Orbits and Kepler's Laws Question

hardygirl989 · Apr 17, 2012

Homework Statement

Studies of the relationship of the Sun to our galaxy—the Milky Way—have revealed that the Sun is located near the outer edge of the galactic disc, about 30 000 ly (1 ly = 9.46 1015 m) from the center. The Sun has an orbital speed of approximately 250 km/s around the galactic center.

(a) What is the period of the Sun's galactic motion?

___________ yr

(b) What is the order of magnitude of the mass of the Milky Way galaxy?

___________ kg

(c) Suppose the galaxy is made mostly of stars of which the Sun is typical. What is the order of magnitude of the number of stars in the Milky Way?

___________

Homework Equations

F=GMm/R^2
v=2∏Rf
GMT^2=4∏R^3

The Attempt at a Solution

a) I got the correct answer. I did:
v=2∏Rf=2∏R/T
T = 2∏R/v = 2∏(2.84x10^17Km)/250Km/s = 7.13x10^15 s
T = 7.13x10^15 s(1/3600)(1/24)(1/365) = 2.26x10^8 yr
b) I got this one wrong...
F = GMm/R^2 = Mv^2/R
M = v^2R/G = (250000 m/s * 2.84x10^20)/6.67x10^-11 = 2.66x10^41 Kg
c) I also got this wrong...
Number of Stars = 2.66*1041kg / 1.99*1030kg= 1.336*1011 stars

Can anyone help me out with the last two parts? I am not sure why they are wrong...

Steely Dan · Apr 17, 2012

If they're asking for an order of magnitude, they might just want [itex]10^{41}[/itex] and [itex]10^{11}[/itex], respectively (assuming those are the correct numbers, which they seem to be).

hardygirl989 · Apr 17, 2012

That makes sense.

The website says only one thing about scientific notation on their formatting page:
Incorrect format: 1.2E15 Correct Format: 1.2e15

I tried typing in e41 and it told me that it cannot understand what I wrote. I understand that you probably are not able to access the website, but do you have any suggestions that I can try?

Steely Dan · Apr 17, 2012

In that notation, "e41" does not make sense, but "1e41" ([itex]=10^{41}[/itex]) does make sense. I would recommend trying that, as well as 2.66e41. The only online homework submission site I am familiar with is WileyPlus, and on that system this notation would be accepted.

hardygirl989 · Apr 17, 2012

1e41 was correct! Thank you so much for your help! =D

SOLVED.

Orbits and Kepler's Laws Question

Homework Statement

Homework Equations

The Attempt at a Solution

1. What are Kepler's Laws of Planetary Motion?

Kepler's Laws of Planetary Motion are a set of three laws developed by astronomer Johannes Kepler in the early 17th century. These laws describe the motion of planets around the sun and have been fundamental in our understanding of orbits and celestial mechanics.

2. How do Kepler's Laws explain the shape of orbits?

Kepler's First Law states that planets orbit the sun in elliptical paths, with the sun located at one of the foci of the ellipse. This explains the shape of orbits as not being a perfect circle, but rather an elongated oval shape.

3. What is the relationship between a planet's orbital period and its distance from the sun according to Kepler's Laws?

4. How do Kepler's Laws apply to objects other than planets?

Kepler's Laws can also be applied to objects other than planets, such as moons orbiting a planet or artificial satellites orbiting Earth. As long as there is a central body, such as a planet or a star, and a smaller object orbiting it, Kepler's Laws can be used to describe the motion of that object.

5. How did Kepler's Laws contribute to our understanding of the universe?

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