Astronomers discover a planet around a star that is exactly like our Sun. The pl

Question

Astronomers discover a planet around a star that is exactly like our Sun. The
planet is in a circular orbit around its sun, and the radius of the orbit is only 1=16 the distance
between the Earth and our Sun. The planet has a radius 3 times larger than the Earth, and a mass
18 times larger than the Earth's mass.
(2) What would a 70 kg person weigh on this new planet?
A.) 700 N
B.) 1,400 N
C.) 2,100 N
D.) 4,200 N
E.) 6,300 N
AB.) 12,600 N
AC.) Not enough information to estimate.
(3) How long does it take this planet to go around its sun?
A.) 1/256 of a year (1.4 days)
B.) 1/64 of a year (5.7 days)
C.) 1/16 of a year (22.8 days)
D.) 1/4 of a year (3 months)
E.) 1 year
AB.) 4 years
AC.) 16 years
AD.) 64 years
AE.) 256 years
BC.) Not enough information to estimate.

PLEASE EXPLAIN!!!

Explanation / Answer

2)B)1400 N

g = G*M/R^2

= G*18*Me/(3*Re)^2
= 2*G*Me/Re^2
= 2*9.8
= 19.6 m/s^2

W = m*g
= 70*19.6
= 1372 N

approximtely 1400 N

3) B.) 1/64 of a year (5.7 days)

T is propportiinaol to r^(3/2)

T2/T1 = (r2/r1)^3/2

= (1/16)^3/2

= 1/64

T2 = T1/64 = 365/64 = 5.7 days

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