Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 3, Problem 1CLC
To determine
The estimated size of the Sun if Aristarchus had estimated the Sun to be
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d. Diameter of the Sun
I h
A
d.
Standing on the beach at sunset, you extend the tip of your finger at your full arm length from
your face, covering the Sun. Upon moving your finger around, you find that only about half of its
width is needed to completely cover the Sun's diameter. You measure your finger width to be 0.5
inches. You know your arm length to be 28.0 inches. You have be told that the Sun is
approximately 93 million miles away. Use this information to determine the approximate
diameter of the Sun, filling in the table below with the proper quantities measure in meters.
1 = ½ finger
g = eye level
height
d = object
h = Diameter
f= object
height from
level to top of eye level
X = Arm
A =
angle
width
length
distance
from eye
of the Sun
object
The Sun occupies an angle of approximately 0.5 degrees to us on Earth, at a distance of 150 million kilometers from the Sun. Given this information, calculate the Sun's radius.
Suppose, hypothetically, that the Earth orbited the Sun at half its current distance. (That is, at 1/2 AU instead of 1 AU). What would be the length of the year? What else would be different?
Chapter 3 Solutions
Universe
Ch. 3 - Prob. 1CCCh. 3 - Prob. 2CCCh. 3 - Prob. 3CCCh. 3 - Prob. 4CCCh. 3 - Prob. 5CCCh. 3 - Prob. 6CCCh. 3 - Prob. 7CCCh. 3 - Prob. 8CCCh. 3 - Prob. 9CCCh. 3 - Prob. 10CC
Ch. 3 - Prob. 11CCCh. 3 - Prob. 12CCCh. 3 - Prob. 13CCCh. 3 - Prob. 14CCCh. 3 - Prob. 1CLCCh. 3 - Prob. 1QCh. 3 - Prob. 2QCh. 3 - Prob. 3QCh. 3 - Prob. 4QCh. 3 - Prob. 5QCh. 3 - Prob. 6QCh. 3 - Prob. 7QCh. 3 - Prob. 8QCh. 3 - Prob. 9QCh. 3 - Prob. 10QCh. 3 - Prob. 11QCh. 3 - Prob. 12QCh. 3 - Prob. 13QCh. 3 - Prob. 14QCh. 3 - Prob. 15QCh. 3 - Prob. 16QCh. 3 - Prob. 17QCh. 3 - Prob. 18QCh. 3 - Prob. 19QCh. 3 - Prob. 20QCh. 3 - Prob. 21QCh. 3 - Prob. 22QCh. 3 - Prob. 23QCh. 3 - Prob. 24QCh. 3 - Prob. 25QCh. 3 - Prob. 26QCh. 3 - Prob. 27QCh. 3 - Prob. 28QCh. 3 - Prob. 29QCh. 3 - Prob. 30QCh. 3 - Prob. 31QCh. 3 - Prob. 32QCh. 3 - Prob. 33QCh. 3 - Prob. 34QCh. 3 - Prob. 35QCh. 3 - Prob. 36QCh. 3 - Prob. 37QCh. 3 - Prob. 38QCh. 3 - Prob. 39QCh. 3 - Prob. 40QCh. 3 - Prob. 41QCh. 3 - Prob. 42QCh. 3 - Prob. 43QCh. 3 - Prob. 44QCh. 3 - Prob. 46QCh. 3 - Prob. 47QCh. 3 - Prob. 48QCh. 3 - Prob. 49QCh. 3 - Prob. 50QCh. 3 - Prob. 53Q
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- Give four ways to demonstrate that Earth is spherical.arrow_forwardThe day on Mars is 1.026 Earth-days long. The martian year lasts 686.98 Earth-days. The two moons of Mars take 0.32 Earth-day (for Phobos) and 1.26 Earth-days (for Deimos) to circle the planet. You are given the task of coming up with a martian calendar for a new Mars colony. Would a solar or lunar calendar be better for tracking the seasons?arrow_forwardThinking about the Scale of the Solar System As we discussed, the radius of the Earth is approximately 6370 km. The Sun, on the other hand, is approximately 700,000 km in radius and located, on average, one astronomical unit (1 au=1.5x108 km) from the Earth. Imagine that you stand near Mansueto Library, at the corner of 57th and Ellis. You hold a standard desk globe, which has a diameter of 12 inches, and you want to build a model of the Sun, Earth, and their separation that keeps all sizes and lengths in proportion to one another. a) How big would the Sun be in this scale model? Give your answer in feet and meters. b) The nearest star to the Solar System outside of the Sun is Proxima Centauri, which is approximately 4.2 light years away (a light year is the distance light travels in one year, or approximately 9.5x1012 km). Given the scale model outlined above, how far would a model Proxima Centauri be placed from you? Give your answer in miles and km.arrow_forward
- A planet's speed in orbit is given by V = (30 km/s)[(2/r)-(1/a)]0.5 where V is the planet's velocity, r is the distance in AU's from the Sun at that instant, and a is the semimajor axis of its orbit. Calculate the Earth's velocity in its orbit (assume it is circular): What is the velocity of Mars at a distance of 1.41 AU from the Sun? What is the spacecraft's velocity when it is 1 AU from the Sun (after launch from the Earth)? What additional velocity does the launch burn have to give to the spacecraft? (i.e. What is the difference between the Earth's velocity and the velocity the spacecraft needs to have?) How fast will the spacecraft be traveling when it reaches Mars? Does the spacecraft need to gain or lose velocity to go into the same orbit as Mars?arrow_forwardThe angle between two lines drawn from a point on Earth to two opposite sides of the Moon make an angle of 0.5 degrees. If you do the same thing for the two opposite ends of Andromeda (as shown above), you find an angle of 5 degrees. Let's assume Andromeda and the Moon are equally far away from our location on Earth (of course that's wrong, but how are we supposed to know?) - then how much larger would the diameter of Andromeda be (as indicated by the arrows at the top), compared to the diameter of the Moon? Pick the answer that's closest to what you get under this hypothetical assumption: A. Equal Diameter B. Twice C. Five times D. Ten timesarrow_forwardFrom a distance of 300 km above the surface of the Moon, what is the angular diameter in arc seconds of an astronaut in a space suit who has a linear diameter of 0.80 m as seen from above?arrow_forward
- The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the Sun. A light-year is the distance that light travels in one year (365 days). How far away, in kilometers, is Proxima Centauri from the Sun?Express your answer using two significant figures.arrow_forwardDione, a moon of Saturn, has an orbital radius of 377,400 km, and an orbital period of about 2.737 Earth days. Find the orbital period of Rhea, another moon of Saturn, which has an orbital radius of 527,040 km. Find the period in Earth days. Round to the nearest hundredth. Don't worry about putting the unit, just put the answer.arrow_forwardThe distance between Jupiter and the sun is usually measured in astronomical units.one astronomical unit is defined as:...arrow_forward
- The Earth is about 12,000 km in diameter. It is therefore how many orders of magnitude wider than you are tall? (i.e., the Earth’s diameter is how many times larger than your height (give an order-of-magnitude estimate)?) (I am 5'2")arrow_forwardRaising a number in scientific notation to a power is easy: (5 x 105)² = (5)² x (105)² = 5 x 5 x 105 x 105 = 25 x 10(5 × 2) = 25 x 1010 = 2.5 x 101¹1 Keeping this in mind, what is the volume of the sun in km³? The radius of the sun is about 7 x 105 km, and the volume of a sphere is 4/3 x Pi x R³. (Use 3.14 for Pi, and enter your answer with two decimal places). km³ 3 What is the average density of the Sun? Density = mass / volume. The mass of the sun is 2.0x10³0 kg. kg/km³arrow_forwardHow would Eratosthenes’s estimate have been different if the sun were actually closer to Earth?arrow_forward
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