Choose language

Gravitational acceleration calculator

With this calculator you can calculate the gravitational acceleration of a body pulled by another body. The calculator will also help to calculate the distance between the centers of the attracting bodies and the mass of the body producing the gravitational field and attracting the body for which the gravitational acceleration is given.

Gravitational acceleration

Gravitational acceleration - information

Gravitational acceleration - acceleration of bodies resulting from gravitational attraction. Under free-fall conditions, it is simply an acceleration of their motion. In a static situation, e.g. of a body resting on a horizontal surface, gravitational acceleration is responsible for the measured weight.

In general, according to Newton's classical theory of gravity, the acceleration of a body in the gravitational field of another body does not depend on the mass of the attracted body but depends on the mass of the attracting body. The acceleration of a point body caused by the gravity of a point or spherically symmetrical (e.g. spherical) body of another body is given by the formula:
$$ a = G \frac{M}{r^2} $$
where:
$ a $– gravitational acceleration of a body attracted by another body,
$ G = 6,67384(80) \cdot 10^{-11} \frac {\operatorname {m}^3}{\operatorname {kg} \, \operatorname {s}^2}\, $ - constant of gravity,
$ M $– mass of the body that produces the gravitational field, i.e. the body that attracts the body for which we calculate the acceleration of gravity,
$ r $– distance between centers of attracting bodies.

In case when the difference of masses of both bodies is very large, then the acceleration of the "big" body by the "small" body is completely negligible. Hence, within the measurement error limits, gravitational acceleration very often does not depend on the mass of the "small" body. The gravitational acceleration of the locomotive and feather falling to the ground is practically the same. The feather falls to the ground slower because it has greater aerodynamic resistance when falling, and not because it is "less" attracted.

This concept is most often used in systems in which one object has a very large mass and the other is very small. At the surface of a large, spherical object (eg a planet), the value of the gravitational acceleration is more or less constant, ie it does not fluctuate by more than 2-3%. Gravitational acceleration tables for celestial bodies usually refer to a value measured either at the body's equator or at 45° latitude at the mean surface level. The difference between the gravitational acceleration of a rotating planet as measured at the equator and the poles is due to the centrifugal force contributed to the measurements at the equator as well as the polar flattening caused by the rotation.

Standard acceleration due to gravity is usually denoted by the letter $g $ and is regarded as a physical constant.

Examples of acceleration values on the surface of selected celestial bodies:
Sun - 273,95 m/s2 (27,9 g)
Mars - 3,69 m/s2 (0,376 g)
Jupiter - 20,87 m/s2 (2,137 g)
Pluto - 0,58 m/s2 (0,059 g)
Earth - 9,80665 m/s2 (standard value)

For the first time, the value of the gravitational constant in laboratory conditions was calculated in 1798 by Henry Cavendish, using the weight of twists (earlier Newton himself estimated the value of the constant at G = 7.35 × 10-11 Nm ² / kg ², but assuming he knows the mass of the Earth). The currently used value was published in 2002 by the Data Committee for Science and Technology (CODATA).

After transformations

Distance between the centers of the bodies:
$$ r = \sqrt{\frac{G · M}{a}} $$

Mass of the body that produces the gravitational field:
$$ M = \frac{a · r^2}{G} $$

Users of this calculator also used

Profitability of investments: NPV (Net Present Value), PI (Profitability Index), IRR (Internal Rate of Return), DPP (Discounted Payback Period)

This calculator helps us check whether the planned investment will be profitable and whether the project should be accepted or rejected.
Thanks to the calculator, we can calculate:
NPV (Net Present Value) - sum of discounted net cash flows
PI (Profitability Index) - investment profitability
IRR (Internal Rate of Return) - internal rate of return
DPP (Discounted Payback Period) - discounted payback period
Value of discounted net cash flow for each period.

Online calculator

M+

M-

log

10^x

asin

acos

atan

e^x

sin^-1

cos^-1

tan^-1

sin

cos

tan

√

x²

1/x

x^M

(

)

exp

M+

M-

sin