College Physics
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Publisher: Cengage Learning
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Use ME = gRE
2
>G to calculate the mass of the Earth.
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- Gravitational force is F = Gm1m2/r². Set G = 1 and m1 = 1, where m2 will be a planet with 1800 times Earth's mass (so m2 = 1800) and 30 times Earth's radius (so r = 30). What will F be?arrow_forwardA sun rays take about 8 minutes to reach the Earth surface travelling at constant speed v= 3,0 * 10^8 m/s. How far is earth from the sun?arrow_forwardConsider the Earth's orbit around the Sun to be circular with radius R = 9.30 x 107 mi and it takes 365 days to complete one revolution. What is the distance Earth traveled for one revolution (circumference of a circle is 2??2πR )?arrow_forward
- 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 5.9 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 massesarrow_forwardThe radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun.arrow_forwardAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0 ✕ 104 light years from its center. (a) What should the orbital period (in y) of that star be? y (b) If its period is 6.9 ✕ 107 y instead, what is the mass (in solar masses) 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 massesarrow_forward
- D Gm₁m₂ Fg KE = mv², Ug = - 2πr , ac = =²₁, v = ²7₁ T Gm₁m₂ GM g = G, Vesc = 2GM R , E = KE + Ug, G = 6.674 x 10-¹1 Nm²/kg² Problem 1: You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its radius to be 9 x 106 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.2 x 10¹¹ m from its star with a period of 402 days (3.473 x 107 sec). Once on the surface you find that the free-fall acceleration is 12.2 m/sec². a) What is the mass of the planet? Answer: 1.5 x 1025 kg. b) What is the mass of the star? Answer: 5.2 x 1030 kg.arrow_forwardYour weight on Earth is W0W0. Let mE≡mE≡ mass of the Earth; RE≡RE≡ radius of the Earth. What would your weight be if you were on a planet with a mass of 3mE3mE and radius of 4RE4RE?arrow_forwardAn extrasolar planet has mass 1.27E+25 kg and radius 67400000_m. What is the escape speed for this planet? 11440_m/s 12230_m/s 5014_m/s А. D. 16190_m/s В. Е. 1973_m/s С. F. 9206 m/sarrow_forward
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