Gravitation homework problem

1. Jan 5, 2009

krimor09

1. The problem statement, all variables and given/known data
Distance of Earth from Sun = 1.50 x 10^11m
Period = 365.2 days
Distance of Mars from Sun = 2.28 x 10^11km
Period of Mars in Earth Years?

2. Relevant equations
(Ta/Tb)^2 = (Ra/Rb)^3

3. The attempt at a solution

(365.2 days/Tm)^2 =(1.50 x 10^11m/2.28x10^14m)^3
=(365.2/Tm)^2 = 2.85 x 10^74

Tm^2= (365.2)^2 (2.85 x 10^74)
= square root of 3.04 x 10^79
Tm = 5.5 x 10^39

Last edited: Jan 5, 2009
2. Jan 5, 2009

any ideas?

3. Jan 5, 2009

krimor09

i just put up my work, i know that its wrong because my physics teacher said so, but i'm not sure what my major error is

4. Jan 5, 2009

5. Jan 5, 2009

jgens

Several errors. First you may want to rewrite your equations (and double check your calculations). Second, you need to convert your time into years.

Start here (t/1 yr)^2 = (2.28 x 10^11/1.50 x 10^11)^3.

6. Jan 5, 2009

krimor09

okay, i tried this way out

(t/365.2days)^2 = (2.28x10^11/1.50x10^11)^3
(T/365.2) = square root of 3.5
T^2/133371 = 1.87
multiply 133371 to both sides
t^2 = the square root of 1.87 X 133371
T = 499

7. Jan 5, 2009

jgens

Again, you need to check your calculations (and convert your time into years!). When you take the sqrt of 3.5 you have (t/365.2) = 1.87, not (t/365.2)^2 = 1.87. Be careful with the algebra.

8. Jan 5, 2009

krimor09

Dm= 2.28 x 10^8m
De= 1.50 x 10^11m
Te= 365.2 days or 1 year
Tm= ?

(T/1 yr)^2 = (2.28 x 10^8m/1.50 x 10^11m)^3
(T^2/1yr) = 3.5 x 10^57)
T^2 = sqrt of 3.5 x 10^57
= 5.9 x 10^28

9. Jan 5, 2009

jgens

Again, incorrect. Be careful with calculations and what numbers you substitute into the equation. Your first equation should read:

t^2 = (2.28 x 10^11/1.50 x 10^11)^3

10. Jan 5, 2009

krimor09

t^2 = (2.28 x 10^11/1.50 x 10^11)^3
t^2 = sqrt of 3.5
t = 1.87 years or about 2 years

11. Jan 5, 2009

jgens

Yes. Given your data, I would use 1.87 years (3 sig. figs.).

12. Jan 5, 2009

krimor09

thank you! i appreciate your patience

13. Jan 5, 2009

jgens

You're welcome! :)