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Class 10 Class 12
A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg; mass of the Sun = 2 × 1030 kg; mass of mars = 6.4 × 1023 kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 × 108kg; G= 6.67 × 10–11 m2kg–2.

Mass of the spaceship, m= 1000 kg

Mass of the Sun, M = 2 × 1030 kg

Mass of Mars, mm = 6.4 × 10 23 kg

Orbital radius of Mars, R = 2.28 × 10kg

=2.28 × 10
11

Radius of Mars, = 3395 km

= 3.395 × 10
6 m

Universal gravitational constant, G = 6.67 × 10–11 m2kg–2

Potential energy of the spaceship due to the gravitational attraction of the Sun =

Potential energy of the spaceship due to the gravitational attraction of Mars = -

Since the spaceship is stationed on Mars, its velocity and hence, its kinetic energy will be zero.

Total energy of the spaceship =
=

Energy required for launching the spaceship out of the solar system,

= – (Total energy of the spaceship)

=

= 6.67 × 1011 × 103 ×

596.97 × 109

=  6 × 10
11 J.
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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.
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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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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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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.
907 Views

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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