Radius of the sun and earth not flat

[quah13579]

Homework Statement

1. (a) Given that the distances to the sun and the moon are approximately 150 million km and 400,000 km respectively. and that the radius of the moon is 1740 km , estimate the radius of the sun.[Hint:k=9*10^9 Nm^2/C^2, g=10ms^-2) ]

(b) Ancient astronomers knew that the Earth was not flat because it cast a circular shadow during a lunar eclipse. state another observation that led them to the same conclusion

Homework Equations

The Attempt at a Solution

what I've done is:
(a). s = m (150 million km / 400,000 km)
= 1740 km * 375 km
= 652,500 km

(b). Ships at sea can be seen farther away from a higher vantage point.

Am I right about those two question? For (a) how do I use hint to do this?
Thank you for any idea that help me.

 

[tiny-tim]

hi quah13579!

yes, your answer to (a) is fine (i assume you're using the fact that the moon is only just large enough to eclipse the sun )

i think the hint is wrong (or maybe it's the right hint to the wrong question) … it's presumably
intended to enable you to compare the centripetal acceleration with Newton's law of gravitation, but the radius of the sun (or moon) isn't relevant to that!

your answer to (b) is true, but it's not really an astronomical observation, is it?

hint: how did the ancient greeks measure the Earth's radius? ​