Orbital Velocity Question (1 Viewer)

[cutemouse]

Hello all,

I have an orbital velocity question. I think the back of the book is wrong, so I'll post my answer and the book's answer aswell.

"Calculate the orbital velocity of the Earth around the Sun given the mass of the Sun is 1.99*10³⁰kg, and its diameter is 1 392 530km. The mass of the Earth is 5.974*10²⁴kg, its diameter 12 756km, and distance between the Sun and Earth is 150 000 000km."

My answer: 4.20*10⁴ms^-1

Books answer: 2.968ms^-1

Thanks guys

 

[cutemouse]

Hi again,

I have another question. I'm not given the mass of the primary for this one, so if you could help me that'd be great.

"Geostationary satellites orbit with a radius of 42 260km. Use this information to find:

a) The period of a staelittle which orbits with a radius of 15 000km

b) The orbital radius of a satellite which has an orbital period of 4.0 hours"

Thanks,

Jason

 

[kaz1]

Hello all,

I have an orbital velocity question. I think the back of the book is wrong, so I'll post my answer and the book's answer aswell.

"Calculate the orbital velocity of the Earth around the Sun given the mass of the Sun is 1.99*10³⁰kg, and its diameter is 1 392 530km. The mass of the Earth is 5.974*10²⁴kg, its diameter 12 756km, and distance between the Sun and Earth is 150 000 000km."

My answer: 4.20*10⁴ms^-1

Books answer: 2.968ms^-1

Thanks guys

v= sqrt(GM/r)

v=sqrt[(6.67x10^-11x1.99x10³⁰)/(150 000 000 000+ 1 392 530 000)

v=29 610 ms^-1

I'm pretty sure the Earth doesn't move only 2ms^-1. The book put the decimal point in the wrong place.

 

[ratcher0071]

Hi again,

I have another question. I'm not given the mass of the primary for this one, so if you could help me that'd be great.

"Geostationary satellites orbit with a radius of 42 260km. Use this information to find:

a) The period of a staelittle which orbits with a radius of 15 000km

Kepler's 3rd law:
r³ / T² = GM/ 4pi²

(6.38 x 10⁶ + 1.5 x 10⁷) / T² = (6.67 x 10^-11) (5.98 x 10²⁴) / 4pi²

T² = (21 380 000 x 4pi²) / 3.98866 x 10¹⁴
T² = 2.12 x 10^-6
T = 1.46 x 10^-3