Download Homework 1 – Exercise 1 1/9

Homework 1 – Exercise 1
The parallax angle for Sirius is 0.379’’. Find the distance to Sirius in units of
(i) parsecs, (ii) light years, (iii) AU and (iv) m.
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Homework 1 – Exercise 2
The Hipparcos Space Astronomy mission was able to measure parallax angles
down to nearly 0.001’’. To get a sense of that level of resolution, how far from a
dime would you need to be to observe it subtending an angle of 0.001’’? [Note:
diameter of a dime is approximately 1.9 cm].
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Homework 1 – Exercise 3
In 1672, an international effort was made to measure the parallax angle of Mars
at the time of opposition, when it was closest to Earth. Consider two observers
who are separated by a baseline equal to Earth’s diameter. If the difference in
their measurements of Mars’s angular position is 33.6’’. What is the estimated
distance between Earth and Mars? Express your answer in both units of [m] and
[AU]. [Data: R=6371km]
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Homework 1 – Exercise 4
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Neutron stars, such as the one at the center of the Crab Nebula, have about the
same mass as our sun, but a much smaller diameter. If you weight 675 N on Earth,
what would you weigh at the surface of a neutron star of one solar mass with a
diameter of 20 km? [Data: M=1.988x1030kg]
Homework 1 – Exercise 5
How much lighter (in [%]) do you weigh on an airplane 10km above the Earth’s
surface? [Recall: R=6371km, M=5.972x1024kg]
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Homework 1 – Exercise 6
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We want to place a 1000-kg satellite into a circular orbit 300 km above the Earth’s
surface.
1.What speed, period and radial acceleration must it have? [Recall: 𝑎𝑟𝑎𝑑𝑖𝑎𝑙=𝑣2/r]
2.How much work must be done to place this satellite in orbit?
3.How much additional work would have to be done for the satellite to escape
the Earth? [Recall: R=6371km, M=5.972x1024kg]
Homework 1 – Exercise 6
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Homework 1 – Exercise 7
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The apparent (visual) magnitude between two stars is measured to be 6.32. What is
the flux ratio between the two stars?
Homework 1 – Exercise 8
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The visible light from Sirius appears to be 24.2 times brighter than the light from
Polaris. What is their magnitude difference? Sirius apparent magnitude is -1.47. What
is the apparent magnitude of Polaris?