Question

(part 1 of 2)

The planet Mars requires 2.46 years to orbit
the sun, which has a mass of 1.989 × 10^30 kg,
in an almost circular trajectory.
Find the radius of the orbit of Mars as it
circles the sun. The gravitational constant is
6.672 × 10-¹¹ N. m²/kg².
Answer in units of m. Answer in units of
m.

(part 2 of 2)
Find the orbital speed of Mars as it circles the
sun.
Answer in units of m/s. Answer in units of
m/s.

Answer 1

To find the radius of the orbit of Mars, we can use the equation T^2 = (4π^2 / G(M)) * r^3, where T is the orbital period, G is the gravitational constant, M is the mass of the sun, and r is the orbital radius.

Plugging in the given values:

(2.46 years)^2 = (4π^2 / 6.672 * 10^-11 Nm^2/kg^2) * r^3

r = ((2.46 years)^2 * (6.672 * 10^-11 Nm^2/kg^2)) / (4π^2) * (1.989 * 10^30 kg)^(1/3)

To find the orbital speed of Mars, we can use the equation v = 2πr / T, where v is the orbital speed, r is the orbital radius, and T is the orbital period.

Plugging in the given values:

v = 2π * r / (2.46 years)

Note: You should convert 2.46 years to seconds using year to seconds conversion factor.