How To Find The Force Of Gravity On An Object

The Value of 1000

In Unit 2 of The Physics Classroom, an equation was given for determining the force of gravity ( F_grav ) with which an object of mass k was attracted to the world

F_grav = yard*g

Now in this unit of measurement, a second equation has been introduced for computing 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.

In the first equation in a higher place, g is referred to equally the acceleration of gravity. Its value is ix.8 m/southward² on Earth. That is to say, the acceleration of gravity on the surface of the world at sea level is nine.8 m/s² . When discussing the acceleration of gravity, it was mentioned that the value of thou is dependent upon location. There are slight variations in the value of g about earth's surface. These variations result from the varying density of the geologic structures below each specific surface location. They also event from the fact that the earth is not truly spherical; the earth'due south surface is further from its center at the equator than information technology is at the poles. This would upshot in larger g values at the poles. As 1 gain further from world's surface - say into a location of orbit virtually the earth - the value of g changes still.

The Value of 1000 Depends on Location

To understand why the value of m is so location dependent, we will utilise the ii equations above to derive an equation for the value of k. First, both expressions for the force of gravity are set equal to each other.

Now observe that the mass of the object - g - is present on both sides of the equal sign. Thus, grand can exist canceled from the equation. This leaves united states with an equation for the acceleration of gravity.

The higher up equation demonstrates that the acceleration of gravity is dependent upon the mass of the world (approx. v.98x10²⁴ kg) and the distance ( d ) that an object is from the center of the earth. If the value 6.38x10⁶ m (a typical world radius value) is used for the distance from Earth's center, then one thousand will be calculated to exist ix.8 thousand/s^two. And of course, the value of g volition change equally an object is moved further from Earth's heart. For instance, if an object were moved to a location that is ii earth-radii from the center of the earth - that is, two times 6.38x10⁶ chiliad - so a significantly different value of m will be constitute. As shown beneath, at twice the distance from the center of the earth, the value of g becomes two.45 yard/southward².

The table below shows the value of thousand at various locations from Earth's centre.

Location	Distance from World's center (chiliad)	Value of g (thousand/south²)
Globe's surface	6.38 x ten⁶ m	9.8
thousand km to a higher place surface	seven.38 x 10⁶ yard	7.33
2000 km above surface	8.38 ten 10^vi m	5.68
3000 km to a higher place surface	9.38 10 10^half-dozen m	4.53
4000 km above surface	1.04 x x⁷ m	iii.70
5000 km above surface	one.14 x ten⁷ yard	3.08
6000 km above surface	i.24 x 10^seven m	2.threescore
7000 km in a higher place surface	1.34 x x^seven m	2.23
8000 km above surface	ane.44 x 10⁷ m	ane.93
9000 km higher up surface	1.54 x 10^seven one thousand	i.69
10000 km above surface	1.64 ten 10⁷ m	ane.49
50000 km to a higher place surface	5.64 10 10^seven m	0.13

Every bit is axiomatic from both the equation and the table to a higher place, the value of g varies inversely with the distance from the center of the world. In fact, the variation in g with distance follows an inverse square law where k is inversely proportional to the distance from earth's center. This inverse square relationship means that as the altitude is doubled, the value of k decreases by a cistron of iv. Every bit the distance is tripled, the value of one thousand decreases by a cistron of ix. So on. This changed foursquare human relationship is depicted in the graphic at the correct.

Calculating thousand on Other Planets

The same equation used to determine the value of k on Earth' surface tin also be used to decide the acceleration of gravity on the surface of other planets. The value of k on any other planet can be calculated from the mass of the planet and the radius of the planet. The equation takes the post-obit form:

Using this equation, the following acceleration of gravity values tin can be calculated for the various planets.

Planet	Radius (thousand)	Mass (kg)	g (chiliad/s^two)
Mercury	2.43 ten 10⁶	3.2 ten 10²³	3.61
Venus	half-dozen.073 ten 10⁶	4.88 x10²⁴	8.83
Mars	three.38 x 10⁶	6.42 x 10²³	3.75
Jupiter	6.98 x 10^seven	1.901 ten 10²⁷	26.0
Saturn	five.82 ten x⁷	v.68 ten 10²⁶	11.2
Uranus	2.35 x ten⁷	8.68 x x²⁵	10.five
Neptune	2.27 x x⁷	ane.03 x 10²⁶	13.3
Pluto	1.xv ten 10⁶	1.2 x 10²²	0.61

The acceleration of gravity of an object is a measurable quantity. Even so emerging from Newton's universal law of gravitation is a prediction that states that its value is dependent upon the mass of the Globe and the distance the object is from the World'south center. The value of grand is independent of the mass of the object and only dependent upon location - the planet the object is on and the altitude from the middle of that planet.

Investigate!

Fifty-fifty on the surface of the Earth, there are local variations in the value of g. These variations are due to latitude (the Earth isn't a perfect sphere; it buldges in the eye), altitude and the local geological structure of the region. Employ the Gravitational Fields widget below to investigate how location affects the value of thousand. And for a more than visual experience, effort the related Value of thousand Interactive from the Physics Interactives section of our website.

We Would Like to Advise ...

Sometimes information technology isn't enough to just read about it. You have to collaborate with it! And that's exactly what y'all do when you utilize i of The Physics Classroom's Interactives. We would like to suggest that yous combine the reading of this folio with the use of our Gravitation Interactive and/or our Value of thousand on Other Planets Interactive. Y'all tin find these in the Physics Interactives department of our website. Both Interactives allow a learner to interactively explore the result of planet characteristics upon the gravitational field.