y-axis?

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter15: Place And Time

Section: Chapter Questions

Problem 1SA: How is the origin defined in a Cartesian coordinate system?

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A) When one object is orbiting a much larger object, the period of the orbit (T) is related to the semi‐major axis (r) by the general form of Kepler’s 3rd Law. Write this general form in the space below: B) What units must the period be in if we want to calculate the semi-major radius in meters? Note that G = 6.67 x 10-11 N m2/kg2. Complete problems using Kepler’s 3rd law as you wrote it down above:
To find the acceleration from equation (a=v^2/r), the velocity of an object traveling in a circle is the distance traveled (i.e. the circumference, which is 2?r) divided by the travel time (i.e. the period T). The Moon’s sidereal period is 27.32 days. Convert this period into seconds. Complete Table 1 for the Moon to find its orbital period in seconds, its average velocity in meters per second and its acceleration in meters per second^2 where Orbital radius (m) = 3.84 x 10^8.
Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let be the displacement vector with a magnitude of two meters due northwest. Express vectors and in unit vector component form. = + = + The net displacement is given by the vector sum: . = + By Pythagorean theorem,the magnitude of the displacement is: = meters. The direction of the resultant displacement is: north of east.
Kepler's third law states that the relationship between the mean distance d (in astronomical units) of a planet from the Sun and the time t (in years) it takes the planet to orbit the Sun can be given by d^3 = t^2. (A). It takes Venus 0.616 years to orbit the Sun. Find the mean distance of Venus from the Sun (in astronomical units). (B). The mean distance of Jupiter from the Sun is 5.24 astronomical units. How many years does it take Jupiter to orbit the Sun?
Estimate the number of steps you would have to take to walk a distance equal to the circumference of the Earth. (We estimate that the length of a step for an average person is about 18 inches, or roughly 0.5 m. The radius of the Earth is 6.38 x 106 m.) 105 steps 108 steps 1011 steps 1015 steps O 1020 steps
A new physics unit of distance is created and called the Zarkov. A student informs you 1 Zarkov (1 Za) is exactly equivalent to 8 inches. Convert 4.44 × 10 5 Z a 3 m i n u t e 2to m 3 h r 2. If hard to read: asking you to convert Zarkov's squared over minutes cubed to meters squared over hours cubed. Answer in E notation without units in the box. I am assuming your output units are m 3 h r 2. Note: for some numbers the computer will convert your E notion to another notation without the E...that will not cost you points. To be clear regarding E notation, I will provide an example of what I'm talking about:
33. If you are at the top of a tower of height h above the surface of the earth, show that the distance you can see along the surface of the earth is approximately s = v2Rh, where R is the radius of the earth. Hints: See figure. Show that h/R = sec 0 – 1; find two terms of the series for sec 0 = 1/ cos 0, and use s = RO. _Thus show that the distance in miles is approximately v3h/2 with h in feet. Rİ
What are the answers for #1 and #2 a, b, and c? Show your complete solutions for each corresponding numbers with 4 significant figures.
Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. A = B = î+ R = î. The net displacement is given by the vector sum: R=A+B. By Pythagorean theorem, the magnitude of the displacement is: IRI= meters. The direction of the resultant displacement is 4= north of east. 7
Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. À = B = The net displacement is given by the vector sum: R = À +B. Ř= By Pythagorean theorem,the magnitude of the displacement is: meters. %3D The direction of the resultant displacement is: north of east.
Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let Å be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. A = B = + The net displacement is given by the vector sum: Ř =Á + B. + By Pythagorean theorem, the magnitude of the displacement is: |Ř = meters. The direction of the resultant displacement is: $ = north of east
Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and in unit vector component form. À= ぐー B = 7+ The net displacement is given by the vector sum: Ř =Á +B. Ř= 7+ By Pythagorean theorem,the magnitude of the displacement is: |Ř = meters. The direction of the resultant displacement is: 3D north of east.