The earth's present orbit being taken to be circular. Find what its path would be if the sun's mass were suddenly reduced to 1/n of what it is now.
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11th
Physics
Gravitation
Kepler's Laws
If the earth were to sudden...
PHYSICS
If the earth were to suddenly contract to
n
1
th of its present radius without any change in its mass then the duration of the new day will be close to
MEDIUM
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ANSWER
Conservation of angular momentum dictates that angular momentum before and aftef contradiction must be the same.
I
1
w
1
=I
2
w
2
I=
5
2
Mr
2
→ Momentum of intertia of earth
w=
T
2π
→ Angular velocity of earth =
day
2π
Let r
2
and T
2
be the new radius and new day duration
Therefore,
T
1
r
1
2
=
T
2
r
2
2
∴T
2
=
r
1
2
r
2
2
T
1
When earth contracts, r
2
=
n
1
r
1
∴T
2
=
r
1
2
(
n
1
r
1
)
2
T
1
T
2
=
n
2
1
T
1
T
1
=24hours
∴T
2
=
n
2
24
hours