Question

Pls help quick!

A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 5r?(1 point)



15√v


1


5


v



15v


1


5


v



5√v


5


v



5v

Answer 1

v / √5

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:

`v_o_r_b_i_t = \sqrt{(G*M)/(r) }`

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:

`v_o_r_b_i_t = \sqrt{(G*M)/(5r) }\\\\v_o_r_b_i_t = (1)/(√(5) ) \sqrt{(G*M)/(r) }\\`

- Now take the ratio of initial orbital speed to the increased orbital radius ( 5r ):

`v_o_r_b_i_t = (1)/(√(5) )*v \\`