AZD2171 in Treating Patients With Recurrent Ovarian, Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * must have histologically or cytologically confirmed epithelial ovarian cancer, primary peritoneal serous cancer, or fallopian tube cancer * must have either measurable cancer by RECIST criteria or an elevated CA125 * Subjects must be asymptomatic or minimally symptomatic * Prior therapy: * Prior chemotherapy must have included a first-line platinum-based regimen only * Prior hormonal-based therapy for ovarian, primary peritoneal serous or fallopian tube cancer is acceptable * Up to two prior lines of chemotherapy in the recurrent setting are allowed * Toxic side effects related to prior chemotherapy or hormonal therapy must have resolved to less than or equal to grade 1 or to baseline (excluding alopecia), or for peripheral neuropathy to less than or equal to grade 2 * Subjects may begin AZD2171 at least 3 weeks after their last dose of chemotherapy or hormonal therapy * Life expectancy of greater than 6 months * ECOG performance status 0-1 (Karnofsky \>= 70%) * must have lab values within normal institutional limits * eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or PK of AZD2171 will be determined following review of their case by the Principal Investigator * Subjects with treated limited stage basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the breast or cervix are eligible; subjects with stage I or II cancer treated with a curative intent are also eligible with no evidence of recurrent disease * No evidence of preexisting uncontrolled hypertension; if patient has hypertension, it must be medically controlled * AZD2171 has been shown to terminate fetal development in the rat, as expected for a process dependent on VEGF signaling; for this reason, women of child-bearing potential must have a negative pregnancy test prior to study entry; must agree to use adequate contraception; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document- No therapeutic anticoagulation; the use of low dose warfarin (1 mg/day), intermittent doses of tPA (2 mg x 1), or heparin flushes to prophylax against central venous catheter-associated clots is permitted * Measurable or non-measurable disease on CT scan or MRI * Consider patients who have the following risk factors to be at increased risk; these patients should have increased monitoring: * Prior treatment with anthracyclines * Prior treatment with trastuzumab * A New York Heart Association classification of II controlled with treatment * Prior central thoracic radiation therapy (RT), including RT to the heart * History of myocardial infarction within 12 months Exclusion Criteria: * Patients who have had chemotherapy, radiotherapy, or major surgery within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier * Patients may not be receiving any other investigational agents nor have participated in an investigational trial within the past 3 weeks; subjects may not have received prior treatment affecting the VEGF pathway; subjects may not have received prior treatment with antibodies that may interfere with CA-125 measurements; subjects may not have received intraperitoneal therapy within the 4 weeks prior to starting AZD2171 and/or the treating physician must confirm the patient has recurrent disease * Patients may not be receiving any medication that may markedly affect renal function * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis * History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD2171 * Mean QTc \> 500 msec (with Bazett's correction) in screening electrocardiogram or history of familial long QT syndrome * Uncontrolled intercurrent illness * Pregnant women are excluded from this study because AZD2171 is a VEGF inhibitor with known abortifacient effects; breastfeeding should be discontinued if the mother is treated with AZD2171 * Major surgical procedure or medical interference with the peritoneum or pleura within 4 weeks of baseline CA-125 assessments * Subjects with a history of an active malignancy during the last 3 years except non-melanomatous skin cancer , in situ breast or cervical cancer or stage I or II cancer treated with a curative intent and no active cancer recurrence * HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with AZD2171 * No therapeutic anti-coagulation; prophylaxis against central venous catheter-associated clots is permitted * A New York Heart Association classification of III or IV * Conditions requiring concurrent use of drugs or biologics with proarrhythmic potentiate