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The planet Saturn has about 100 times the mass of the earth and is about 10 times farther from the sun than the earth is. Compared to the acceleration of the earth caused by the sun’s gravitational pull, how great is the acceleration of Saturn due to the sun’s gravitation? (i) 100 times greater; (ii) 10 times greater; (iii) the same; (iv)
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- Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forwardWhich of the following statements are fundamental postulates of the special theory of relativity? More than one statement may be correct. (a) Light moves through a substance called the ether. (b) The speed of light depends on the inertial reference frame in which it is measured. (c) The laws of physics depend on the inertial reference frame in which they are used. (d) The laws of physics are the same in all inertial reference frames. (e) The speed of light is independent of the inertial reference frame in which it is measured.arrow_forwardWhich of the following statements are fundamental postulates of the special theory of relativity? More than one statement may be correct. (a) Light moves through a substance called the ether. (b) The speed of light depends on the inertial reference frame in which it is measured. (c) The laws of physics depend on the inertial reference frame in which they are used. (d) The laws of physics are the same in all inertial reference frames. (e) The speed of light is independent of the inertial reference frame in which it is measured.arrow_forward
- The planet Mars has two moons, phobos and delmos. (1) phobos has a period 7 hours, 39 minutes and an orbital radius of 9.4 × 10 km . Calculate the mass of mars. (ii) Assume that earth and mars move in circular orbits around the sun. with the martian orbit being 1: 52 times the orbital radius of the earth. What is the length of the martian year in days?arrow_forward3. An asteroid in an elliptical orbit about the Sun travels at 1.23 x 10^6 m/s at perihelion (the point of closest approach) at a distance of 2.03 x 10^8 km from the Sun. How fast is it traveling at aphelion (the farthest point), which is 8.03 x 10^8 km from the Sun?arrow_forwardYou may have an image of Sir Isaac Newton sitting under a tree and after being hit on the head by an apple he suddenly "discovered" the Law of Universal Gravitation. In fact, the theory was a result of years’ worth of research, which in turn was based on centuries of accumulated knowledge. He is credited with determining that the following relationship is universal. The gravitational attraction between two objects varies jointly with their masses (m1 and m2) and inversely with the square of the distance (d) between them. By what percent does the force of gravitational attraction change if one mass is increased by 20%, the other mass decreased by 20%, and the separation is reduced by 25%?arrow_forward
- A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. (a) One of these stars is believed to be in an approximātely circular orbit with a radius of about 1.50 x 10° AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting. kg (b) What is the speed of this star? V star m/s How does it compare with the speed of the Earth in its orbit? V star VEarth How does it compare with the speed of light? V stararrow_forwardSo let's consider a person with a mass of 51.0 kg standing on the Earth. To find the gravitational force on the person, we'll again use Newton's law of universal gravitation with the Earth as m2 and the radius of the Earth for the distance F = GmME RE2 . Now all we need to do is substitute values and calculate. We already said m = 51.0 kg, and we know G = 6.67 ✕ 10−11 N · m2/kg2. The Earth is not a perfect sphere, but, its average radius is RE = 6.37 ✕ 106 m. The mass of the Earth is ME = 5.97 ✕ 10−24 kg. We can then substitute these values in the following formula. (Enter your answer in N.) F = (6.67 ✕ 10−11 N · m2/kg2)(51.0 kg)(5.97 ✕ 1024 kg) (6.37 ✕ 106 m)2 (A) = _______ N Now let's compare this result to the person's weight (in N) found by multiplying the person's mass by g (or, that is, w = mg) where g = 9.80 m/s2. w = (51.0 kg)(9.80 m/s2) =(b) __________________ N You should have found that these two methods give about the same result!…arrow_forwardA research team has discovered that a moon is circling a planet of our solar system: The moonorbits the planet once every 7 hours on a nearly circular orbit in a distance R of 48000 km fromthe centre of the planet. Unfortunately, the mass m of the moon is not known. Use Newton’s lawof gravitation with G = 6.67 · 10−11 m3/(kg·s2) to approach the following questions:F = G ·mMR2(1)(a) Based on the observations, determine the total mass M of the planet.(b) Which moon and planet of our solar system is the team observing? (Use literature.)arrow_forward
- An object of mass m is launched from a planet of mass M and radius R. a)Derive and enter an expression for the minimum launch speed needed for the object to escape gravity, i.e. to be able to just reach r = ∞. b)Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M = 6 × 1023 kg and R = 76 × 104 km.arrow_forwardThe law of universal gravitation says that there is a force between two objects in the universe. Can there ever be a physical instance when the two objects will never have an influence on each other? Hint: look at the equation that relates force, mass, distance, and the gravitational constant G: Gxm, xma F = O No, no matter how far apart they are, there will always be some tiny force acting between the two. O No, Since the distance between two objects can never be zero. All listed answers here are correct. O No, they will always influence each other. You cannot divide by zero.arrow_forwardWonder Woman and Superman fly to an altitude of 1530 km, carrying between them a chest full of jewels that they intend to put into orbit around Earth. They want to make this tempting treasure inaccessible to their evil enemies who are trying to gain possession of it, yet keep it available for themselves for future use when they retire and settle down. But perhaps the time to retire is now! They accidentally drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed vf does the chest impact the surface of the water? Ignore air resistance (in reality, it would make large difference). The radius and mass of Earth are 6370 km and 5.98 x 1024 kg, respectively. m/s %3Darrow_forward
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