Question

A planet of mass m moves in an elliptical path around the Sun (which is at one of the foci of the ellipse), so that
its maximum and minimum distances from the Sun are Tmax and I'min, respectively. Taking the gravitational constant
to be G and the mass of the Sun to be M., what is the angular momentum of the planet relative to the center of the Sun?
o [2GM,mºr
maxTmin / (Tmax
I'min
in)]"2
2G (Mmrmax 'min / (rmax - Tmin
)]1/2
o [2GM2mºrmax/min / (rmax + tmin)]"/2
2G
[M mr maxľmin / ("max + 7 min)]"/2​

Answer 1

Answer:

From law of conservation of angular momentum

mv

1

r

1

=mv

2

r

2

⇒v

2

=

r

2

v

1

r

1

→(1)

From law of conservation of total mechanical energy

r

1

−GMm

+

2

1

mv

1

2

=

r

2

−GMm

+

2

1

mv

2

2

→(2)

From equation (1) and (2)

v

1

=

(r

1

+r

2

)r

1

2Gmr

2

Angular momentum

L=mv

1

r

1

=m

r

1

+r

2

2GMr

1

r

2

solution