Although a large number of astronomical craters are actually produced by the oblique impacts onto inclined surfaces , most of the laboratory experiments mimicking the impact cratering have been performed by the vertical impact onto a horizontal target surface .
In previous studies on the effects of oblique impact and inclined terrain , only one of the impact angle \varphi or target inclination angle \theta has been varied in the experiments .
Therefore , we perform impact-cratering experiments by systematically varying both \varphi and \theta .
A solid projectile of diameter D _ { i } = 6 mm is impacted onto a sand surface with the range of impact velocity v _ { i } = 7 – 97 m s ^ { -1 } .
From the experimental result , we develop scaling laws for the crater dimensions on the basis of \Pi -group scaling .
As a result , the crater dimensions such as cavity volume , diameter , aspect ratio , and depth-diameter ratio can be scaled by the factors \sin \varphi and \cos \theta as well as the usual impact parameters ( v _ { i } , D _ { i } , density of projectile , and surface gravity ) .
Finally , we consider the possible application of the obtained scaling laws to the estimate of impact conditions ( e.g. , impact speed and impact angle ) in natural crater records .