64. A planet in another solar system orbits a star with a mass of 4.0 × 1030 kg.
ID: 1781373 • Letter: 6
Question
64. A planet in another solar system orbits a star with a mass of 4.0 × 1030 kg. At one point in its orbit it is 250 × 106 krm from the star and is moving at 35 km/s. Take the universal gravitational constant to be 6.67 x 10-11 m2/s2 * kg and calculate the semimajor axis of the planet's orbit. The result is: A) 79x106 km B) 140×106 km C) 290x106 km D) 320×106 km E) 590×106 km 65. In Einstein's theory of gravitation, gravity is due to: A) the acceleration of the universe B) the presence of mass C) the rotation of the universe D) the curvature of spacetime E) the speed of lightExplanation / Answer
64)(C)a = 290 x 10^6 km
explanation:
we know that the orbital speed is given by:
v = sqrt (GM (2/r - 1/a))
(35 x 10^3)^2 = 6.67 x 10^-11 x 4 x 10^30 [2/(250 x 10^9) - 1/a]
[2/(250 x 10^9) - 1/a] = (35 x 10^3)^2/[6.67 x 10^-11 x 4 x 10^30 ] = 4.59 x 10^-12
1/a = 8 x 10^-12 - 4.59 x 10^-12 = 3.41 x 10^-12
a = 1/3.41 x 10^-12 = 0.290 x 10^12 m = 290 x 10^9 m
Hence, (C)a = 290 x 10^6 km
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