Question

Ten days after it was launched toward Mars in December 1998, the Mars Climate Orbiter spacecraft (mass 629 kg) was 2.87×106km from the earth and traveling at 1.20×104km/h relative to the earth.At this time, what were the following. (a) the spacecraft's kinetic energy relative to the earth J (b) the potential energy of the earth-spacecraft system J

Answer 1

Answer:

3494444444.44444 J

-87077491.39453 J

Explanation:

M = Mass of Earth = $6.371\times 10^{6}\ kg$

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

R = Radius of Earth = $6.371\times 10^{6}\ m$

h = Altitude = $2.87\times 10^9\ m$

m = Mass of satellite = 629 kg

v = Velocity of spacecraft = $1.2\times 10^4\ km/h$

The kinetic energy is given by

$K=\frac{1}{2}629\times \left(1.2\times 10^4\times \dfrac{1000}{3600}\right)^2\\\Rightarrow K=3494444444.44444\ J$

The spacecraft's kinetic energy relative to the earth is 3494444444.44444 J

Potential energy is given by

$U=-\dfrac{GMm}{R_e+h}\\\Rightarrow U=-\dfrac{6.67\times 10^{-11}\times 5.97\times 10^{24}\times 629}{2.87\times 10^9+6.371\times 10^{6}}\\\Rightarrow U=-87077491.39453\ J$

The potential energy of the earth-spacecraft system is -87077491.39453 J