This paper investigates the constraints on the Lorentz symmetry-breaking parameter $ l $ in Kalb-Ramond (KR) gravity by analyzing the precession of the S2 star's orbit around Sgr A* and geodesic precession around Earth. The study compares the orbital precession in KR gravity with that in General Relativity (GR), using data from the Event Horizon Telescope (EHT) and the Gravity Probe B (GP-B) experiment. The results show that the parameter $ l $ is constrained to the range $ -0.185022 \leq l \leq 0.060938 $ based on the S2 star's precession, and to $ -6.30714 \times 10^{-12} \leq l \leq 3.90708 \times 10^{-12} $ based on GP-B data. These values are consistent with the Schwarzschild limits. The paper also examines the innermost circular orbit (ICO) and innermost stable circular orbit (ISCO) for timelike geodesics, showing how the symmetry-breaking parameter $ l $ affects these orbits. The analysis reveals that the ICO radius increases for $ l < 0 $ and decreases for $ 0 < l < 1 $, while the ISCO radius slightly increases for $ l < 0 $ and decreases for $ l > 0 $. The zoom-whirl orbits are also analyzed, showing that the radius $ R_{zw} $ approaches the Schwarzschild value for $ l < 0 $ and moves away for $ l > 0 $. For lightlike geodesics, the paper determines the lower and upper bounds of the photon sphere and finds that the shadow radius decreases with increasing $ l $. The shadow radius for an observer at a finite distance from the black hole is compared with that for an observer at infinity, showing no significant difference between the two. The results indicate that the shadow radius decreases with increasing $ l $, consistent with the spontaneous symmetry-breaking effects in KR gravity. The study concludes that the results align with experimental observations, particularly in the limit $ l \rightarrow 0 $, and that further tests are needed to fully constrain the Lorentz symmetry-breaking parameter. The findings provide important insights into the behavior of gravity in the presence of spontaneous Lorentz symmetry breaking and have implications for the understanding of black hole physics and fundamental interactions.This paper investigates the constraints on the Lorentz symmetry-breaking parameter $ l $ in Kalb-Ramond (KR) gravity by analyzing the precession of the S2 star's orbit around Sgr A* and geodesic precession around Earth. The study compares the orbital precession in KR gravity with that in General Relativity (GR), using data from the Event Horizon Telescope (EHT) and the Gravity Probe B (GP-B) experiment. The results show that the parameter $ l $ is constrained to the range $ -0.185022 \leq l \leq 0.060938 $ based on the S2 star's precession, and to $ -6.30714 \times 10^{-12} \leq l \leq 3.90708 \times 10^{-12} $ based on GP-B data. These values are consistent with the Schwarzschild limits. The paper also examines the innermost circular orbit (ICO) and innermost stable circular orbit (ISCO) for timelike geodesics, showing how the symmetry-breaking parameter $ l $ affects these orbits. The analysis reveals that the ICO radius increases for $ l < 0 $ and decreases for $ 0 < l < 1 $, while the ISCO radius slightly increases for $ l < 0 $ and decreases for $ l > 0 $. The zoom-whirl orbits are also analyzed, showing that the radius $ R_{zw} $ approaches the Schwarzschild value for $ l < 0 $ and moves away for $ l > 0 $. For lightlike geodesics, the paper determines the lower and upper bounds of the photon sphere and finds that the shadow radius decreases with increasing $ l $. The shadow radius for an observer at a finite distance from the black hole is compared with that for an observer at infinity, showing no significant difference between the two. The results indicate that the shadow radius decreases with increasing $ l $, consistent with the spontaneous symmetry-breaking effects in KR gravity. The study concludes that the results align with experimental observations, particularly in the limit $ l \rightarrow 0 $, and that further tests are needed to fully constrain the Lorentz symmetry-breaking parameter. The findings provide important insights into the behavior of gravity in the presence of spontaneous Lorentz symmetry breaking and have implications for the understanding of black hole physics and fundamental interactions.