# The Impact of Gravity on Different Height Systems: A Case Study on Mt. Medvednica
## 4 Gravity Measurements
### Corrections of Gravity Measurements
#### 4.1.1 Corrections Related to the Measuring Instrument  
Corrections related to the measuring instrument include the following:  
* Correction for the air pressure  
The redistribution of air masses in the Earth's atmosphere causes constant variations in gravity. Gravity and air pressure are inversely proportional, meaning that as air pressure increases, gravity decreases. The correction for gravity due to the influence of air pressure, expressed in mGal (i.e., \(10^{-5}\)ms\({}^{-2}\)), is calculated using the following equation [28; 29]:  
\[g_{ap}=\alpha(p_{m}-p_{0}), \tag{34}\]  
where \(\alpha\) is the barometric admittance factor for Central Europe with a value of 0.0003 mGal/hPa, \(p_{m}\) the air pressure measured at the moment of gravimetric measurement in hPa, and \(p_{0}\) the mean long-term air pressure at the height (\(H\)) of the gravimetric point in hPa which can be obtained by the following equation:  
\[p_{0}=1013.25\bigg{(}1-\frac{0.0065H}{288.15}\bigg{)}^{5.2559}; \tag{35}\]
* Correction for Earth's polar motion  
Daily or secular variations in the dynamics of Earth's rotation are caused by the redistribution of Earth's masses due to geophysical processes and gravitational influences from celestial bodies. The result of this is a change in the position of Earth's pole relative to the celestial pole, which manifests as a variation in gravity. The correction to eliminate this variation can be calculated using the following equation [28; 29; 30]:  
\[g_{epm}=-\delta\omega^{2}a\sin\varphi\cos\varphi(x_{i}\cos\lambda-y_{t}\sin \lambda)\cdot 10^{5}, \tag{36}\]  
where \(\delta\) is the gravimetric factor, which represents the ratio of the actual to the theoretical change in gravity, and for the approximation of Earth as a perfectly elastic sphere, it has a value of 1.164; \(\omega\) is the angular velocity of Earth's rotation (\(\omega=7.2921159\cdot 10^{-5}\) rad s\({}^{-1}\)), \(a\) is the equatorial radius of Earth (\(a=6378136.6\) m), \(\varphi\) and \(\lambda\) are the geodetic latitude and longitude of the measurement point, and \(x_{t}\) and \(y_{t}\) are the pole coordinates at the moment of gravity measurement. In Equation (36), \(g_{epm}\) is expressed in mGal. The values of pole coordinates at midnight of every day are provided by IERS [31], and with linear interpolation, pole coordinates at the moment of gravity measurement can be calculated. * Correction for the Earth's tides. The correction for the influence of Earth's tides needs to be made due to the error in the measured gravity acceleration caused by the gravitational effects of celestial bodies on Earth. The Sun and the Moon have, by far, the greatest influence of all celestial bodies, so the influence of other celestial bodies can be neglected. The correction for the influence of Earth's tides can be calculated using the following equation [32]:  
\[g_{et}=\delta(g_{s}+g_{m}), \tag{37}\]  
where \(\delta\) is the gravimetric factor, \(g_{s}\) component of the Moon's influence on Earth's tides, and \(g_{m}\) component of the Sun's influence on Earth's tides. These two components can becalculated using the Longman model for the calculation of Earth's tides [29; 32]. Although the _Scintrex CG-6_ instrument has the capability to automatically calculate Earth's tidal waves, in this study, raw gravity values were used, and the correction for tide influence was calculated using the Longman model. In Equation (37), \(g_{et}\) is expressed in mGal. Corrections related to the Earth's geophysical processes include the following:  
Correction for the height of the measuring sensor  
When conducting gravimetric measurements at a given point, the gravimeter measures the gravity value at the height of its sensor. However, in practice, this measured value is not directly useful, as the required value is gravity at the actual point, i.e., on the physical surface of the Earth.