Question

Suppose one of the Global Positioning System satellites has a speed of 4.42km/s at perigee and a speed of 3.64km/s at apogee. If the distance from the center of the Earth to the satellite at perigee is 2.24×104 , what is the corresponding distance at apogee?

Answer 1

Answer:
`2.71* 10^4 km`

Step-by-step explanation:

Given

Speed of satellite
`v_1=4.42 km/s` At Perigee

Speed at apogee
`v_2=3.64 km/s`

Distance from center to Perigee
`r_1=2.24* 10^(4) Km`

Let
`r_2` be the distance of Apogee

According to Kepler's Second law angular Momentum is conserved

`mv_1r_1=mv_1r_2`

`v_1r_1=v_2r_2`

`4.42* 2.24* 10^4=3.64* r_2`

`r_2=(4.42)/(3.64)* 2.24* 10^4`

`r_2=2.71* 10^4 Km`