A space probe is going to land on Mars to bring food to astronaut Matt Damon, wh

Question

A space probe is going to land on Mars to bring food to astronaut Matt Damon, who has been stranded on the planet. The satellite weighs 1000 kg and the food supply onboard weighs an additional 500 kg (that’s a lot of food!). There is not much friction in Mars’ atmosphere to slow the probe down. As it orbits, it enters the atmosphere of Mars at a velocity of 6 km/s at a height of 125 km from the surface of Mars. Note that Mars has a radius of 3400 km and mass of 6.39 x 1023 kg.

a) What is the total orbital energy of the satellite as it orbits?

b) What is the kinetic energy of the probe as it enters the Martian atmosphere?

c) What is the potential energy of the space probe as it enters the Martian atmosphere?

Explanation / Answer

The total orbital energy of the satellite is E = K + U = - G M m / 2 r
Where G is the gravitational constant, M is the mass of the mars and m is the mass of the satellite , r is the radius of the orbit
The value of the gravitational constant is G = 6.67 x 10-11 N m2/ kg2 , r = 3400 km + 125 km = 3525 km
The total energy is
E = - 6.67 x 10-11 x  6.39 x 1023 x 1500 / 2 x 3525 x 103
E = - 9.068 x 109 J
b) The kinetic energy is
K = (1/2) m v2
K = (1/2) 1500 x (6000 m/s )2
K = 2.7 x 1010 J
c) The potential energy
U = - G M m / r
U = -  6.67 x 10-11 x  6.39 x 1023 x 1500 / 3525 x 103
U = -1.81 x 1010 J

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