Answer:
v / √5
Step-by-step explanation:
Solution:-
- We have a satellite of mass ( m ) that orbits the earth of mass ( M ). The radius of orbit is ( r ) : center of earth - to - center of satellite radial distance.
- The satellite orbits the Earth with constant tangent velocity ( v ). The velocity ( v ) is a function of massive body ( M ) about which the smaller body orbits and orbital radius ( r ).
- The formulation is given by:
[tex]v_o_r_b_i_t = \sqrt{\frac{G*M}{r} }[/tex]
Where,
G: The universal gravitational constant
- We are to compare the orbital speeds by changing some of the parameters in the above relation.
- The effect on the orbital speed ( v_orbit ) by increasing the orbital radius to ( 5r ) can be evaluated using the given relation. Such that:
[tex]v_o_r_b_i_t = \sqrt{\frac{G*M}{5r} }\\\\v_o_r_b_i_t = \frac{1}{\sqrt{5} } \sqrt{\frac{G*M}{r} }\\[/tex]
- Now take the ratio of initial orbital speed to the increased orbital radius ( 5r ):
[tex]v_o_r_b_i_t = \frac{1}{\sqrt{5} }*v \\[/tex]
