Problem 1: The orbital period of Mars is 1.881 yrs. When Mars is ...

Problem 1: The orbital period of Mars is 1.881 yrs. When Mars is
opposite the Sun in the sky its position with respect to the background
of fixed stars is measured at sunset and again at sunrise. The
effective baseline between these two positions is 11,700km and the
change in its position on the sky is 30.8”. Calculate the length of the
Astronomical Unit in metres.

Problem 1: The orbital period of Mars is 1.881 yrs. When Mars is opposite
the Sun in the sky its position with respect to the background of fixed stars is
measured at sunset and again at sunrise. The effective baseline between
these two positions is 11,700km and the change in its position on the sky is
30.8”. Calculate the length of the Astronomical Unit in metres.

Problem 2: The orbital period of Venus is 0.6152 yrs. When Venus is between
the Earth and Sun (at inferior conjunction) radar signals are launched from the
Earth and the reflected signal arrives after 276.2s. Calculate the length of the
Astronomical Unit in metres.

Problem 3:
What is the shift in position of the Sun due to the influence of Jupiter?
Express your answer in solar radii, R סּ = 69510 3 km. (The Sun’s mass is
1047 Jupiter’s mass, distance from Sun to Jupiter is 5.2AU ).

Problem 4: What is the velocity of the Sun due to the influence of Jupiter?
(The Sun’s mass, M סּ = 2 10 30 kg, is 1047 Jupiter’s mass and the semimajor
axis of Jupiter’s orbit is 5.2 AU)

Problem 4 cont.: In 1995 the first planet detected by the radial velocity technique was
that around the star 51 Peg. The velocity amplitude was measured to be 60m/s
and the period is 4.2days. Assuming the orbit is edge–on and that host star has
the same mass as the Sun estimate (i) the mass of the planet (give your answer in
Jupiter masses) and (ii) the radius of the orbit in Astronomical Units.