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Tardigrade
Question
Physics
A planet revolves around the sun in an elliptical orbit. If vp and va are the velocities of the planet at the perigee and apogee respectively, then the eccentricity of elliptical orbit is given by
Q. A planet revolves around the sun in an elliptical orbit. If
v
p
and
v
a
are the velocities of the planet at the perigee and apogee respectively, then the eccentricity of elliptical orbit is given by
3790
171
Gravitation
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A
v
a
v
p
10%
B
v
a
+
v
p
v
a
−
v
p
20%
C
v
p
−
v
a
v
p
+
v
a
23%
D
v
p
+
v
a
v
p
−
v
a
47%
Solution:
As
=
v
a
v
p
=
a
(
1
−
e
)
a
(
1
+
e
)
where a is semi-major axis of the ellipse
v
p
(
1
−
e
)
=
v
a
(
1
+
e
)
or
v
p
−
e
v
p
=
v
a
+
e
v
a
e
(
v
a
+
v
p
)
=
v
p
−
v
a
or
e
=
v
a
+
v
p
v
p
−
v
a