This phase 2 trial studies radium Ra 223 dichloride, hormone therapy and stereotactic body radiation in treating patients with prostate cancer that has spread to other places in the body. Radium Ra 223 dichloride contains a radioactive substance that collects in the bone and gives off radiation that may kill cancer cells. Hormone therapy using leuprolide acetate or goserelin acetate may fight prostate cancer by lowering the amount of testosterone the body makes. Stereotactic body radiation therapy is a specialized radiation therapy that sends x-rays directly to the tumor using smaller doses over several days and may cause less damage to normal tissue. Giving radium Ra 223 dichloride, hormone therapy and stereotactic body radiation may work better at treating prostate cancer.

PRIMARY OBJECTIVES: I. To assess the time to treatment failure (TTF) in patients who initiated the protocol regimen of androgen deprivation therapy (ADT) with stereotactic body radiation therapy (SBRT) and radium Ra 223 dichloride and received at least one dose with radium Ra 223 dichloride. SECONDARY OBJECTIVES: I. To assess the safety of adding radium Ra 223 dichloride to SBRT and ADT in patients with oligometastatic castration sensitive prostate cancer. II. To assess the prostate-specific antigen (PSA) and overall response rate (ORR) after 6 cycles of radium Ra 223 dichloride (cycle 8 day 1). III. To assess the progression-free survival (PFS) in patients with oligometastatic castration sensitive prostate cancer who initiated the protocol regimen of ADT with SBRT and radium Ra 223 dichloride and received at least one dose of radium Ra 223 dichloride. IV. To assess time to bone specific PFS in patients with oligometastatic castration sensitive prostate cancer who initiated the protocol regimen of ADT with SBRT and radium Ra 223 dichloride and received at least one dose of radium Ra 223 dichloride. V. To assess overall survival, complete response rate, duration of response, and duration of overall complete response and duration of stable disease in patients with oligometastatic castration sensitive prostate cancer who initiated the protocol regimen of ADT with SBRT and radium Ra 223 dichloride. VI. To assess long-term toxicities during 5-year follow-up in patients with oligometastatic castration sensitive prostate cancer who initiated the protocol regimen of ADT with SBRT and radium Ra 223 dichloride and received at least one dose of radium Ra 223 dichloride. TERTIARY OBJECTIVES: I. To perform exploratory analysis of primary or metastatic tumor mutation patterns in this study population at baseline. II. To identify immune system factors in the blood that change during the course of ADT-radiotherapy for metastatic prostate cancer. III. To describe the rate of normalization of the total alkaline phosphatase level (defined as a return to a value within the normal range) at the end of protocol therapy in patients oligometastatic castration sensitive prostate cancer with total alkaline phosphatase values above the upper limit of the normal range at baseline. OUTLINE: Beginning 4 weeks (28 days) prior to radiation therapy, patients receive leuprolide acetate or goserelin acetate, or degarelix for up to 32 weeks. Patients also undergo 3-5 fractions of SBRT every 40 hours over 7-21 days beginning on day 1 of course 1, and receive radium Ra 223 dichloride intravenously (IV) over 1 minute on day 1 of courses 2-7. Treatment repeats every 28 days for up to 7 courses in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up for up to 5 years.