Please make the steps readable and clear,plz show every steps and equations A sm

Question

Please make the steps readable and clear,plz show every steps and equations

A small satellite is in orbit around planet earth at an altitude of 300 km. what is the required tangential speed of the satellite to maintain a circular orbit at this altitude? what increase or decrease in speed is required so that the satellite would be put on an elliptical path to reach an altitude of 24,000 km? how long would it take the satellite to get to the higher altitude from 300km once its speed has been changed?

Explanation / Answer

a)

radius of orbit(r)=radius of earth + altitude =6371+300=6671 km

G=6.67*10^-11

Let the velocity of satelite be v mass be m,

mv^2/r = G*m(earth)*m/r^2

v=(G*m(earth)/r)^0.5

=(6.67*10^-11*5.97*10^24/6671*10^3)^0.5=7725.76 m/s7

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b)

radius of orbit(r)=radius of earth + altitude =6371+24000=30371 km

G=6.67*10^-11

Velocity=(G*m(earth)/r)^0.5

=(6.67*10^-11*5.97*10^24/30371*10^3)^0.5 =3622.33 m/s

Decrease in velocity =7725.76-3622.33=4103.43 m/s

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c)

Length of semi-major axis=a=(r1+r2)/2=(6671+30371)/2=18521 km

Standard Gravitational parameter =gR^2 =9.8*(6371*10^3)^2=3.97* 10^14

Since the satelite covers half of the parameter before reaching the altitude 24000 km

Time Period will be half of the elliptical orbit time period,

T=pi*(a^3/mew)^0.5

=3.14*((18521*1000)^3/(3.97* 10^14))^0.5=12561.97 seconds

Time required=12561.97 seconds

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