Question

How to find velocities of aphelion and perihelion?

Answer 1

Answer:

The speed of the Earth in its orbit is given by the formula V² = GM(2/r - 1/a), where G and M are the gravitational constant (6.67259×10^-11 m³/kg/s²) and the mass of the Sun (1.9891×10^30 kg),

r is the Earth’s distance from the Sun, and a is the semi-major axis of the Earth’s orbit (149,597,870.7 km).

After some calculation, the speeds at perihelion and aphelion come down to V(peri)² = GM{(1+e)/(1-e)}/a and V(aph)² = GM{(1-e)/(1+e)}/a,

where e is the eccentricity of the Earth's orbit (0.01671).

From this, the speeds at perihelion and aphelion are 30.288 km/s and 29.292 km/s.

HOPE..IT..HELPS..!!