Gravitational Field Lines and Equipotential Line

Jupiter is the largest planet in the Solar system.

(a)

(i) Draw a diagram of Jupiter and its gravitational field lines.

(ii) Add the gravitational equipotentials to your sketch, ensuring that the field lines and equipotentials are clearly labelled.

(b) A satellite is in a circular orbit around Jupiter. The radius of the satellite’s orbit is 1.20 x 108 m. Jupiter’s mass is 1.90 x 1027 kg. Show that the speed of the orbiting satellite at any instant is 3.25 x 104 ms-1

(c) Now consider that the satellite follows an elliptical orbit. At which point or points of the orbit does the satellite have:

(i) Greatest gravitational potential energy?

(ii) Greatest kinetic energy?

Briefly explain your answers.

(d) The satellite sends a signal of 2.00 x 104 photons of frequency 5.60 x 1014 Hz back to Earth. The photons are detected in a digital camera.

(i) Calculate the total momentum transferred to the camera.

(ii) The detector in the camera is manufactured from Gallium-Arsenide, an extrinsic semiconductor with a band-gap of 1.40 eV. Will the photons create a current in the detector?

Justify your answer.