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 km from the star and is moving at 35km/s. Take the universal gravitational
constant to be 6.67 × 10−11 m2/s2 · kg and calculate the semimajor axis of the planet’s orbit.
The result is:
A. 79 × 106 km
B. 160 × 106 km
C. 240 × 106 km
D. 320 × 106 km
E. 590 × 106 km
I used the formula for the orbital speed v^2 = GM [2/r - 1/a].
Solving for a, I got 1/a=2/r-v^2/GM. Plugging in the given data I got 293x10^6 km. None of the options is relevant with mine. Can someone show me what I did wrong?
orbit it is 250×106 km from the star and is moving at 35km/s. Take the universal gravitational
constant to be 6.67 × 10−11 m2/s2 · kg and calculate the semimajor axis of the planet’s orbit.
The result is:
A. 79 × 106 km
B. 160 × 106 km
C. 240 × 106 km
D. 320 × 106 km
E. 590 × 106 km
I used the formula for the orbital speed v^2 = GM [2/r - 1/a].
Solving for a, I got 1/a=2/r-v^2/GM. Plugging in the given data I got 293x10^6 km. None of the options is relevant with mine. Can someone show me what I did wrong?
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