You send a probe to orbit Mercury at 195 km above the surface. What orbital velocity (in km/s) is needed to keep it in orbit? (The mass of Mercury is 3.30 x 1023 kg, and the radius of Mercury is 2.44 x 10° km.)
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- Neptune orbits the Sun with an orbital radius of 4.495 x 10^12 m. If the earth to sun distance 1A.U. = 1.5 x 10^11 m, a) Determine how many A.U.'s is Neptune's orbital radius (Round to the nearest tenth). b) Given the Sun's mass is 1.99 x10^30 kg, use Newton's modified version of Kepler's formula T^2 = (4pi^2/Gm(star)) x d^3 to find the period in seconds using scientific notation. (Round to the nearest thousandth). C) Convert the period in part b) to years (Round to the nearest tenth)You are a rover pilot on the crew of the initial exploration team sent to Kepler 22b,the first extrasolar planet discovered within the habitable zone of a sun-like star. Thescience team recently discovered liquid water on the surface. (Hurrah!) Your rover isat point A on the shore of a circular lake with radius 4 km collecting samples. Thescience team wants to send your rover to a point C diametrically opposite A. Therover can drive around the circumference of the lake at a rate of 4 km per hour andfly over the lake at a rate of 3 km per hour.(a) How long will it take the rover to fly across the lake?(b) How long will it take the rover to drive around the shore of the lake?You could also fly at an angle θ along a chord inside the circular lake, andcomplete the rest of the path driving along the circumference of the lake.(c) Find the length of the chord in terms of θ. How long will it take the drone totraverse the chord?(d) Find the length of the remaining shoreline after the cord in…Since 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?
- The Small Magellanic Cloud is a dwarf galay orbiting the Milky Way at a distance of 50 kiloparsecs from its center, on a circular orbit. It is moving at a velocity. rolative to the Milky Way, of 207 km/s. What is the mass of the Milky Way, in units of solar masses, inside the Cloud's orbit? B !! 245 If'a quasar emits 10^(10) times the Sun's luminosity, converting 10% of the mass of the material it eats into radiation, how many stars (ach of the Sun's mans) must it consume per year?What is the value of the IR transmission factor (f) for a Venus-like planet, if the measured average surface temperature is 706 K? Assume the following values for the planet: E, = 2.60x10³ W m² and a = 0.71. Would the average temperature increase or decrease if f decreased?Moon is at the distance 384400 km from Earth and orbits the Earth every ∼28 days. Ifthe radius of the Moon is 1737 km (consider it to be spherical), what is the area of themoon as measured by the observer on Earth? (Hint: Length contraction)
- We would like to be able to make meaningful interpretations of variations in the acceleration due to gravity, g, as small as 0.1 mgal. How accurate must our knowledge of the latitude of our gravity stations be? (A “gravity station" is just a location at which you make a gravity measurement.) You can assume your latitude is 45°.The speed of light is exactly e = 299792458 m - s1. (Also written 299, 792, 458 m - s-1 or 2.99792458 × 10°m - s1. This is exact because it is the definition of the metre.) It takes light 8.3 minutes to get from the sun to the earth. Assuming that the earth's orbit is exactly circular (an approximation) and that its speed is constant, and using the data in this question, calculate the speed of the earth in its orbit around the sun in km · hr. Practise writing your conversions clearly using the 'multiply by 1' technique. Speed of the earth =_ km per hour. Write your answer in standard (not scientific) notation, i.e. without using exponents, and without using commas. However, remember to use the correct number of significant figures. (Hint: which is the least precise of the given data?) Do not include units.3) A spacecraft is in a circular orbit of 180 km altitude and inclination 30 deg. What is the spacing in kilometers, between successive ground tracks at the equator, including the effect of Earth's oblateness (that is, including the J2 effect). Ans: 2511.4 km
- A Mars observing satellite is orbiting on a circular orbit at an altitude of 1000 km above Mars’s equator. Find satellite’s acceleration and velocity as seen from a deep space communications station located on Earth’s equator, when they are on a direct line of sight (see the Fig. below). Assume for simplicity that planetary orbits and their equatorial planes are all in the plane of ecliptic (that is all, motion is in a 2D plane). Earth radius is 6300 km, Mars radius 3400 km, Mars mass 6.4x1023 kg. Assume that all circular motions are counter clockwise (i.e., orbital motions of Earth and Mars, Earth spin, and satellite orbital motion).A sateltle orbits at a height of 6,000 km above the earth's surface. REarth = 6.38 x 10° m, mEarth = 5.98 x 1024 kg. What is this satelite's speed, in km/s (kilometer per second)? Use G = 6.67 x 10-11 N-m2/kg2. Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. A Moving to another question will save this response.How long would it take an instruction to a Martian rover to travel to Mars from NASA site on Earth when Earth and Mara are 68.4 million km apart?