he 0. 15 : The masses of two plane ratio 1 : 2. Their radii are in the ratio 1 : 2. The acceleration due to gravity on the planets are in ratio (a) 1:2 (b) 2:1 (c) 3:5 (d) 5:3
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- A satellite of mass 53.6 kg in geosynchronous orbit at an altitude of 3.58 * 10^4 km above the Earths' surface remains above the same spot on the Earth. Assume its orbit is circular. Find the magnitude of the gravitational force exerted by the Earth on the satellite. Hint: The answer is not 526 N.In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?Mass M is divided into two parts xM and (1-x)M. For a given separation, the value of x for which the gravitational attraction between the two pieces becomes maximum. Find this maximum value of x.
- Astronomers have observed a small, massive object at the center of our Milky Way Galaxy. A ring of material orbits this massive object; the ring has a diameter of about 17 light-years and an orbital speed of about 100 km/s. A) Determine the mass M of the massive object at the center of the Milky Way Galaxy. Give your answer in kilograms.Express your answer in kilograms. B) Give your answer in solar masses (one solar mass is the mass of the sun). Express your answer in units of solar masses. C) Many astronomers believe that the massive object at the center of the Milky Way Galaxy is a black hole. If so, what must the Schwarzschild radius RS of this black hole be? Express your answer in meters.Three lead balls of mass m₁ = 14 kg, m₂ = 27 kg, and m3 = 9.7 kg are arranged as shown in the figure below. Find the total gravitational force exerted by balls 1 and 2 on ball 3. Be sure to give the magnitude and the direction of this force. N magnitude direction ° counterclockwise from the +x-axis y (m) 4 m1 3 L- 2+ m₂ 1 0 2 3. 4 5 M3 -x-(m)A newly discovered planet has the same acceleration due to gravity as Earth with a value of g. If the new planet has twice the radius of Earth, what must be its mass? a me/4 b 4me c 2me d me/√2 e √2 me f me/2
- Two planets P₁ and P₂ orbit around a star S in circular orbits with speeds v₁ = 43.4 km/s, and v₂ = 57.0 km/s respectively. If the period of the first planet P₁ is 790 years what is the mass, in kg, of the star it orbits around? kg Determine the orbital period, in years, of P2. yrA satellite of Mars, called Phobos, has an orbital radius of 9.4 ✕ 106 m and a period of 2.8 ✕ 104 s. Assuming the orbit is circular, determine the mass of Mars. (ans kg)Aliens declare war on Earth by dropping an asteroid on our planet. The asteroid starts at rest from a distance of 37 x 106 m from the center of Earth. Calculate the speed with which the asteroid hits Earth's surface, in km/s. Use that G = 6.7 x 10-11 N m2 / kg2, MEarth = 6 x 1024 kg, and REarth = 6 x 106 m. (Please answer to the fourth decimal place - i.e 14.3225)
- 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 0/99Two satellitess, and S, orbit around a planet P in circular orbits of radil r, = 5.15 x 106 m, and r, = 8.40 x 106 m respectively. If the speed of the first satellite S, is 1.65 x 10 m/s, what is the speed of the second satellite S,? m/sEarth’s gravitational field strength at the surface is 9.80 N/kg. Determine the distance, as a multiple of Earth’sradius, rE, above Earth’s surface at which the magnitude of the acceleration due to gravity is 3.20 N/kg.