Calculate the fraction of time a spacecraft spends in daylight given a celestial body with a radius 5,709 km at an altitude of 686 km. Use the extreme case (minimum alpha) when the angle between the orbit plane and the direction of the sunlight is 0.
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- 1. 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?What is the wavelength of maximum intensity (in nm) and the total energy emitted (in J/s/m2) by a celestial object at 9 K above absolute zero?The temperature (T) of a planet (ignoring any other sources of heating) is solely a function of how far away the Sun is (d) and how bright it is (luminosity, L); planets are also reflective, so the light that they reflect (A) will not change their temperature: 1/4 L(1-A) T = 16σπα? o here is just a constant, like TT. 10. How much hotter is the Earth at perihelion than at aphelion? To answer this, solve for the ratio TT, where d, = r, (the perihelion distance) and d, = r, (the aphelion distance). You should have found that r, = 1.034rp. If you did not, use this new value and redo the previous problems.
- Earth is about 150 million kilometers from the Sun (1 Astronomical Unit, or AU), and the apparent brightness of the Sun in our sky is about 1300 watts/m^2. Using these two facts and the inverse square law for light, determine the apparent brightness that we would measure for the Sun if we were located at the following positions. a) At the orbit of Venus (67 million km from the Sun). b) At the orbit of Jupiter (780 million km from the Sun). c) At the mean distance of Pluto (40 Astronomical Units).Part 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.What is the wavelength of maximum intensity (in nm) and the total energy emitted (in J/s/m2) by a celestial object at 7 K above absolute zero? wavelength of maximum intensity? 414285.71 Total Energy? -----
- Recall that Hubble’s Law is given by V=HR; this means that H has units of inverse seconds (1/sec). A convenient laboratory set of units is to give H in km per sec per megaparsec. A parsec is 3.26 light years and the speed of light is 3 X 105 km/sec. Use 3.156 X 107 sec/yr. The first data off the then new Hubble Space telescope suggested a value of H equal to 108 km per sec per megaparsec. What is H in inverse seconds? Hint divide by the number of km in a megaparsec.Earth is about 150 million kilometers from the Sun (1 Astronomical Unit, or AU), and the apparent brightness of the Sun in our sky is about 1300 watts/m2. Using these two facts and the inverse square law for light, determine the apparent brightness that we would measure for the Sun if we were located at the following positions. a) At the orbit of Jupiter (780 million km from the Sun).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.
- Your research team analysis the light of a mysterious object in space. By using a spectrometer,you can observe the following spectrum of the object. The Hα line peak is clearly visible. Answer the questions from given graph (a) Mark the first four spectral lines of hydrogen (Hα, Hβ, Hγ, Hδ) in the spectrum.(b) Determine the radial velocity and the direction of the object’s movement.(c) Calculate the distance to the observed object.(d) What possible type of object is your team observing?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…Appendix I lists some of the nearest stars. Are most of these stars hotter or cooler than the Sun? Do any of them emit more energy than the Sun? If so, which ones?