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(a) The Sun orbits the Milky Way galaxy once each
(b) Calculate the average speed of the Sun in its galactic orbit. Does the answer surprise you?
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- Calculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?arrow_forwardLet gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)arrow_forwardThe Sun orbits the center of the Milky Way galaxy once each 2.60 × 108 years, with a roughly circular orbit averaging 3.00 × 104 light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the centripetal acceleration of the Sun in its galactic orbit in m/s2.arrow_forward
- The Sun orbits the Milky Way galaxy once each 2.60 × 108 years, with a roughly circular orbit averaging a radius of 3.00 × 104 light-years. (A light-year is the distance traveled by light in 1 year.) Calculate the centripetal acceleration of the Sun in its galactic orbit. Does your result support the contention that a nearly inertial frame of reference can be located at the Sun? (b) Calculate the average speed of the Sun in its galactic orbit. Does the answer surprise you?arrow_forwardAn elephant is located on Earth’s surface at a latitude λ. Calculate the centripetal acceleration of the elephant resulting from the rotation of Earth around its polar axis. Express your answer in terms of λ, the radius RE of Earth, and time T for one rotation of Earth. Compare your answer with g for λ = 40°.arrow_forwardA satellite travels with constant speed v in a circular orbit 320 km above the earth’s surface. Calculate v knowing that the acceleration of the satellite is the gravitational acceleration at its altitude. (Note: Review Art. 1/5 as necessary and use the mean value of g and the mean value of the earth’s radius. Also recognize that v is the magnitude of the velocity of the satellite with respect to the center of the earth.)arrow_forward
- To find some of the parameters characterizing an object moving in a circular orbit.The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit: a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass M. For all parts of this problem, where appropriate, use G for the universal gravitational constant. Find the orbital speed v of a satellite in a circular orbit of radius R around a planet of mass M . Express the orbital speed in terms of G , M , and R . Find the kinetic energy K of a satellite with mass m in a circular orbit of radius R around a planet of mass M . Express your answer in terms of m , M , G , and R . Find the satellite's orbital…arrow_forwardA rocket moving around the earth at height "H", If the gravitational acceleration "gl" at height “H" is ½ of gravitational acceleration 'g' at earth surface. If Earth radius is"R", find "H" using R.arrow_forwardThe Sun orbits the center of the Milky Way galaxy once each 2.60 × 108 years, with a roughly circular orbit averaging 3.00 × 104 light years in radius. (A light year is the distance traveled by light in 1 y.) a) Calculate the centripetal acceleration of the Sun in its galactic orbit in m/s2. b) Calculate the average speed of the Sun in its galactic orbit in m/s.arrow_forward
- A communication satellite in geosynchronous orbit remains above a single point on the Earth's equator as the planet rotates on its axis. (a) Calculate the radius of its orbit. (b) The satellite relays a radio signal from a transmitter near the North Pole to a receiver, also near the North Pole. Traveling at the speed of light, how long is the radio wave in transit?arrow_forwardA spacecraft revolves around the Earth in an elliptical orbit at an average distance equal to 10 times the radius of the Earth. Calculate the duration of its orbit around the Earth. The answer is 1.86 day but i need explainarrow_forwardAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0 • 104 light years from its center. What should the orbital period of that star be in years? Part (b) If its period is 6.0 • 107 years instead, what is the mass of the galaxy in solar masses? 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.arrow_forward
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