Home > 0877 > GR0877 Problem 53

GR0877 Problem 53

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (D) According to the problem statement, the angular momenta are the same: m_1 v_1 R = m_2 v_2 R, therefore m_1/m_2 = v_2/v_1. For the orbital periods one has T_1 = 2\pi R/v_1 and T_2 = 2 \pi R/v_2 (orbits are circles!). Thus, m_1/m_2 = v_2/v_1 = T_1/T_2 = 3. Think about why cannot we apply Kepler’s third law in its usual form.

Found a typo? Comment!

Jump to the problem

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Want to get a full PDF with solutions? Read THIS.

The comments appending particular solutions are due to the respective users. Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 2008 by ETS.

Advertisements
Categories: 0877 Tags: , , , ,
  1. DD
    05.03.2014 at 06:40

    The main reason we can’t apply Kepler’s third law is that the corresponding masses of their suns are different.

  2. physics_dan
    01.04.2014 at 05:03

    Why isn’t it stated in the question that two solar system has different solar mass? At first I thought they meant they observed two suns, like two stars with identical solar mass of 1.

  3. 24.10.2014 at 06:43

    It’s stupidly worded. Thanks again, ETS. You’re always so clear and concise.

  4. Arturodonjuan
    29.08.2016 at 09:20

    Alternatively, remember that L=m*(dA/dt), where dA/dt is the rate at which area swept out by the planet. Integrate both sides from t=0 to t=T to get that LT=mA, or rather, m=LT/A. This says that the ratio (m1/m2) is equal to (L1*T1/A1)/(L2*T2/A2). But L1=L2 and A1=A2, so (m1/m2)=(T1/T2).

  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: