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**Astronomy Problems HELP * URGENT***

i am struggling with the following problems for my astronomy class.

1.) calculate the weight of a 91.0 kg (approx. 200 pounds at the surface of the earth) astronaut when his spaceship is at a point 51200.0 km above the earth's center. also calculate his mass at that point in space.

(i don't know what formulas to use or how to start this problem)

2.) If the wavelength of a particular type of light is 10,000 nm, what is the frequency? What would be the temperature of an object that had this wavelength as its peak intensity? What part of the spectrum is it in?

frequency = 3 X10^13 Hz

temp = 300 Kelvin

spectrum = infrared

( NOT SURE IF RIGHT)

3.) suppose a student discovers a new asteroid named starbright which has a semimajor axis 884,404,000 km from the sun. what would be its period of rotation around the sun?

( i got 2.352 X10^12 days) not even sure how. what formulas do i used to do this problem? can someone show me an example?

4.) if mars were 2.352 AU away from the earth during the mars rover sojourner mission how long did it take for radio messages to be sent round trip to mars to earth to mars? why did the sojourner have to be able to navigate with minimal guidancew from earth?

(once again i have no idea, i need help identifying what forumlas to use, how to get started)

5.) if the moon's distance from the earth varies from 492,065 km to 276,743 km, what would be the eccentricity of the moon's orbit?

(NO IDEA)

6.) what is the speed of an object that produces a dopple shift of 1.234 nm for a normal wavelength of 10,000.00 nm ( observed wavelength of 10,001.234)? is it moving towards ore away from the observer?

(no idea)

i need help identifying what formulas to use, and how to solve these problems, correctly.