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Class 10 Class 12
Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is 4.22 × 108 m. Show that the mass of Jupiter is about one-thousandth that of the sun.

Orbital period of  I0 , TI0 = 1.769 days

=  1.769 × 24 × 60 × 60 s

Orbital radius of  I0 , RI0 = 4.22 × 108 m

Satellite I0 is revolving around the Jupiter

Mass of the Jupiter is given by,

MJ = 4π2RI03 / GTI02                         ...(i)

where,

MJ = Mass of Jupiter,

G = Universal gravitational constant,

Orbital period of the earth,

T= 365.25 days

= 365.25 × 24 × 60 × 60 s

R
= 1 AU = 1.496 × 1011

Mass of sun is given as,

Ms = 4π2Re3 / GTe                           ...(ii)

Therefore,

Ms / MJ  =

=

Substituting the values,

=

= 1045.04

∴ Ms / MJ  ~ 1000

M~ 1000 × M

Hence, it can be inferred that the mass of Jupiter is about one-thousandth that of the Sun.
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What is Geocentric theory?

According to the geocentric theory, all the astronomical bodies like the moon, the sun and stars revolve around the earth, and the earth is at the centre of the universe.
1256 Views

The position co-ordinates of two particles of masses m1 and m2are (x1, y1, z1) and (x2, y2, z2) respectively. Find the coordinates of the centre of mass.

The position vectors of masses m1 and m2 are respectively,

Let the position coordinates of the centre of mass be (X, Y, Z).

Therefore the position vector of centre of mass is,

Since,

Comparing the coefficients of  , we get

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What is Heliocentric theory?

According to the Heliocentric theory, the sun is at the centre and various planets revolve around the sun at their axis.
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What is the celestial sphere?

At night, if we see the planets and the stars in the sky, all appear to lie in the hemisphere (rest of the hemisphere we are unable to see because of being on the other side of the earth). This sphere is called the celestial sphere.
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Is Geodesic always a straight line?

No, Geodesic is a straight line if and only if,  the two points lie on the flat surface. If the two points lie on the curved surface then it is a curved line.
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