Astronomy 3 Spring 2015 Problem Set #1 Due Wednesday Feb 18 Please explain your reasoning and show your work on each problem. 1. Suppose the Eart h’s mass is twice as larg e as it is, but is at the same distanc e from the Sun. How would this affect its orbital period around the Sun? 2. Mars’ orbit has a semi-major axis of 1.5 AU. From Kepler’s third law, calculate Mars’ period using ratios. 3. Expla in why Kepler’s second law impli es that a planet mo ves on its orbit non- uni for mly . That is, it move s faster in some par ts of its orbit and slower in others. 4. Astro nauts in orbit around the Eart h are weightl ess. Why are they then not massless? 5. Imagine that you are in a roc ke t ship far from any celes tial object so there is no gra vit y and the roc ke t ship is acceler ati ng in the forward directio n. The floor of the rock et ship is perpendi cular to the direc tion of mot ion. Imagine further that there is a scale on the floor of the rocket ship. If you’re standing on the scale, would it show that you had weight or not? Explain. 1
Please explain your reasoning and show your work on each
problem.
1. Suppose the Earths mass is twice as large as it is, but is at
the same distancefrom the Sun. How would this affect its orbital
period around the Sun?
2. Mars orbit has a semi-major axis of 1.5 AU. From Keplers
third law, calculateMars period using ratios.
3. Explain why Keplers second law implies that a planet moves on
its orbit non-uniformly. That is, it moves faster in some parts of
its orbit and slower inothers.
4. Astronauts in orbit around the Earth are weightless. Why are
they then notmassless?
5. Imagine that you are in a rocket ship far from any celestial
object so there isno gravity and the rocket ship is accelerating in
the forward direction. Thefloor of the rocket ship is perpendicular
to the direction of motion. Imaginefurther that there is a scale on
the floor of the rocket ship. If youre standingon the scale, would
it show that you had weight or not? Explain.
