How Do I Solve These Complex Astronomy Problems?

[astronomystudent]

I don't even know how to begin these problems. If someone could leave me tips or formulas or anything to help me solve these it would be greatly appreciated. Here are the following:
1. What is the diameter (in Kilometers) of Mars if it appears 18 arcsec in sized when it is 0.520 AU from Earth?

2. What is the focal length of the Meade 12 inch LX200 (12 inch x 25.4 mm/inch aperture) when it is used at f/5.86? How would a 15 sec exposure at f/5.86 compare to an exposure at f/20? What would be the pixel resolution for a 9 micron pixel at f/5.86?

3. What is the rotation period of Io (in days) if it is in a 1:1 resonance with Jupiter like our Moon is with Earth. Jupiter has a mass of 318 M(earth). Io's mass is insignificant and it has a semimajor axis of 421,600 Km. Remember you must use EMDs and lunar sidereal months with Earth masses or change to Solar masses, years and AUs!

4. If the diameter of a new Kuiper object was found to be 1/10th the diameter of Earth and its mass was 1/3000th of Earth, what would its density be (in g/cc or kg/m^3).

5. If a new asteroid has a period of exactly one year, but an eccentricity of 0.25, wherer are the aphelion and perihelion points (in AU).

6. What woul be your weight on a planet with a mass of 5.67 times the mass of the Earth and a radius of 13,456 km? What would be the density of this planet?

 

[tony873004]

Hi. Most of these questions are pretty straightforward and are probably covered in your textbook.

Let me see if I can point you in the right direction without actually doing them since they seem like homework questions.

1. There's 2 ways to do this. One is with trig. Draw a triangle and label what you can. The trickiest part of this is the unit conversion. You're given your angle, 18 arc seconds. Maybe your calculator let's you do trig on arcseconds, but if it doesn't, divide by 3600 to get degrees. You also know your side adajacent to the angle. Any your hyponeneuse is almost identical to your side adjacent. So there's 2 trig formulas you can use to get your side opposite, which is the diameter of Mars.

But the easier way is to use the small angle approximation. Theta = a/d. If a and d are expressed in the same units, then Theta will be in radians. So you need to convert your arcseconds to radians. But if a is in AU and d is in parsecs, then Theta is expressed in arcseconds.

2. Just look up focal length in the index of your book, or Google it. It's just a straight forward division problem.

3. If it's 1:1, then it's rotation period equals its orbital period. Just Google for formula for orbital period. It's just a straightforward formula, containing square roots and cube roots, where you plug in your knowns to solve for your unknown.

4. Just look at your output units, g/cc or kg/m^3. It tells you your density formula. g and kg are mass, and cc (aka cm^3) and m^3 are volumes. Therefore density = mass / volume. You're given mass. You need volume, and you're given diameter. Just look up the formula for volume of a sphere. You'll also need to look up Earth's mass and diameter.

5. Any 2 objects that have the same period also have the same semi-major axis. Can you think of any other object that orbits the Sun in exactly 1 year? What is its semi-major axis? This will also be the Semi-major axis of your asteroid. Now just look up the formula eccentricity. It's a simple one. BTW... your asteroid is probably Cruithne or 2002AA29.

6. The density part is just like #4. Your weight can be expressed in Newtons. If your teacher wants pounds, you have to do a simple conversion. To find your weight in Newtons, you must know your mass and the acceleration at the surface of the planet. The acceleration is found with a=GM/r^2. Then once you have your mass and acceleration (g), you can solve for your force (weight). F=ma.

Good luck with the unit conversions. They're the trickiest part of these problems. See how far you can get and post what you've done so far.