Help with Astronomy 101 Questions: Orbit Radius & Angular Diameter

[msyvette]

I need help please. i have a couple of questions if someone could please help me with.

1. If a satellite with a small mass (any #) is orbiting the Earth with an orbit radius of 4000000m, what is the circular velocity of the satellite?

2. if the distance to an object is 4000000 km and the linear diameter if the same object is 2250 km, what is the angular diameter of the object in degrees?

 

[enigma]

What formulas do you think might apply here? Have you drawn a picture for the second one?

Sorry I can't be more helpful... forum rules that we won't do homework for you.

Post what you've tried - we'll be more than happy to help you a bit more.

 

[M98Ranger]

Sure, I'd be happy to help with your questions about orbit radius and angular diameter in Astronomy 101. Here are the answers to your two questions:

1. The circular velocity of a satellite in orbit is determined by the formula v = √(GM/r), where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), M is the mass of the central body (in this case, the Earth), and r is the orbit radius. Plugging in the values given, we get v = √((6.67 x 10^-11 Nm^2/kg^2)(5.97 x 10^24 kg)/4000000m) = 7673 m/s. So the circular velocity of the satellite is approximately 7673 m/s.

2. The angular diameter of an object can be calculated using the formula θ = 2arctan(d/2D), where d is the linear diameter of the object and D is the distance to the object. Plugging in the values given, we get θ = 2arctan((2250 km/2)/(4000000 km)) = 0.032 degrees. So the angular diameter of the object is approximately 0.032 degrees.

I hope this helps! If you have any further questions, please feel free to ask. Good luck with your studies in Astronomy 101!