The mass of the Hubble spacecraft is 1.11 x 10ʻkg. Determine the weight of the spacecraft at the orbital altitude, which is 560km above the Earth's surface. The mass of the Earth is 5.972 x 1024kg and the radius of the Earth is 6370 km.
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- Compare the magnitude of the gravitational field at the surface of the earth due to the moon with that due to the sun. (Hint: The mass of the sun is 1.99 x 10^30 kg, the mass of the moon is 7.36 x 10^22 kg, and the distance from the surface of the earth to the moon is 3.78 10^8 m.)The Moon has a mass 7.35 x 1022 kg of and a radius of 1740 km. Air resistance can be neglected on the Moon. G = 6.67 x 10-11 m3 kg-1 s-2 is the universal gravitational constant. (a) If a ball is launched upwards from the surface of the moon with an initial speed of 1.15 km/s, what height maximum height above the surface of the moon will it reach? Give your answer in kilometers. (b) What is the escape speed of the moon? Give your answer in km/s.During a solar eclipse, the Moon is positioned directly between Earth and the Sun. The masses of the Sun, Earth, and the Moon are 1.99×10^30 kg, 5.98×10^24 kg, and 7.36×10^22 kg, respectively. The Moon's mean distance from Earth is 3.84×10^8 m, and Earth's mean distance from the Sun is 1.50×10^11 m. The gravitational constant is G=6.67×10^−11 N·m2/kg^2. Find the magnitude F of the net gravitational force acting on the Moon during the solar eclipse due to both Earth and the Sun.
- Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 1011 solar masses. A star orbiting near the galaxy's periphery is 5.6 x 104 light-years from its center. (a) What should the orbital period (in y) of that star be? y (b) If its period is 5.3 x 107 years instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way. solar massesThe acceleration due to gravity at the moon's surface is 1.67 ms^-2. If the radius of the moon is 1.74 x 10^6 m. Calculate the mass of the moon. Use the known value of G.The gravitational acceleration constant gx on Planet X can be approximated by determining the acceleration of an object assuming Newton's Law of Universal Gravitation. If gx = 3.8 m/s^2 , G = 6.7 x 10^-11 Nm^2/kg^2, and Planet X's radius is 4000 km, what is the approximate mass of planet X? Give answer in kg.
- Two spherical objects have a combined mass of 160 kg . The gravitational attraction between them is 7.61×10−6 NN when their centers are 21.0 cm apart. What is the mass of the heavier object? What is the mass of the lighter object?An Earth satellite has an orbital period of 5.3 h. What is its orbital radius? (ME = 5.98 x 1024 kg)The International Space Station (ISS) is a space station orbiting the earth above the ground. If the radius of the earth is 3,958.8 miles, mass of earth is 5.972 x 10 24 kg, the period of the ISS at the orbit around the earth is 9.16 hours, can you calculate what is the distance from the ISS to the surface of the earth, in unit of miles? Use G=6.674 x 10 -11 Nm2/kg2. Write your answer in pure numbers, for example, 4567.8. Please keep at least on digit after the decimal point.
- Problem 6: Two satellites are in circular orbits around a planet that has radius 9 x 106 m. One satellite has mass 68.0 kg, orbital radius 7 x 107 m, and orbital speed 4800 m/sec. The second satellite has mass 84.0 kg and orbital radius 3 × 107 m. What is the orbital speed of this second satellite? Answer: 7332.1 m/sec. Problem 7: Planets Beyond the Solar System. On October 15, 2001, a planet was discovered orbiting around the star HD 68988. Its orbital distance was measured to be 1.05 × 1010 m from the center of the star, and its orbital period was estimated at 6.3 days = 5.44 × 105 sec . What is the mass of HD 68988? Express your answer in kilograms and in terms of our sun's mass (Msun =1.99 × 1030 kg) Answer: M = 2.31 × 1030 p kg. = 1.16MSun-The 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.The International Space Station (ISS) completes one orbit of Earth in 92 minutes. What is the radius of the orbit in kilometers (km)? You may assume the orbit is circular. The mass of the ISS is 420 kg, and the mass of the Earth is 6.0×10246.0×1024kg. Newton’s gravitational constant is 6.7×10−11N⋅m2kg26.7×10−11kg2N⋅m2.