at what altitude above the earths surface is the acceleration due to gravity equal to g/ 5?
The Value of grand
In Unit 2 of The Physics Classroom, an equation was given for determining the force of gravity ( Fgrav ) with which an object of mass grand was attracted to the earth Now in this unit of measurement, a second equation has been introduced for calculating the force of gravity with which an object is attracted to the earth. where d represents the altitude from the center of the object to the center of the earth. To understand why the value of grand is so location dependent, we will use the ii equations above to derive an equation for the value of g. Showtime, both expressions for the force of gravity are set equal to each other. At present observe that the mass of the object - 1000 - is present on both sides of the equal sign. Thus, m tin can be canceled from the equation. This leaves usa with an equation for the acceleration of gravity. The above equation demonstrates that the acceleration of gravity is dependent upon the mass of the earth (approx. v.98x1024 kg) and the distance ( d ) that an object is from the heart of the earth. If the value 6.38x10half dozen m (a typical world radius value) is used for the altitude from Earth's center, then g will exist calculated to exist 9.viii m/stwo. And of course, the value of g volition change as an object is moved further from Earth's middle. For example, if an object were moved to a location that is two globe-radii from the center of the earth - that is, two times 6.38x106 m - so a significantly different value of g will be establish. As shown below, at twice the distance from the middle of the earth, the value of thousand becomes 2.45 yard/southward2. The table below shows the value of g at diverse locations from Earth'due south center. Location Distance from World's center Value of yard Earth's surface vi.38 x ten6 thousand 9.viii g km above surface 7.38 x 106 m 7.33 2000 km above surface 8.38 x x6 m 5.68 3000 km in a higher place surface 9.38 ten x6 m 4.53 4000 km above surface 1.04 10 x7 m iii.70 5000 km above surface 1.xiv x 10vii k 3.08 6000 km above surface 1.24 x 10seven m two.threescore 7000 km above surface 1.34 x 107 thousand 2.23 8000 km to a higher place surface 1.44 x ten7 thousand ane.93 9000 km above surface 1.54 x x7 yard 1.69 10000 km to a higher place surface 1.64 x ten7 m 1.49 50000 km to a higher place surface 5.64 x ten7 m 0.13 The same equation used to decide the value of g on Earth' surface tin can also be used to determine the acceleration of gravity on the surface of other planets. The value of g on any other planet can be calculated from the mass of the planet and the radius of the planet. The equation takes the following form: Using this equation, the post-obit acceleration of gravity values can be calculated for the various planets. Planet Radius (k) Mass (kg) thou (m/due south2) Mercury 2.43 x 106 3.two x ten23 3.61 Venus vi.073 x ten6 four.88 x1024 eight.83 Mars three.38 x 10six vi.42 x x23 3.75 Jupiter half-dozen.98 x 10seven 1.901 x 1027 26.0 Saturn five.82 10 x7 v.68 x 1026 eleven.2 Uranus 2.35 x x7 8.68 x 1025 10.v Neptune two.27 x 107 1.03 x x26 xiii.three Pluto 1.15 10 106 1.2 x 1022 0.61 The acceleration of gravity of an object is a measurable quantity. Yet emerging from Newton'due south universal law of gravitation is a prediction that states that its value is dependent upon the mass of the Earth and the distance the object is from the Earth'south center. The value of m is independent of the mass of the object and only dependent upon location - the planet the object is on and the distance from the heart of that planet. 
In the first equation above, g is referred to as the acceleration of gravity. Its value is 9.eight thousand/sii on Globe. That is to say, the dispatch of gravity on the surface of the earth at sea level is ix.8 chiliad/southwardtwo . When discussing the acceleration of gravity, it was mentioned that the value of one thousand is dependent upon location. There are slight variations in the value of one thousand about earth'due south surface. These variations upshot from the varying density of the geologic structures below each specific surface location. They also result from the fact that the earth is not truly spherical; the earth'southward surface is further from its center at the equator than it is at the poles. This would result in larger one thousand values at the poles. As one proceeds further from earth'south surface - say into a location of orbit about the earth - the value of g changes notwithstanding. The Value of one thousand Depends on Location
(m)
(grand/s2) 
As is evident from both the equation and the tabular array higher up, the value of g varies inversely with the distance from the center of the earth. In fact, the variation in g with distance follows an inverse square law where g is inversely proportional to the distance from earth's center. This inverse square relationship ways that as the distance is doubled, the value of g decreases by a factor of 4. As the distance is tripled, the value of g decreases by a factor of ix. And then on. This changed square human relationship is depicted in the graphic at the correct.
Computing g on Other Planets
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