Can an electric field exist in a vacuum?

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

Exercise 2. find the wavelength of a photon emitted when an electron jumps from the n = 3 energy level down to the n = 2 energy level. where is this photon in the electromagnetic spectrum?

Amother used 150 watts of power to raise a 15 newton object in a time interval of 8.0 seconds. through what vertical distance was the object raised ?