A newly discovered planet is in a circular orbit around a distant star with an o

Question

A newly discovered planet is in a circular orbit around a distant star with an orbital period of 350 Earth days. The planet also rotates on its axis, making one full rotation every 4.50 Earth days. The radius of the planet is rp = 4.50 106 m and the radius of the planet's orbit about the star is rs = 7.00 1011 m.

Determine the ratio of the radial acceleration, due to the rotation of the planet, of an object at the equator of the planet (acp) to the radial acceleration of the planet in its orbit about the star (acs). acp acs =

Explanation / Answer

Radial acceleration a = v^2/r
vp = (2**rp)/T
acp = vp^2/rp = (4*^2*rp)/T^2

Now due to orbital motion,
Vs = 2*pi*rs/To
acs = vo^2/rs = (4*^2*rs)/To^2

acp/acs = (4*^2*rp)/T^2 / (4*^2*rs)/To^2
acp/acs = (To^2* rp^2 )/ (T^2 * rs^2)
acp/acs = (350^2 * (4.50*10^6)^2 ) / ((7.0 * 10^11)^2 * 4.5^2)
acp/acs = 2.5 * 10^-7

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