advanced functions

The Moon has a diameter of about 3480 km and an orbital radius of about 384 400 km from the centre of Earth. Suppose that the Moon is directly overhead. What is the measure of the angle subtended by the diameter to the Moon as measured by an astronomer on the surface of Earth? Answer in both radians and degrees.

  1. 👍 2
  2. 👎 1
  3. 👁 2,281
  1. Diameter of the moon = 3480 km
    Distance from surface of the earth
    = Distance to centre - radius of the earth
    = 384400-6400 km
    = 378000 km

    Since the angle is very small, we can approximate the arc-length by the chord length, equal to the diameter.

    Angle subtended
    = 3480/378000
    = 0.0092 radian

    If we had used the chord instead, the difference in angle calculated would have been 0.0000000325 radians more.
    i.e.
    angle
    = 2*sin-1(1740/37800)
    = 0.0092 radian

    1. 👍 2
    2. 👎 0
  2. Sorry, I actually have a question. According to the question that was posted. If I were to solve this question, without knowing the radius of the earth before hand. Is there any other solution??

    1. 👍 2
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Science

    Can someone please check my answers and if they are wrong can you help me fix them? Thank so much!! 1. Which of the following determines the strength of the force of gravity between two objects? Check all that apply. (2 points)

  2. Physics Please help!

    Calculate the position of the center of mass of the following pairs of objects. Use acoordinate system where the origin is at the center of the more massive object. Give youranswer not in meters but as a fraction of the radius as

  3. Physics

    The average distance separating Earth and the Moon (center to center) is 384 000 km. Use the data in Table 7.3 to find the net gravitational force exerted by Earth and the Moon on a 3.00 multiplied by 104 kg spaceship located

  4. Mathematics

    1. Find the circumference of the given circle. Round to the nearest tenth. (Circle with radius of 3.5 cm) -22.0 cm -38.5 cm -11.0 cm -42.8 cm 2. Find the area of the given circle. Round to the nearest tenth. (Circle with a

  1. math

    The Moon orbits Earth every 27.3 days. Determine the angular velocity of the Moon, in degrees per day and in radians per day. The radius of the orbit of the Moon is about 384 400 km. How far does the Moon move along an arc of it's

  2. physics

    The moon's diameter is 3.48 106 m, and its mean distance from the earth is 3.85 108 m. The moon is being photographed by a camera whose lens has a focal length of 48.5 mm. (a) Find the diameter of the moon's image on the slide

  3. gravity

    You are an astronaut in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (450 km above the Earth), but 24 km behind it. How long will it take to overtake the

  4. science

    which of the following would happen to the moon if gravity no longer affected it ? a) the moon would continue to move on it's orbital path b) the moon stop moving all together c) the moon would move in a spiral toward earth d) the

  1. math;)

    Apollo 8 orbited the moon in a circular orbit. Its average altitude was 185 km above the moon's surface. Create an equation to model the path of Apollo 8 using the center of the moon as the origin. Note that the radius of the moon

  2. physics

    Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 720 km above the surface of the Moon, where the acceleration due to gravity is 0.839 m/s2. The

  3. physics

    (a) One of the moons of Jupiter, named Io, has an orbital radius of 4.22 108 m and a period of 1.77 days. Assuming the orbit is circular, calculate the mass of Jupiter. (b) The largest moon of Jupiter, named Ganymede, has an

  4. Physics

    The diameter of the Moon is 3480km. What is the volume of the Moon? How many Moons would be needed to create a volume equal to the Earth? How do you find the volume of the Moon from just the diameter? Also, does anybody know how

You can view more similar questions or ask a new question.