Abstract We show that the Gravity Probe B (GP-B) and the Satellite Test of Equivalence Principle (STEP) missions, with their disturbance-free orbits and precise tracking, will facilitate determination of at least two effects of post-Newtonian gravitation. First, for Einstein's classical test of general relativity, the advance of periapse of an orbit, the GP-B determination will be 3 parts in 1000. Second, for the eccentricity of objects orbiting the Earth as it orbits the sun, the GP-B determination will be 200 times more sensitive than lunar laser ranging measurements and at least 5 times more sensitive than Lageos due to GP-B's lower orbit. Nordtvedt shows that the annual variation in the eccentricity of such an orbit is zero only if general relativity is correct in its choice of parameters in the Parameterized Post-Newtonian generalized formulation of metric theories of gravitation. This test will discriminate between relativity and other theories at a level of 6 parts in 10 4. The perigee advance test also provides the most sensitive available test of the exotic β parameter associated in competing theories of gravitation with the second moment of the Earth's gravitational self-energy.