21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 4, Problem 22QP
To determine
Find the observational quantities needed to make estimate an object’s mass.
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Why are all large celestial bodies (stars, planets, larger moons) very nearly spherical in shape?
a
because of the centrifugal force from the body's rotation
b
because of tidal forces
c
because gravity tries to pull every part of the celestial body to the center
d
because of the pressure from the heat in the body's core
1. Planet A has an orbital period of 12 years and radius that is 0.033 times the radius of the star. Calculate the fractional dip of the star brightness in the case that planet A is transiting. Give the answer as a number. Quote the formula you use and explain any assumptions you have to make.
2. Planet B has an orbital period of 1 year and is located closer to its star than planet A. You succeed in detecting planet B with the radial velocity technique as well! From this measurement you calculate a minimum mass of planet B to be 75% that of the Earth. (a) Since you detect the planet with both transit method and radial velocity method, what do you know about the inclination of the planetary system? (b) Given this inclination, estimate the true mass of planet B (in units of Earth mass). You do not need to do a detailed calculation, just explain the argument.
3. You also measure the radius of planet B to be the same as Earth, one Earth radius. (a) How does the density of planet B compare…
Use Kepler's 3rd Law and the small angle approximation.
a) An object is located in the solar system at a distance from the Sun equal to 41 AU's . What is the objects orbital period?
b) An object seen in a telescope has an angular diameter equivalent to 41 (in units of arc seconds). What is its linear diameter if the object is 250 million km from you? Draw a labeled diagram of this situation.
Chapter 4 Solutions
21st Century Astronomy
Ch. 4.1 - Prob. 4.1ACYUCh. 4.1 - Prob. 4.1BCYUCh. 4.2 - Prob. 4.2CYUCh. 4.3 - Prob. 4.3CYUCh. 4.4 - Prob. 4.4CYUCh. 4 - Prob. 1QPCh. 4 - Prob. 2QPCh. 4 - Prob. 3QPCh. 4 - Prob. 4QPCh. 4 - Prob. 5QP
Ch. 4 - Prob. 6QPCh. 4 - Prob. 7QPCh. 4 - Prob. 8QPCh. 4 - Prob. 9QPCh. 4 - Prob. 10QPCh. 4 - Prob. 11QPCh. 4 - Prob. 12QPCh. 4 - Prob. 13QPCh. 4 - Prob. 14QPCh. 4 - Prob. 15QPCh. 4 - Prob. 16QPCh. 4 - Prob. 17QPCh. 4 - Prob. 18QPCh. 4 - Prob. 19QPCh. 4 - Prob. 20QPCh. 4 - Prob. 21QPCh. 4 - Prob. 22QPCh. 4 - Prob. 23QPCh. 4 - Prob. 24QPCh. 4 - Prob. 25QPCh. 4 - Prob. 26QPCh. 4 - Prob. 27QPCh. 4 - Prob. 28QPCh. 4 - Prob. 29QPCh. 4 - Prob. 30QPCh. 4 - Prob. 31QPCh. 4 - Prob. 32QPCh. 4 - Prob. 33QPCh. 4 - Prob. 34QPCh. 4 - Prob. 35QPCh. 4 - Prob. 36QPCh. 4 - Prob. 37QPCh. 4 - Prob. 38QPCh. 4 - Prob. 39QPCh. 4 - Prob. 40QPCh. 4 - Prob. 41QPCh. 4 - Prob. 42QPCh. 4 - Prob. 43QPCh. 4 - Prob. 44QPCh. 4 - Prob. 45QP
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- 3.6 A spacecraft is approaching Venus with V = 10 km/s and b = 10,000 km. What will be the periapsis radius at Venus? Solution: 7266 km.arrow_forwardPart 3 1. The diameter of the Sun is 1,391,400 km. The diameter of the Moon is 3,474.8 km. Find the ratio, r= Dsa/Dsvan between the sizes. 2. From the point of view of an obs erver on Eanth (consider the Earth as a point-like object), during the eclipse, the Moon covers the Sun exactly. Sketch a picture to illustrate this fact. Use a nuler to get a straight line. Your drawing does not need to be in scale. 3. The Sun is 1 Astronomical Unit (AU) away from the Earth. Find the distance between the Earth and the Moon in AU's using the ratio of similar triangles. Show your work. DEM= AU. Convert this to kilometers. Use 1 AU = 149,600,000 km. DEM = km.arrow_forwardMercury's orbit ranges from 46 to 70 million km from the Sun, while Earth orbits at about 150 million km. a. The Sun has a 30-arc-minute diameter viewed from Earth; what range of sizes does it have when viewed from Mercury? When Mercury is 46 million km from the Sun, the Sun has a diameter of When Mercury is 70 million km from the Sun, the Sun has a diameter of arc-minutes. arc-minutes. b. At Mercury's orbital extremes, how many times stronger is the Sun's radiation on Mercury than on Earth? At 46 million km, the Sun's radiation is times stronger than on Earth. At 70 million km, the Sun's radiation is times stronger than on Earth.arrow_forward
- For centuries, astronomers wondered whether comets were true celestial objects, like the planets and stars, or a phenomenon that occurred in the atmosphere of Earth. Describe an experiment to determine which of these two possibilities is correct.arrow_forward1. a) Why is it necessary to have a long baseline when using triangulation to measure the distances to objects in space? b) Of all visible objects in the celestial sphere, which appears to move the least? Why?arrow_forwardQuestion 1 (Total: 30 points) a. What is a repeat ground-track orbit? b. Explain why repeat ground-track and Sun-synchronous orbits are typically used for Earth observation missions. c. The constraint for a Sun-synchronous and repeat ground-track orbit is given by T = 286, 400, where I is the orbital period in seconds, m the number of days and k the number of revolutions. Explain why this is, in fact, a constraint on the semi-major axis of the orbit.arrow_forward
- The angle on the sky between Venus and the Sun is measured to be 46.3° when Venus is at greatest eastern elongation. What is the distance of Venus from the Sun, measured in AU? Choose the answer below that most closely matches your answer. Select one: а. 1.763 AU O b. 0.587 AU Ос. 0.652 AU O d. 0.846 AU Ое. 0.723 AUarrow_forwardCould you find the Mass of the Sun using the slope of the of T2 versus a3, using the values that are in units of years and AU? Explainarrow_forwardSolve the following problem: Two stars, named A and B, each with a mass equal to the Sun's mass are in orbit around each other. If the distance between the two stars is 1.0 AU. What is the period of their orbit? Describe each step in solving the problem:arrow_forward
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