To find the acceleration, we first need to calculate the force exerted on the astronaut in outer space. We can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):

F = m * a

Given that the weight of the astronaut is p = 700N, we can convert this to mass using the formula:

Weight = mass * gravity

700N = 75kg * 9.8 m/s^2

75kg = 700N / 9.8 m/s^2

Next, we can substitute the astronaut's mass (75kg) into the equation for force and solve for acceleration:

F = 75kg * a

700N = 75kg * a

a = 700N / 75kg

a = 9.33 m/s^2

Therefore, the jet engines should provide an acceleration of 9.33 m/s^2 for the astronaut to have a weight of 700N in outer space.