Respuesta :
The work which is required for spacecraft engines to perform to move the spacecraft to a circular orbit that is 4000 km above the surface is 5.336×10¹¹ J.
What is work done?
Work done is the force applied on a body to move it over a distance. Work done in case of spacecraft is equal to the change in potential energy. It can be given as,
[tex]W=GmM(\dfrac{1}{r_1}-\dfrac{1}{r_2})[/tex]
Here, (m) is the mass of the spacecraft, (M) is the mass of and (r1 and r2) are the radius of the circular orbit from the surface.
The spacecraft has mass of 5000-kg and it is circular orbit 2000 km above the surface of Mars.
The work which is required spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface has to be find out.
The mass of the Mars is 6.4×10²⁷ kg and the value of G is 6.67×10⁻¹¹ Nm²/kg⁻². Thus using the above formula,
[tex]W=(6.67\times10^{-11})(5000)(6.4\times10^{27})(\dfrac{1}{2000\times10^{3}}-\dfrac{1}{4000\times10^{3}})\\W=5.336\times10^{11}\rm\; J[/tex]
Hence, the work which is required for spacecraft engines to perform to move the spacecraft to a circular orbit that is 4000 km above the surface is 5.336×10¹¹ J.
Learn more about the work done here;
https://brainly.com/question/25573309
