In May 2008, the United States successfully landed a spacecraft named Phoenix ne

Question

In May 2008, the United States successfully landed a spacecraft named Phoenix near the northern polar regions of Mars. Immediately upon landing, the craft sent a message indicating that all had gone well.

A radio signal was sent to a deep space probe traveling in the plane of the solar system. Earth received a response 4.5 days later. Assuming the probe computers took 3.0 hours to process the signal instructions and to send out the return message, was the probe within the solar system? (Assume a solar system radius of about 40 times the Earth-Sun distance.)

Explanation / Answer

Given a) Speed of the signal is ,v = 3 *10^8 m/s     Radius of Mar's orbit around sun, Rm = 227.9 *10^6 km     Radius of Earth's orbit around sun , Re = 149.6 *10^6 km     The greatest distance between earth and mars is          R = Rm + Re = 377.5 *10^6 km     The time taken for the signal to reach earth is                  T = ( 377.5 *10^9 m) /  3 *10^8 m/s                   T = 21 min b) Power of the signal is , P = 500 W     closest distance between earth and mars is        R = Rm - Re = 78.3 *10^9 m     Since power P = I * 4R^2                          I = 500 W / 4 *3.14 *(78.3 *10^9 m)^2                          I = 6.5 *10^-21 W /m^2 ---------------------------------------------------------------------------------- Radius of solar system , R = 5925 *10^9 m Time taken for the signal to reach earth is T = (5925 *10^9 m) / 3 *10^8 m/s T = 5.5 hrs Normally it takes only 3hrs for the probe , but here it is 5.5 hrs so, the probe is outside the solar system

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