21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 6.4, Problem 6.4CYU
To determine
The reason for using spacecrafts as one of the best ways to study about planets.
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Kepler’s First Law: Elliptical Planetary Orbits:
The solar system major planet in the most elliptical solar orbit is little Mercury, which is the closest planet to the Sun. At Perihelion, Mercury’s distance from the Sun (Rp) is 0.31 AU. At Aphelion, Mercury’s distance from the Sun (Ra) is 0.47 AU.
The intensity of Sunlight (I) that a planet receives from the Sun is inversely proportional to the square of that planet’s distance from the Sun (R). in other words,
I = Constant / R2.
Calculate how much more intense the Sunlight received by Mercury is at perihelion (p) than at aphelion (a):
Rp2 = Ra2 = Ip / Ia = Ra2 / Rp2 =
Voyager 2.
When the Voyager 2 spacecraft was approaching towards its Neptune encounter in
1989, it was 4.5 × 10° km away from the earth. Its radio transmitter, with which it
communicated with us (and we communicated with it), broadcast with a mere 22 Watt
of power at the S-band (2.1 GHz). (Your home wi-fi router emits around 2 Watt at 2.4
GHz wi-fi band). Assuming the Voyager transmitter broadcast equally in all directions,
(a) What signal intensity was received on the earth?
(b) What electric and magnetic field amplitudes were detected?
(c) How many 2.1 GHz photons were arriving per second on a radio-receiver antenna
with a circular cross-section of diameter 34 meters?
Two counter-propagating plane waves
(a) Let E(z, t) = E0 cos(kz – wt)â + E, cos(kz + wt)x. Write E(z, t) in simpler form
and find the associated magnetic field.
(b) For the fields in part (a), find the instantaneous and time-averaged electric and
magnetic field energy densities.
(c) Let E(z, t) = E, cos(kz – wt)x + E,…
1- MODIS is an Earth Observation sensor onboard TERRA spacecraft flying in a near-polar circular orbit with an orbital period of 98.8 minutes. The width of the swath imaged by MODIS is 2330 km.
A- How many orbits does TERRA trace in one day?
B- Assuming that the Earth rotates around its polar axis at a rate of 0.2618 rd/hr and that the equatorial radius is 6378 km, do two consecutive swaths of MODIS overlap at the equator? (hint: the length of an arc = angle in rd * radius)
C- The radius of the latitude circle at 35 deg is 5224.5 km. Do two consecutive swaths of MODIS overlap at latitude 35 deg?
2- An aerostationary orbit for Mars is equivalent to a geostationary orbit for Earth. It is designed to enable a satellite in that orbit to image always the same surface of Mars. Calculate the altitude of an aerostationary orbit assuming that Mars is spherical, that its sidereal rotational period is 1.02595676 Earth days, its equatorial radius is 3389.50 km and its mass is…
Chapter 6 Solutions
21st Century Astronomy
Ch. 6.1 - Prob. 6.1ACYUCh. 6.1 - Prob. 6.1BCYUCh. 6.2 - Prob. 6.2CYUCh. 6.3 - Prob. 6.3CYUCh. 6.4 - Prob. 6.4CYUCh. 6.5 - Prob. 6.5CYUCh. 6 - Prob. 1QPCh. 6 - Prob. 2QPCh. 6 - Prob. 3QPCh. 6 - Prob. 4QP
Ch. 6 - Prob. 5QPCh. 6 - Prob. 6QPCh. 6 - Prob. 7QPCh. 6 - Prob. 8QPCh. 6 - Prob. 9QPCh. 6 - Prob. 10QPCh. 6 - Prob. 11QPCh. 6 - Prob. 12QPCh. 6 - Prob. 13QPCh. 6 - Prob. 14QPCh. 6 - Prob. 15QPCh. 6 - Prob. 16QPCh. 6 - Prob. 17QPCh. 6 - Prob. 18QPCh. 6 - Prob. 19QPCh. 6 - Prob. 20QPCh. 6 - Prob. 21QPCh. 6 - Prob. 22QPCh. 6 - Prob. 23QPCh. 6 - Prob. 24QPCh. 6 - Prob. 25QPCh. 6 - Prob. 26QPCh. 6 - Prob. 27QPCh. 6 - Prob. 28QPCh. 6 - Prob. 29QPCh. 6 - Prob. 30QPCh. 6 - Prob. 31QPCh. 6 - Prob. 32QPCh. 6 - Prob. 33QPCh. 6 - Prob. 34QPCh. 6 - Prob. 35QPCh. 6 - Prob. 36QPCh. 6 - Prob. 37QPCh. 6 - Prob. 38QPCh. 6 - Prob. 39QPCh. 6 - Prob. 40QPCh. 6 - Prob. 41QPCh. 6 - Prob. 42QPCh. 6 - Prob. 43QPCh. 6 - Prob. 44QPCh. 6 - Prob. 45QP
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- K What is the wavelength (in nm) of the most intense radiation emitted from the surface of Mercury at high noon? (Hint: Use Wien's law, Amax = 2.90 x 10° m: K %3D T (in K) nm In which band of the electromagnetic spectrum is that wavelength? (Hint: Examine the following figure.) Visible light Short wavelengths Long wavelengths 4 x 107 5x 107 6x 107 7x 10meters (400 nm) (500 nm) (600 nm) /(700 nm) Wavelength (meters) 10 12 10 10 10 104 102 1 102 104 Gamma- ray Ultra- violet Micro- Radio X-ray Infrared wave UHF VHF FM AM a Opaque Visual window Radio window Transparent Short Wavelength Long b O gamma-ray O X-ray O ultraviolet O visual O infrared O microwave O radio оооо о оо Opacity of Earth's atmospherearrow_forwardThe planet Uranus was discovered in 1781, and Neptune, the next planet outward from the Sun, was discovered in 1846. Imagine you're an astronomer in 1846, and you start wondering if there's another planet out beyond Neptune. You decide to try and discover its existence using the same method that was used for Neptune. How will you do this? Group of answer choices You'll recruit a large number of astronomers to use their telescopes to carefully scan the sky in directions that are far from the ecliptic. The regions around the north and south celestial poles will probably be the best "hunting grounds" for the new planet. You'll examine Uranus and Neptune very carefully, on every clear night, for several years, to see if you can find any evidence that sunlight has been reflected off of the `new' planet, then off of Uranus or Neptune, before arriving on Earth. On rare occasions when Neptune passes in front of the Sun, as seen from Earth, you'll look carefully at the Sun (with a safe…arrow_forwardYou decide to go on an interstellar mission to explore some of the newly discovered extrasolar planets orbiting the star ROTOR. Your spacecraft arrives in the new system, in which there are five planets. ROTOR is identical to the Sun (in terms of its size, mass, age and composition). From your observations of these planets, you collect the following data: Density Average Distance from star (AU] Planet Mass Radius Albedo Temp. [C] Surf. Press. MOI Rotation [Earth = 1] (Earth = 1] [g/cm³] [Atm.] Period (Hours] Factor SIEVER EUGENIA 4.0 0.001 2.0 0.1 5.0 1.0 0.3 20 0.8 N/A 3.0 0.2 N/A 0.3 0.4 0.35 20 10 500 1000 5.0 4.0 0.5 0.8 0.4 0.7 -50 MARLENE CRILE 1.0 1.0 3.0 8.0 1,5 0.0 0.50 0.50 0.25 150 0.4 JANUS 100 12 0.1 10 -80 0.2 200 Figure 1: А Rotor 850 890 900 Wavelength (nm) A Sun В C 860 900 910 Wavelength (nm) 2414 a asarrow_forward
- Mercury'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_forwardA surprisingly large number of people in the world don’t believe that astronauts havewalked on the Moon. They believe the Moon landing to have been a hoax. One argumentthey use is that if there are astronaut footprints on the Moon, we should be able to seethem using a powerful telescope. The fact that we do not, they say, is evidence that theywere never there.The Lunar Reconnaissance Orbiter (LRO) is a NASA robotic spacecraft currently orbitingthe Moon. The LRO gets as close as 35 km to the Moon’s surface. The diameter ofthe camera’s primary mirror is 195 mm. If the camera is sensitive to optical light at awavelength of 600 nm, show that it would not be able to spatially resolve a foot print ofphysical length 30 cm when it is 35 km above the Moon’s surface.Tip: You’ll need to calculate the angular size of the footprint, as seen from a height of35 km. θ = S/D, where S is the physical size of the footprint and D = 35 km, is theangular size of the footprint in radians.arrow_forwardWhile looking through the Mt. Palomar telescope, you discover a large planetary object orbited by a single moon. The moon orbits the planet every 7.35 hours with the centers of the two objects separated by a distance roughly 2.25 times the radius of the planet. Fellow scientists speculate that the planet is made of mostly iron. In fact, the media has dubbed it the ''Iron Planet'' and NASA has even named it Planet Hephaestus after the Greek god of iron. But you have your doubts. Assuming the planet is spherical and the orbit circular, calculate the density of Planet Hephaestus.arrow_forward
- If we send astronauts to Mars, there will be a time delay anytime we send or receive messages to them here on Earth. Given that Mars is an average of 54.6 million km away from Earth, how long is this time delay for a 2-way 'round-trip' communication - sent to Earth, then back to Mars? (this might be important in emergency situations) answer choices a)About 4 minutes. b)About 30 seconds. c)About 10 seconds. d)About 6 minutes.arrow_forwardQuestion 7 What type of mission collects information about multiple planets? Sample returns. Rovers. Flybys. Atmospheric probes. Question 8 Why are neutrinos so difficult to detect? There are very few of them, so collecting enough to study takes a long time. They are theoretical and may not exist. They move so fast they pass right through the telescope. They don't interact strongly with matter, so they will not cause a reaction on a CCD imager.arrow_forwardWhich of the following is least reasonable regarding the "water hole"? Group of answer choices It consists of frequencies which are greater than the frequencies of atmospheric emissions. It relates to the natural frequencies of vibration of hydroxyl (OH) and hydrogen (H), respectively. It occurs in that part of the electromagnetic spectrum where the galactic "noise" from stars and interstellar clouds is minimized. It is considered the "electromagnetic oasis" for interstellar communication. It corresponds to wavelengths in the 18-21 cm range.arrow_forward
- 2. How long would a radar signal take to complete a round-trip between Earth and Mars when the two planets are 0.7 AU apart?arrow_forwardWhich of these things did the Voyager spacecraft discover about Enceladus in the early 1980s, indicating that it is somewhat unusual among planetary bodies in our solar system? Check the TWO items that apply. a It has a thick atmosphere, made mostly of nitrogen. b It has the darkest, least reflective surface of all the known planetary bodies. c It is the brightest (i.e. most reflective) object in the solar system. d The entire surface is more heavily-cratered than any other body in our solar system. e Its surface is very smooth in some places.arrow_forwardIn Table 2, there is a list of 15 planets, some of which are real objects discovered by the Kepler space telescope, and some are hypothetical planets. For each one, you are provided the temperature of the star that each planet orbits in degrees Kelvin (K), the distance that each planet orbits from their star in astronomical units (AUs) and the size or radius of each planet in Earth radii (RE). Since we are concerned with finding Earth-like planets, we will assume that the composition of these planets are similar to Earth's, so we will not directly look at their masses, rather their sizes (radii) along with the other characteristics. Determine which of these 15 planets meets our criteria of a planet that could possibly support Earth-like life. Use the Habitable Planet Classification Flow Chart (below) to complete Table 2. Whenever the individual value you are looking at falls within the range of values specified on the flow chart, mark the cell to the right of the value with a Y for…arrow_forward
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