PraOSP-RWP Page 1 Quiz 1 Working time : 90 minutes Essay 1. Find the distance between Helsinki and Seattle along the shortest route. Where is the northernmost point of the route, and what is its distance from the North Pole? The longitude of Helsinki is 25°E and latitude 60°N; Seattle is located at 122°W 48°N. [points: 15] 2. You are an astronaut on the moon. You look up, and see the Earth in its full phase and on the meridian. What lunar phase do people on Earth observe? What if you saw a first quarter Earth? new Earth? third quarter Earth? Draw a picture showing the geometry. [points: 15] 3. Assu me that the radius of the Earth is 6370 km. A planet (mass m) is orbiting a star (mass M) at a distance a. The distance of the star from the centre of gravity of the system is a’. Show that: ( ) where P is period in years, distances are in AU’s and masses in solar masses. [points: 20] 4. Assume that all the stars located in galactic plane orbiting the center of Milky Way with the same speed, 250 km/s. From the Sun (8.5 kpc from galactic center), star ICE-01 is observed at galactic longitude with radial velocity +120 km/s. Estimate the distance of that star from the Sun! Illustration below will be helpful. [points: 25] 5. The mass of a pulsar is 1.5 M sun , radius 10 km, and rotation period 0.033 s. What is the angular momentum of the pulsar? Variations of 0.0003 s are observed in the period. If they are due to radial oscillations (“starquakes”), how large are these oscillations? [points: 25]
1. Find the distance between Helsinki and Seattle along the
shortest route. Where is the northernmost point of the route, and
what is its distance from the North Pole? The longitude of Helsinki
is 25E and latitude 60N; Seattle is located at 122W 48N. [points:
15]
2. You are an astronaut on the moon. You look up, and see the
Earth in its full phase and on the meridian. What lunar phase do
people on Earth observe? What if you saw a first quarter Earth? new
Earth? third quarter Earth? Draw a picture showing the geometry.
[points: 15]
3. A s s u m e t h a t t h e r a d i u s o f t h e E a r t h i s
6 3 7 0 k m . A planet (mass m) is orbiting a star (mass M) at a
distance a. The distance of the star from the centre of gravity of
the system is a. Show that:
( )
where P is period in years, distances are in AUs and masses in
solar masses. [points: 20]
4. Assume that all the stars located in galactic plane orbiting
the center of Milky Way with the same speed, 250 km/s. From the Sun
(8.5 kpc from galactic center), star ICE-01 is observed at galactic
longitude with radial velocity +120 km/s. Estimate the distance of
that star from the Sun! Illustration below will be helpful.
[points: 25]
5. The mass of a pulsar is 1.5 Msun, radius 10 km, and rotation
period 0.033 s. What is the angular momentum of the pulsar?
Variations of 0.0003 s are observed in the period. If they are due
to radial oscillations (starquakes), how large are these
oscillations? [points: 25]
