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Home » A satellite is in an elliptic orbit around the earth with an aphelion of 6R and perihelion of 2R where R = 6400 km is the radius of the earth. Find eccentrically of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R?
A satellite is in an elliptic orbit around the earth with an aphelion of 6R and perihelion of 2R where R = 6400 km is the radius of the earth. Find eccentrically of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R?
CBSE | Class 11 | Gravitation | NCERT Exemplar | Physics
A satellite is in an elliptic orbit around the earth with an aphelion of 6R and perihelion of 2R where R = 6400 km is the radius of the earth. Find eccentrically of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R?

Solution:

Radius of perigee is given as r_{p}=2R

Radius of apogee is given as r_{a}=6R

And we know,

r_{p}=a(1-e)=2R
and,
r_{a}=a(1+e)=6R

From the above equations, we get e = 1/2

From the law of conservation of angular momentum, we have,

L_{1}=L_{2}

Let m be the mass of satellite

v_{a}/v_{p}=r_{p}/r_{a}=1/3

So, v_{p}=3v_{a}

From conservation of energy we get,

\frac{1}{2} m v_{p}^{2}-\frac{G M m}{r_{p}}=\frac{1}{2} m v_{a}^{2}-\frac{G M m}{r_{a}}

v_{a}=2.28km/s

v_{c}=3.23km/s

The velocity at the apogee will be,

v_{c}-v_{a}=0.95km/s

i

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