Astronomers observe a small moon of a planet and find that its average orbital radius is 5.67 x10^8 m, while its average orbital speed is 2.50 km/s (a) With reference to Kepler's first law of planetary motion, explain why the small moon may not be exactly 5.67 x 10^8 m away from the planet at all times. (b) Find the orbital period of the moon and hence the mass of the planet being orbited by the moon.
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Astronomers observe a small moon of a planet and find that its average orbital radius is 5.67 x10^8 m, while its average orbital speed is 2.50 km/s
(a) With reference to Kepler's first law of planetary motion, explain why the small moon may not be exactly 5.67 x 10^8 m away from the planet at all times.
(b) Find the orbital period of the moon and hence the mass of the planet being orbited by the moon.
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- Problem 5: Suppose you are told that a satellite orbiting the Earth has a orbital period of 0.85 hours. a)Using the orbital characteristics of the Moon (RM = 3.84 × 105km and TM = 0.0748 y), use Kepler's laws to calculate the orbital radius for the satellite, in kilometers. b)What is unreasonable about this result?MultipleChoice :1) This radius is unreasonable because it is smaller than the orbital radius of the Moon.2) There is nothing unreasonable about the result.3) This radius is unreasonable because it is greater than the radius of the Earth.4) This radius is unreasonable because it is greater than the orbital radius of the Moon.5) This radius is unreasonable because it is smaller than the radius of Earth.Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 435 km above the surface of the Moon, where the acceleration due to gravity is 1.08 m/s2. The radius of the Moon is 1.70 x 10 m. (a) Determine the astronaut's orbital speed. 1.67e x m/s (b) Determine the period of the orbit. 4.5563 XSThe earth is 150 × 10^9 m from the Sun. Earth and Sun masses are 5.97 × 10)^24 ?? and 1.99 × 10^30 ??, respectively. (a) Find the gravitational attraction between the Earth and the Sun. (b) Find the orbital period of the Earth around the Sun based on these numbers.
- A landing craft with mass M is in a circular orbit a distance d above the surface of a planet. The period ofthe orbit is T. The astronauts in the landing craft measure the diameter of the planet to be D. The landing craft sets down at the north pole of the planet. a)What is the weight of a person of mass m as they step out onto the plant’s surface? b)Suppose days on this planet last t seconds (i.e. the planet rotates about its axis once every t seconds).Write an expression for the astronaut’s perceived weight at the equator in terms of their weight at the north pole. (Hint: think about centripetal force)Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 x 1011 solar masses. A star orbiting near the galaxy's periphery is 5.7 x 104 light years from its center. (For your calculations, assume that the galaxy's mass is concentrated near its center.) (a) What should the orbital period of that star be? yr (b) If its period is 5.2 x 10 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar massesCalculate the period of a satellite orbiting a planet with the mass 8.7 x 1022 kg given the height of the satellite's orbit is 300 km and the radius of the planet is 2000 km. Provide your answer in Sl units.
- Suppose an asteroid named Sparty has been discovered revolving around the Sun on a circular orbit with radius rs. Calculate the period of Sparty's orbit, in years. DATA for the orbit radii: Earth re 1.50×10¹¹ m; = Sparty rs = 2.75×1011 m; A: 2.482 B: 2.805 C: 3.170 D: 3.582 E: 4.047 OF: 4.574 G: 5.168 H: 5.840 Submit Answer Tries 0/99Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 x 10¹¹ solar masses. A star orbiting near the galaxy's periphery is 5.9 x 104 light years from its center. (For your calculations, assume that the galaxy's mass is concentrated near its center.) What should the orbital period of that star be? yr If its period is 5.8 x 107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar massesScientists have discovered a distant planet with a mass of 8.2x1023 kg. The planet has a small moon that orbits with a period of 6 hours and 36 minutes. Use only this information (and the value of G) to calculate the radius of the moon's orbit (in units of 106 m).