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from the average value of T 2 /a 3 in V o R f R e a T=500 T 2 /a 3 7.91 6.39E+06

ID: 2020836 • Letter: F

Question

from the average value of T2/a3 in

Vo

Rf

Re

a

T=500

T2/a3

7.91

6.39E+06

6.32E+06

6.35E+06

5050

4.016

0.0055

8.00

6.61E+06

6.37E+06

6.49E+06

5200

4.166

0.0185

8.2

7.34E+06

6.37E+06

6.85E+06

5650

4.660

0.0708

8.8

1.03E+07

6.37E+06

8.32E+06

7600

6.942

0.2361

9.2

1.32E+07

6.37E+06

9.79E+06

9700

9.611

0.3488

9.6

1.77E+07

6.37E+06

1.20E+07

13150

14.41

0.4721

10

2.52E+07

6.37E+06

1.58E+07

19750

9.89

0.5959

10.2

3.13E+07

6.37E+06

1.88E+07

25650

35.0

0.6630

a)Calculate the Mass of the earth
b)Compare it to (5.97*1024).Find the difference
c) Explain how the mass of the sun could be determined from informayion about the planetary orbits

Vo

Rf

Re

a

T=500

T2/a3

7.91

6.39E+06

6.32E+06

6.35E+06

5050

4.016

0.0055

8.00

6.61E+06

6.37E+06

6.49E+06

5200

4.166

0.0185

8.2

7.34E+06

6.37E+06

6.85E+06

5650

4.660

0.0708

8.8

1.03E+07

6.37E+06

8.32E+06

7600

6.942

0.2361

9.2

1.32E+07

6.37E+06

9.79E+06

9700

9.611

0.3488

9.6

1.77E+07

6.37E+06

1.20E+07

13150

14.41

0.4721

10

2.52E+07

6.37E+06

1.58E+07

19750

9.89

0.5959

10.2

3.13E+07

6.37E+06

1.88E+07

25650

35.0

0.6630

Explanation / Answer

(a) For earth, orbital velocity vo = 7.91 km/s Average value of T^2/a^3 = 11.1 x10^-20 s^2/ m^3 [ from the table ] T^2 /a^3 = 4^2 / GMe 11.1 x10^-14 = 4^2 / GMe Mass of the earth, Me = 4^2/ (11.1 x10^-14* 6.67x10^-11)                                    = 5.33 x 10^24 Kg (b) Difference = 5.97x10^24 - 5.33 x 10^24                  = 0.64 x 10^24 kg (c) Mass of the sun, Ms = (4^2 /G) (a^3/T^2)