21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 3, Problem 24QP
To determine
If Kepler lived in Mars does he arrived the same empirical law of motion of the planets.
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How do you express the coordinates of an object in cylindrical and spherical coordinates when its coordinates in a Cartesian reference frame are (3, 4, 5). Assume that all three coordinate systems share a common origin.
Newton’s law of gravitation and the formula for centripetal acceleration can be used to show that:
T^2=(4π^2/Gms)R^3 where G is the universal constant of gravitation and MS is the mass of the Sun. Take logarithms to base 10 of both sides of the equation to complete the expression for 2 lg T.2 lg T = ……………… × lg R + ……………………
Mars' period (its "year") was noted by Kepler to be about 687 days (Earth days), which is (687d /
365 d) = 1.88 yr. Determine the distance of Mars from the Sun using the Earth as reference.
(The distance of
Earth from the Sun is 1.50 x 10 m)
!3!
Thu
TMS
IMS
TE
TES
TES
TE
2 28 x 10 m
TES
yr
After reading and understanding the concept Gravity, please do the following problems:
1. What keeps a satellite up in its orbit around the Earth?
Chapter 3 Solutions
21st Century Astronomy
Ch. 3.1 - Prob. 3.1ACYUCh. 3.1 - Prob. 3.1BCYUCh. 3.2 - Prob. 3.2CYUCh. 3.3 - Prob. 3.3CYUCh. 3.4 - Prob. 3.4CYUCh. 3 - Prob. 1QPCh. 3 - Prob. 2QPCh. 3 - Prob. 3QPCh. 3 - Prob. 4QPCh. 3 - Prob. 5QP
Ch. 3 - Prob. 6QPCh. 3 - Prob. 7QPCh. 3 - Prob. 8QPCh. 3 - Prob. 9QPCh. 3 - Prob. 10QPCh. 3 - Prob. 11QPCh. 3 - Prob. 12QPCh. 3 - Prob. 13QPCh. 3 - Prob. 14QPCh. 3 - Prob. 15QPCh. 3 - Prob. 16QPCh. 3 - Prob. 17QPCh. 3 - Prob. 18QPCh. 3 - Prob. 19QPCh. 3 - Prob. 20QPCh. 3 - Prob. 21QPCh. 3 - Prob. 22QPCh. 3 - Prob. 23QPCh. 3 - Prob. 24QPCh. 3 - Prob. 25QPCh. 3 - Prob. 26QPCh. 3 - Prob. 27QPCh. 3 - Prob. 28QPCh. 3 - Prob. 29QPCh. 3 - Prob. 30QPCh. 3 - Prob. 31QPCh. 3 - Prob. 32QPCh. 3 - Prob. 33QPCh. 3 - Prob. 34QPCh. 3 - Prob. 35QPCh. 3 - Prob. 36QPCh. 3 - Prob. 37QPCh. 3 - Prob. 38QPCh. 3 - Prob. 39QPCh. 3 - Prob. 40QPCh. 3 - Prob. 41QPCh. 3 - Prob. 42QPCh. 3 - Prob. 43QPCh. 3 - Prob. 44QPCh. 3 - Prob. 45QP
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- Kepler’s Law relates the period T ( in a sec) of a satellite to the distance from the center of the earth r (in m) to some physical constants as shown: T2 = (2π/ G ME) r3 Where G = Universal Constant of Gravitation and ME is the mass of the earth. A stationary satellite is one that circles the earth in a circular orbit but stays exactly above the same spot on the earth. Calculate the distance above the earth in m for this “geo-synchronous satellite” to orbit, then convert that height to miles.arrow_forwardA planet with mass 9.69x1023 kg orbits a star with mass 9.21x1030 kg. The orbit is circular, and the distance from the planet to the sun is 225x106 km. What is the length of a year on this planet? Give your answer in earth years (1 earth year = 31,557,600 seconds).arrow_forwardMars has an orbital radius of 1.523 AU and an orbital period of 687.0 days. What is its average speed v in SI units? (1 AU is the astronomical unit, the mean distance between the Sun and the Earth, which is 1.496×1011 m) a. 0.00221 AU/day b. 3838 m/s c. 0 d. 1.28×10−9 m/sarrow_forward
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