An Earth Satellite is in elliptical orbit with minimum altitude h1=300 miles abo

Question

An Earth Satellite is in elliptical orbit with minimum altitude h1=300 miles above the Earth’s surface and maximum altitude h2=21,000 miles above the Earth’s surface. Determine the velocity at the minimum approach.
Note: Radius of the Earth, Re =3960 miles Mass of the Earth,Me= 5.976x10^24 kg (not needed)
Will rate please show every step!
An Earth Satellite is in elliptical orbit with minimum altitude h1=300 miles above the Earth’s surface and maximum altitude h2=21,000 miles above the Earth’s surface. Determine the velocity at the minimum approach.
Note: Radius of the Earth, Re =3960 miles Mass of the Earth,Me= 5.976x10^24 kg (not needed)
Will rate please show every step!
An Earth Satellite is in elliptical orbit with minimum altitude h1=300 miles above the Earth’s surface and maximum altitude h2=21,000 miles above the Earth’s surface. Determine the velocity at the minimum approach.
Note: Radius of the Earth, Re =3960 miles Mass of the Earth,Me= 5.976x10^24 kg (not needed)
Will rate please show every step!

Explanation / Answer

h1 = 300 miles  

h2 = 21000 miles

a = (2 Re + h1 + h2) / 2 = (7920 + 300 + 21000)/2

a = 14610 miles

v = sqrt[ G M (2/r - 1/a)]

v = sqrtp[ (6.67 x 10^-11 x 5.976 x 10^24)(2/(4260 x 1609) - 1/(14610 x 1609))]

v = 9967 m/s

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