Suppose you are on the surface r 6685 times 107 m of Jupite

Suppose you are on the surface (r = 6.685 times 10^7 m) of Jupiter (M = 1.899 times 10^7 kg) sending a signal with frequency f = 1.3 MHz up to a satellite in orbit (r = 9.8 times 10^7 m). (a) Calculate the gravitational potential difference between the two points (b) Calculate the shift in frequency W-

Solution

[a]

Gravitational potential difference is work done in moving a unit mass

W= GM[ 1/x₂-1/x₁]

x₂= 9.8*10⁷m

x₁=6.685*10⁷ m

W= 6.67*10^-11*1.899*10²⁷[ -4.755*10^-9]=-6.02*10⁸ J

[b] Shift in frequency is

W= E = h* delta f

-6.02*10⁸ J= 6.6*10^-34_* delta f

Shift in frequency, delta f= 9.13*10 ⁴¹ Hz