Objects in elliptical orbits sweep out equal areas in equal times. This implies that the orbital speed of a planet around the Sun is not uniform – it moves fastest at the point closest to the Sun (known as the perihelion) and slowest at the point farthest away from the Sun (known as aphelion).

Pluto's Minimun orbital Velovity is 3.7km/sec. Determine values for V_{aphelion }and V_{perihelion. }

$${\mathtt{Da}} = {\mathtt{7\,375\,000\,000}} = \left({\mathtt{7.375}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{9}}}\right)$$

$${\mathtt{Dp}} = {\mathtt{4\,425\,000\,000}} = \left({\mathtt{4.425}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{9}}}\right)$$

$${\frac{{\mathtt{Va}}}{{\mathtt{Vp}}}} = {\frac{{\mathtt{Dp}}}{{\mathtt{Da}}}} = {\frac{{\mathtt{4\,425\,000\,000}}}{{\mathtt{7\,375\,000\,000}}}} = {\frac{\left({\mathtt{4.425}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{9}}}\right)}{\left({\mathtt{7.735}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{9}}}\right)}} = {\frac{{\mathtt{3}}}{{\mathtt{5}}}} = {\mathtt{0.6}}$$

$${\mathtt{Va}} = \left({\mathtt{0.6}}\right){\mathtt{\,\times\,}}{\mathtt{Vp}}$$

How do I solve for V_{aphelion }& V_{pherihelion}?

How do I solve for the velocity?

MsTeya
Jan 25, 2015

#1**+5 **

The minimum velocity occurs at aphelion. This value (3.7Km/s) is stated in the question.

D_perihelion = 7.735E9Km

D_aphelion = 4.425E9Km

Orbital eccentricity is the ratio of P/A (perihelion/aphelion) values. (Either distance or velocity values).

Orbital eccentricity (P/A)= (7.735E9) / (4.425E9) = 1.66

The product of eccentricity and V_aphelion gives V_ perihelion.

(P/A)(Va)=Vp

**(1.66)(3.7Km/s) = 6.14Km/s**

_7UP_

SevenUP
Jan 25, 2015

#1**+5 **

Best Answer

The minimum velocity occurs at aphelion. This value (3.7Km/s) is stated in the question.

D_perihelion = 7.735E9Km

D_aphelion = 4.425E9Km

Orbital eccentricity is the ratio of P/A (perihelion/aphelion) values. (Either distance or velocity values).

Orbital eccentricity (P/A)= (7.735E9) / (4.425E9) = 1.66

The product of eccentricity and V_aphelion gives V_ perihelion.

(P/A)(Va)=Vp

**(1.66)(3.7Km/s) = 6.14Km/s**

_7UP_

SevenUP
Jan 25, 2015