Sensitivity of the Gravity Assist to Variations of the Impact Parameter

Modified Gravity and a Space Probe–Venus Mission

“…A type of standard trajectory should be chosen, to compare deflections from it. In previous papers [7,8] we suggested such a trajectory satisfying the following setting conditions: a space probe is supposed to move in an ideal model of a planetary system comprising a spherically symmetric star (the sun) and two planets imitating the Earth and Venus, which orbit the star by coplanar circular trajectories (the masses, velocities, and orbit characteristics of the bodies are close to real physical parameters). The motion is described in polar (R, Φ) coordinates, with the sun placed at the initial point.…”

“…To get another standard trajectory, we can variate the h value by a virtual choice of Venus' initial position, while leaving conditions (1) intact. With the help of this scheme, we managed to build an empiric GA sensitivity function S(h) [7,8] which gave the values of the probe's FP deflection under a relatively small IP change dh. The results were surprising: for h = (16 − 10) • 10 4 km, S(h) ∼ = 10 4 − 10 5 ; this means that, e.g., for h = 10, 000 km (4000 km over Venus' surface) an IP change dh = 1 km entails the FP shift of ~82,000 km, which can be detected from Earth (for simplicity, the Earth's gravity is not taken into consideration).…”

“…Analytical calculations and numerical modeling, however, have demonstrated that a planet's gravity assist (GA)-a frequent element in current space missions-can amplify the deflection of a spacecraft's orbit sufficiently to make the shift observable [7,8]; moreover, the GA sensitivity-the ability to amplify a small change of the probe-planet impact parameter (IP)-turns out to be great enough to detect the sun's specific GR features in general, as well as to identify the type of Schwarzschild field variant.…”

An Artificial Experiment Aimed to Specify the Gravity Law in the Solar System

“…Для определения функции чувствительности достаточно, чтобы в планетной системе действовал закон гравитации Ньютона. В этих условиях сначала предлагается осуществить следующий математический (мыслительный) эксперимент [4].…”

“…Здесь зонды ускоряются и по новым баллистическим траекториям возвращаются к орбите Земли, где одновременно подают сигнал, позволяющий наблюдателю достаточно точно определить их положение в пространстве. Очевидно, в конечный момент времени зонды окажутся в различных точках пространства; наблюдаемое расстояние между ними определяет значение функции чувствительности ГМ при данном значении ПП 4 . Последовательно выбирая ряд характерных значений ПП зондов от 18 до 8 тыс.…”